HYPER Feasibility Study

Transcription

1 B Page 1 of 126 Hyper Initial Feasibility Orbit Trade-Off Report HYP-1-01 Prepared by: Date: September2002 Stephen Kemble Checked by: Date: September 2002 Stephen Kemble Authorised by: Date: September2002 Stephen Kemble Astrium Ltd 2003 Astrium Ltd owns the copyright of this document which is supplied in confidence and which shall not be used for any purpose other than that for which it is supplied and shall not in whole or in part be reproduced, copied, or communicated to any person without written permission from the owner. Astrium Ltd Gunnels Wood Road, Stevenage, Hertfordshire, SG1 2AS, England

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3 Page 3 of 126 Contents 1 Introduction The Lense-Thirring effect and orbit requirements Disturbance requirements Orbital Environment Earth s Gravity Knowledge requirements Tidal effects The effect of the Earth s atmosphere Summary in gravity gradient knowledge Magnetic field Solar radiation pressure modelling Earth radiation and albedo pressure modelling Gravitational perturbations from other major bodies Atmospheric effects Atmospheric density and atmospheric drag modelling for Hyper High altitude Winds Radiation environment Effect of orbital debris Summary of orbital perturbations Operational orbit issues Orbit dynamics Orbit options Availability of guide stars Orbit maintenance Thrust requirements Ground stations End of life de-orbit Launch options Rockot DNEPR COSMOS PSLV Summary Orbit selection Baseline option 1: 700km orbit category Baseline option 2: 900km orbit category Baseline option 3: 1000km orbit category Simulation Baseline option 4:1200km orbit category Summary of orbit altitude features Conclusions Consequences of baseline orbit modification Summary of baseline orbit features REFERENCES... 81

4 Page 4 of 126 Appendices Appendix 1 The Lense Thirring effect on satellite orbits Appendix 2 Gravity gradients Appendix 1.1 Case 1 Altitude = 1000 km Appendix 1.2 Case 2 Altitude = 500 km Appendix 3 Radiation analysis Appendix 1.3 Methodology Appendix 1.4 Varying the Altitude for a LST 06:00 Ascending node Appendix 1.5 Varying the LST Ascending node for a 700km circular Sun-Synchronous orbit Appendix 1.6 Conclusions Appendix 4 Atmospheric wind effects Figures Figure 2-1 The magnitude of the Lense-Thirring effect with varying latitude for polar orbit, 90 deg inclination10 Figure 2-2 Magnitude of maximum Lense-Thirring effect with orbit altitude...10 Figure 2-3 The magnitude of the components of Lense-Thirring effect vs orbital anomaly measured from equator, components in polar/equatorial axes...11 Figure 2-4 The magnitude of the components of Lense-Thirring effect vs orbital anomaly measured from equator, components in orbit plane axes...12 Figure 2-5 Illustration of Sun-Synchronous dawn-dusk orbit at Equinox...13 Figure 4-1 J2 radial gravity increment with respect to central square field at altitude of 1000km...16 Figure 4-2 Earth Gravitational radial acceleration variations with respect to central and J2 fields up to order 4 at an altitude of 1000km. (Incremental terms above order 2 up to and including order 4 )...16 Figure 4-3 Earth Gravitational acceleration variations with respect to central and fields up to order 4 up to order 16 at an altitude of 1000km. (Incremental terms above order 4 up to and including order 16 )...16 Figure 4-4 Illustration of gravity gradient components...17 Figure 4-5 Radial gravity gradient vs orbital altitude...18 Figure 4-6 Magnitudes of differential acceleration due to gravity gradient vs angular offset from radial vector and orbital altitude...18 Figure 4-7 Differential Acceleration due to gravity gradient for separation along Earth rotation axis at 1000km orbit altitude and 99.5 deg inclination Figure 4-8 Differential Acceleration due to gravity gradient for separation along Orbit anti-node at 1000km orbit altitude and 99.5 deg inclination Figure 4-9 Earth Gravitational gradient variations with respect to central fields at altitude of 1000km Figure 4-10 Earth Gravitational gradient variations with respect to central and J2 fields up to order 10, at altitude of 1000km Figure 4-11 Worst case Fractional uncertainties in harmonic series coefficients orders 3 to Figure 4-12 Worst case Fractional uncertainties in harmonic series coefficients orders 11 to Figure 4-13 Recent and Predicted Solar Flux F10.7 Variation (taken from NOAA website)...28 Figure 4-14 Example of high Frequency atmospheric density variation expressed as PSD Figure 4-15 Deceleration due to drag Vs orbit altitude...30

5 Page 5 of 126 Figure 4-16 Force due to drag Vs orbit altitude...31 Figure 4-17 Force noise PSD Vs Altitude for mean and maximum atmospheres...33 Figure 4-18 RMS Force noise Vs Altitude for mean and maximum atmospheres...33 Figure 4-19 Force noise data for maximum atmospheric density case...34 Figure 4-20 Force noise data for mean atmospheric density case Figure 4-21 Variation in maximum frequency for drag force Vs altitude...35 Figure 4-22 Global Wind Speeds for a 1000km orbit with a 6am local time...37 Figure 4-23 Contour plots of the electron and proton radiation belts...38 Figure PI Total Dose in Si at centre of Al Spheres for various Sun-Synchronous altitudes for a 06:00 Ascending Node...39 Figure 4-25 Effect of orbital perturbations for 700 and 1000km altitude orbits...42 Figure 5-1 The effect of orbital altitude on eclipse duration and season duration...46 Figure 5-2 Effect of orbital altitude on number of measurements Figure 5-3 Yearly evolution of Sun-Synchronous dawn-dusk orbit at Equinox...48 Figure 5-4 Example of ground station visibility to Kiruna for a 1000km SSO...51 Figure 5-5 De-orbit times assuming a nominal Area/Mass of 0.01 m 2 /kg...52 Figure 5-6 Duration of Low Thrust de-orbit manoeuvre for 750kg spacecraft...52 Figure 5-7 Rockot injection capabilities in LEO...53 Figure 5-8 DNEPR injection mass capacity with altitude...54 Figure 5-9 COSMOS injection mass capacity with altitude...54 Figure 5-10 Dispersion correction DeltaVs...55 Figure 6-1 Orbital altitude trade-offs...58 Figure 6-2 Repeating ground track for 700 km orbit with 2 day repeat...60 Figure 6-3 Sun-synchronous Nodal regression for 700 km orbit with 2 day repeat over 10 day period...61 Figure 6-4 Ground station visibility for 700 km orbit with 2 day repeat...62 Figure 6-5 Orbit altitude history for 700 km orbit with 2 day repeat...62 Figure 6-6 Repeating ground track for 900 km orbit with 1 day repeat...64 Figure 6-7 Ground station visibility for 900 km orbit with 1 day repeat...65 Figure 6-8 Orbit altitude history for 900 km orbit with 1 day repeat...65 Figure 6-9 Repeating ground track for 1000 km orbit with 3 day repeat...67 Figure 6-10 Ground station visibility for 1000 km orbit with 3 day repeat...67 Figure 6-11 Orbit altitude history for 1000 km orbit with 3 day repeat...68 Figure 6-12 Orbit altitude history for 1000 km orbit with 3 day repeat...69 Figure 6-13 Eclipse durations over an operational year, for a 1000km altitude orbit...69 Figure 6-14 Gravity gradient evolution in 1000km SSO...71 Figure 6-15 Drag deceleration in 1000km orbit at maximum in Summer and Winter...72 Figure 6-16 Repeating ground track for1200 km orbit with 6 day repeat...74 Figure 6-17 Ground station visibility for 1200 km orbit with 6 day repeat...74

6 Page 6 of 126 Figure 6-18 Orbit altitude history for 900 km orbit with 1 day repeat...75 Appendices Figure 9-1Gravity gradient increment due to orders 8 to10 with 1000km altitude...88 Figure 9-2Gravity gradient increment due to orders 18 to20 with 1000km altitude...89 Figure 9-3 Gravity gradient increments due to orders 18 to 20 at altitude 1000km...91 Figure 9-4Gravity gradient increment due to orders 8 to10 with 500km altitude...92 Figure 9-5Gravity gradient increment due to orders 18 to20 with 500km altitude...93 Figure 9-6Gravity gradient increment due to orders 28 to30 with 500km altitude...94 Figure 9-7Gravity gradient increment due to orders 38 to40 with 500km altitude...95 Figure 9-8Gravity gradient increment due to orders 46 to 48 with 500km altitude...96 Figure 9-9 Range of Orbit Cases...99 Figure 9-10 Trapped Proton Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node101 Figure 9-11 Trapped Proton Differential Fluxes and 1 year Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node Figure 9-12 Trapped Electron Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node Figure 9-13 Trapped Electron Differential Fluxes and 1 year Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node Figure 9-14 Solar Proton Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node 105 Figure 9-15 Solar Proton 1 year Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node Figure PI Total Dose in Si at centre of Al Spheres for various Sun-Synchronous altitudes for a 06:00 Ascending Node Figure PI Total Dose in Si at centre of Al Spheres for various Sun-Synchronous altitudes for a 06:00 Ascending Node Figure 9-18 Trapped Proton Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude Figure 9-19 Trapped Proton Differential Fluxes and 1 year Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude Figure 9-20 Trapped electron Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude Figure 9-21 Trapped Electron Differential Fluxes and 1 year Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude Figure 9-22 Solar Proton Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude113 Figure 9-23 Solar Proton 1 year Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude Figure PI Total Dose in Si at centre of Al Spheres for various LST Ascending Nodes for a Sun- Synchronous orbit of altitude 700km Figure PI Total Dose in Si at centre of Al Spheres for various LST Ascending Nodes for a Sun- Synchronous orbit of altitude 700km...116

7 Page 7 of 126 Figure 9-26 Variation of total wind speed with latitude for various orbit altitudes with a 6am/pm local time, and a fixed longitude of 0deg Figure 9-27 Variation of total wind speed with latitude for various orbit altitudes with a 12pm local time, and a fixed longitude of 0deg Figure 9-28 Global Wind Speeds for a 700km orbit with a 6am local time Figure 9-29 Global Wind Speeds for a 700km orbit with a 12pm local time Figure 9-30 Global Wind Speeds for a 1000km orbit with a 6am local time Figure 9-31 Global Wind Speeds for a 1000km orbit with a 12pm local time Figure 9-32 Variation of total wind speed with latitude, for various F10.7 and Ap values, for an orbit altitude of 1000km, fixed local time of 6am and fixed longitude of 0deg Tables Table 4-1 Total Force Due to Residual Magnetic Moment...26 Table 4-2 Accelerations due to non-keplerian perturbations...41 Table 5-1 Selection issues for orbital elements...45 Table 6-1 Orbit selection factors...56

8 Page 8 of Introduction A number of factors influence orbit selection, including the magnitude of the predicted observations, disturbances to the measurement process, stability and implications for spacecraft design. The assessment requires a detailed analysis of orbital environmental factors. The key issues assessed are: The Lense-Thirring effect: Orbital perturbations: Orbital environment: Orbit selection: Thruster requirements: Relationship to orbit selection. Gravitational and non-gravitational, including gradient effects. Radiation, eclipse. Altitude selection and refinement of orbit parameters. Trade-offs with respect to altitude selection including launcher Performance. Minimum requirements to maintain a drag-free mission in the presence of perturbations. Detailed thruster requirements will be addressed in Reference 2, taking into account the required control authority. Issues regarding straylight and guide-star selection are considered in Reference 3.

9 Page 9 of The Lense-Thirring effect and orbit requirements Hyper has a number of scientific objectives. One of the principal aims is a test of General Relativity. Specifically, this involves the mapping of the so-called gravitomagnetic field of the Earth to an accuracy of better than 10%. This is the Lense-Thirring effect. This objective forms the focus of this study. It should be noted that although denoted a gravitomagnetic effect, magnetism plays no part in the effect. It is purely because of the analogous field structure to a magnetic dipole. The Lense-Thirring effect predicts a rotation of an object in the presence of a large, rotating gravity field, such as that of the Earth. However, this rotation is very small and consequently high precision measurement devices are required. Furthermore, the experiment must be isolated from sources of disturbance that would otherwise mask the measurement of the effect. In fact, two rotation effects occur, these are the geodetic or de-sitter effect and the Lense-Thirring effect, whose causes are attributed to gravitational potential gradient and Earth s rotation, respectively. Hyper will specifically attempt to measure this later term, which varies with the observatories latitude. ie: where: J is the Earth s rotational angular momentum G LT J 3ˆ( r rˆ J ) LT, 3 r and the geodetic or de-sitter term is given by: v is the velocity, U is gravitational potential (1.5) v U c G 2 The following figure: Figure 2-1shows the magnitude of the Lense-Thirring effect under the assumption of a polar orbiting satellite (ie inclination of 90 deg). The magnitudes plotted are relative, with a value of unity at the equator and a 1000km altitude. The geodetic term is significantly greater in amplitude than the Lense-Thirring term. However, it does not exhibit the same positional dependence, as in a circular orbit the term: v U is constant as Potential gradient, or gravity vector lies along the orbit radius vector. Furthermore, the direction of the rotation axis lies normal to the orbit plane where as the Lense-Thirring rotation axis lies in the plane containing the Earth s rotation axis and the Orbital position vector. For a near polar orbit, this is approximately in the orbit plane. In the following plot, the vertical axis corresponds to a location above the Earth s geographic North pole (or spin axis). The latitude variation is extensive, with smaller amplitude near the Earth s equator and larger amplitude near the geographic poles. Orbital radius does play a part in the amplitude, but is a much weaker term than the latitude effect. Therefore orbital design need not be too strongly influenced by altitude requirements, in terms of the amplitude of the observation to be measured.

10 Page 10 of deg latitude Relative amplitude w.r.t. 0 latitude in 1000km orbit deg latitude h=500 h=700 h=1000 h=1200 Figure 2-1 The magnitude of the Lense-Thirring effect with varying latitude for polar orbit, 90 deg inclination 2.8E-14 Max LT effect (rad/s) 2.7E E E E E E E-14 2E Altitude (km) Figure 2-2 Magnitude of maximum Lense-Thirring effect with orbit altitude

11 Page 11 of 126 The Lense-Thirring rotation vector varies in both magnitude and direction during the course of an orbit. A typical Sun-synchronous orbit will have an orbital inclination of deg. At an altitude of 1000km, the inclination is 99.5 deg. This means that the maximum latitude achieved is 80.5 deg. The components of the LT rotation vector, in X,Y,Z axes, are shown in the following plot, Figure 2-3, for an orbit altitude of 1000km and 99.5 deg inclination. The amplitudes are plotted against orbital true anomaly (zero at the equator crossing). The De-Ditter rotation effect is considerably larger than the Lense-Thirring effect (ie times bigger), but acts in a fixed direction normal to the orbit plane. For comparison, the De-sitter rotation rates for this orbit are: Y: 8.8e-13 rad/sec Z: 1.47e-13 rad/sec This a factor of approximately 40 times larger than the peak Lense-Thirring effect occurring at the orbit antinode. However, advantage can be taken of the fact that the rotation only applies in a direction normal to the orbit plane, with zero components in this plane. The Lense-Thirring effect has a significant effect in the orbit plane. Therefore alignment of the sensitive axes of the gyros in the orbit plane will remove the rotation arising from the De-Sitter effect. 2E E-14 1E-14 5E E-15-1E E-14-2E E Z X Y Figure 2-3 The magnitude of the components of Lense-Thirring effect vs orbital anomaly measured from equator, components in polar/equatorial axes

12 Page 12 of 126 The axes systems assumed are: Z, polar Yorbit X, equatorial Inclination Zorbit Y, equatorial Orbit plane LT effect in orbit plane system 2E E-14 1E-14 LT amplitude 5E E-15-1E E-14-2E X Yorbit Zorbit -2.5E-14 True anomaly (deg) Figure 2-4 The magnitude of the components of Lense-Thirring effect vs orbital anomaly measured from equator, components in orbit plane axes

13 Page 13 of 126 Sun Figure 2-5 Illustration of Sun-Synchronous dawn-dusk orbit at Equinox The spacecraft axes show an axis in an orbit normal direction nominally pointing to a guide star. The other axes also maintain a fixed orientation through the orbit and the sensitive axes of the ASU may be placed in these directions.

14 Page 14 of Disturbance requirements To enable the correct functioning of the Atomic Sagnac Unit (ASU) the acceleration and rotational environments of the spacecraft must be strictly controlled. Spacecraft control can be used to compensate for these disturbances, by providing both translational and rotational authority. However, the disturbance is seldom completely compensated and so selection of an environment in which these effects are low is of some importance. The residual acceleration experienced by the ASU should lie below 1.7*10-8 m/s/s. (Reference 1, R1-ENL- 02) It should be noted that these acceleration requirements are those with respect to the local free fall condition, ie with respect to the path taken by a mass only under only gravitational influence. This may, therefore, include any gravitational perturbations to the nominally considered central inverse square field. The residual accelerations experienced by the ASU are the effect after the application of a drag free control system, designed to cancel out non gravitational perturbations. Therefore the orbital environment must be assessed in order to ultimately derive the performance of the drag free control system. The performance of this control system will be assessed in Reference 2 The key frequency range is 0.3 to 0.03 Hz. Therefore perturbing forces (ie leading to accelerations experienced by the ASU) in this frequency range must be assessed. Furthermore, the sampling frequency is 0.3 Hz, therefore frequency aliasing of acceleration effects at higher frequency will occur. However, such high frequency perturbations are not anticipated. Many environmental perturbations are low frequency, occurring at typically the orbit frequency. However, effects are present at higher frequencies, such as local atmospheric density variations. Atmospheric density also gives rise to the highest frequency perturbations due to molecular free path effects. These are subsequently discussed in Once again, these perturbations are attenuated by the drag-free control system.

15 Page 15 of Orbital Environment A detailed analysis of the orbit environmental characteristics is required to assess the external disturbances that will apply to the measurement platform. The key disturbances are non-gravitational. However, gravity effects are of importance in terms of knowledge requirements. Gravity gradient knowledge is required for compensation and modelling of the ASU 4.1 Earth s Gravity Earth s gravity field is effectively the summation of fields from a set of distributed masses, with a dominant central term. These all contribute to the free fall environment of the spacecraft. They are of importance in accurate prediction of orbit evolution. The Earth s gravity field can be expressed by a series of Legendre polynomials to derive the coefficients for a set of harmonic terms up to the required order of the model. The dominant perturbation from a central square field is the J2 harmonic. The following equation shows the potential field expressed as the a series of Legendre polynomials n n n re re m U J n Pn (sin ) J n m Pn (sin ) cos( r n2 r n2 m1 r is latitude, is longitude, r e is mean Earth equatorial radius 1, n, m The terms J n are the zonal harmonics The terms J nn are sectorial harmonics The terms J nm are Tesseral harmonics ) Longitude (deg) Lat

16 Page 16 of 126 Figure 4-1 J2 radial gravity increment with respect to central square field at altitude of 1000km The above plot illustrates the latitude and longitude dependence of acceleration variations with respect to the main fields (ie inverse square), at an orbital altitude of 1000km. The following analysis illustrates the diminishing effect of higher order harmonic terms Longitude (deg) Lat Figure 4-2 Earth Gravitational radial acceleration variations with respect to central and J2 fields up to order 4 at an altitude of 1000km. (Incremental terms above order 2 up to and including order 4 ) Longitude (deg) Lat Figure 4-3 Earth Gravitational acceleration variations with respect to central and fields up to order 4 up to order 16 at an altitude of 1000km. (Incremental terms above order 4 up to and including order 16 )

17 Page 17 of 126 Although the field variations are not significant for Hyper as the satellite is required to be nominally in free fall, knowledge of the gravity field gradients is of importance in assessing differential acceleration effects within the payload and inertia sensor. If firstly only an inverse square, radially dependent field is considered, the differential gravity vector caused by a displacement in the gravity field is given by: r r ˆ rˆ off r GG 3 3 r r r where r is Earth position wrt the perturbing body. is the perturbing body gravitational parameter r off is spacecraft position wrt the Earth. off 3 This means that the differential acceleration due to gravity, between two separated points, has both a component in a radial direction, proportional to their radial separation, and also a component along their separation direction, which may be transverse (in orbit plane or out of orbit plane). This later transverse term has at its maximum half of the magnitude of the maximum radial term. Two transversely separated objects in free fall will accelerate in a direction towards each other. Radial perturbation roff roff Tangential perturbation r Figure 4-4 Illustration of gravity gradient components

18 Page 18 of 126 The major contributor to gravity gradient is clearly the central inverse square gravity field. The following plot shows the radial (or maximum) component of this gravity gradient 2.60E-06 Gravity gradient (/s/s) 2.50E E E E E E E Orbital altitude (km) Figure 4-5 Radial gravity gradient vs orbital altitude The magnitude of the differential gravitational acceleration varies with the differential displacement direction. It is maximum in the radial and anti-radial direction, with a minimum in transverse directions deg offset from radial deg offset from radial h=500 h=700 h=1000 H=1200 Figure 4-6 Magnitudes of differential acceleration due to gravity gradient vs angular offset from radial vector and orbital altitude

19 Page 19 of 126 The gravity gradient can be translated to a differential effect after making assumptions about the separation vector between the two points in question. Two examples are shown. The first assumes that a fixed inertial separation exists in the Earth polar direction (ie in a direction parallel to the Earth rotation axis). Differential Acceleration components with 1m separation along Earth rotation axis Acceleration (m/s/s) Z X Y Orbit latitude( deg) Figure 4-7 Differential Acceleration due to gravity gradient for separation along Earth rotation axis at 1000km orbit altitude and 99.5 deg inclination. The results are qualitatively the same as those for the Lense-Thirring effect as the form of the vector field is the same in the case of a separation along the rotation axis. The X,Y,Z components are a polar/equatorial system as shown in section 2. The peak accelerations are approximately 2*10-6 m/s/s. This is two orders of magnitude above the compensated acceleration requirement (Reference 1, R1-ENL-02). Hence significant differential acceleration compensation is required. If alternatively, a constant inertial displacement in the direction of the orbit anti-node is considered (ie vector from Earth centre to orbital position at maximum latitude) then the differential acceleration terms are modified:

20 Page 20 of 126 Differential Acceleration components with 1m separation along direction of Orbit anti-node Acceleration (m/s/s) Z orbit X orbit Y orbit Orbit latitude( deg) Figure 4-8 Differential Acceleration due to gravity gradient for separation along Orbit anti-node at 1000km orbit altitude and 99.5 deg inclination. This second example is now expressed with respect to a modified reference frame, with Xorbit - Zorbit in the orbit plane and Yorbit perpendicular to the orbit plane. The harmonic terms also contribute to gravity gradient. The following figures show the effect in LEO of J2 only and terms from J2 to 16, showing both radial and transverse components.

21 Page 21 of Longitude (deg) Lat Longitude (deg) Lat Figure 4-9 Earth Gravitational gradient variations with respect to central fields at altitude of 1000km. (Radial and transverse components are shown )

22 Page 22 of 126 2E E-10 1E E Longitude (deg) Lat 1.4E E-10 1E-10 8E E-11 4E-11 2E-11 0 Longitude (deg) Lat Figure 4-10 Earth Gravitational gradient variations with respect to central and J2 fields up to order 10, at altitude of 1000km. (Radial and transverse components are shown )

23 Page 23 of Knowledge requirements The current requirement for gravity gradient knowledge is 2.4 *10-11 /s/s (Reference 1, R1-ASU-01). In fact, this requirement is orbit altitude dependent and would lower to 2.12*10-11 /s/s at an orbital altitude of 1000km This raises two questions. What order of gravity model is needed to model the field to this accuracy What are the uncertainties in the Earth s gravity model that will in turn be reflected as uncertainties in gravity gradient knowledge. The following summarises the effects of model order at different altitudes. Altitude (km) Order required Clearly, increasing operational orbit altitude allows a significant simplification in the order of modelling required. The uncertainties in the gravity models can be summarised as follows: Central inverse square term: The nominal gravitational parameter for Earth is given by: GM = *10 14 m 3 /s 2 with a standard deviation of: 8*10 5 m 3 /s 2 (ie less than one part in 10 8 ) (these values are defined by the WGS84 standard and used by EGM96) Higher order harmonic terms. The gravity model, EGM96, provides standard deviations in the coefficients used. These can be expressed as a fraction of the nominal terms. The following figure shows, for each order 2 to 20, the maximum fraction from the set of coefficients at a given order, where Fraction = standard deviation/max coefficient at this order. This allows a preliminary analysis to determine the fractional contribution of the uncertainty in any given order. Comparison of this fraction with the gravity gradients arising from this order allows an assessment of the feasibility of reaching the required knowledge. At an altitude of 1000km Gradient contributions at order 0: 10-6 Fractional Uncertainty at order 0: 1.0e-8 Maximum gradient uncertainty: Gradient contributions at order 2: 10-8 Fractional Uncertainty at order 2: 1.5e-5 Maximum gradient uncertainty: 10-13

24 Page 24 of 126 Gradient contributions order 3 to 10: 2*10-10 Fractional Uncertainty order 3 to Maximum gradient uncertainty: 6*10-13 Gradient contributions order 11 to 20: 6*10-11 Fractional Uncertainty order 11 to Maximum gradient uncertainty: 1.2*10-12 In the following figures, the maximum fractional uncertainty (for a given model harmonic) is the greatest error in any one coefficient (ie all for all zonal and tesseral coefficients at the harmonic order under consideration) divided by the maximum coefficient value at that harmonic. This criterion is used to de-weight relatively large uncertainties in the smaller terms at any given order. Maximum Fractional uncertainity Order Figure 4-11 Worst case Fractional uncertainties in harmonic series coefficients orders 3 to Maximum Fractional uncertainity Order

25 Page 25 of 126 Figure 4-12 Worst case Fractional uncertainties in harmonic series coefficients orders 11 to Tidal effects The Earth s ocean ides influence the total gravity field. The tides basically move under the combined influence of the Sun and Moon. The tidal bulge is basically formed under the combined influence of thee fields. However, tidal friction means that the bulge is offset from the expected direction. The effects of the tides can be expressed in a similar manner to the Earth s nominal field. The major difference in principle is the time dependence of the potential. A series of Legendre polynomials can be expressed as: U s1 s 1 k s re 4 GrE D, st cos(2f T t, s0 t0 2s 1 r st ) P st (sin ) where D and are the amplitude and phase for each tidal constituent,. +- label alternate modes f is the frequency s and t are degree and order T is the mean Solar Time P st is a Legendre polynomial in latitude r E is Earth radius is the density of seawater. ks is the Love number Typical amplitudes (D) are several cm, which yield gravitational acceleration effects in the region of 10-9 m/s/s at 1000km altitude and a gravity gradient in the region of /s/s The effect of the Earth s atmosphere The Earth s gravity field nominally includes the effect of the mass of the atmosphere. The gravity parameter due to the atmosphere is : GM = 3.5*10 8 m 3 /s 2 with a standard deviation of: 1*10 7 m 3 /s 2 The atmosphere is tidal in the same manner as the oceans. However, the effects are considerably lower in their effect on the spacecraft. This uncertainty is greater than that in the gravity parameter due to the total Earth mass and is not a contributor to overall gravity field or gradient uncertainty Summary in gravity gradient knowledge When all of the uncertainties in the gradient terms are considered, it is possible to meet the knowledge requirement. This includes both static and dynamic effects on the gravity field. Other factors contributing to gravity gradient uncertainty are uncertainty in the knowledge of the position used to predict gravity gradient and gradient terms arising from spacecraft self-gravity. These are addressed in Reference 2

26 Page 26 of Magnetic field The Earth s magnetic field is described by the Definite/International Geomagnetic Reference Field (DGRF/IGRF) The mathematical model was developed by NASA/Goddard Space Flight Centre. The principle field structure is that of a dipole, with a series of harmonic terms described by Legendre polynomials in the manner of gravity potential. The magnetic field intensity at a radius of 7378km is e-5 Tesla and the magnetic field intensity gradient is e-12 Tesla/m. The magnetic field strength variation over short distances is effectively linear: Local electromagnetic effects on the spacecraft can give rise to small torques. A net force can be also be generated due to such local electromagnetic effects, but this arises from the gravity gradient of the Earth s magnetic field across the spacecraft. The effect is therefore very small. Total Force (N) Residual Magnetic Moment (Am 2 ) Radius (km) E E E E E E E E E E E E E E E E E E E E-10 Table 4-1 Total Force Due to Residual Magnetic Moment Typical magnetic moments for small spacecraft are in the region of 1 to 10 Am 2. therefore the net forces likely to be experienced by Hyper are very small. 4.3 Solar radiation pressure modelling Solar radiation pressure is dependent on the spacecraft position and orientation with respect to the Sun. The magnitude obeys an inverse square dependence on heliocentric distance and is therefore effectively a constant in any Earth bound orbit. At Earth distance, the force is approximately 4.5*10-6 N /m 2.The magnitude is also dependent on Solar activity and does therefore show periodic variations. This corresponds to 1371 W/m 2, varying over a range between 1316 W/m 2 to 1428 W/m 2. (ie approximately a 4% variation) Solar radiation pressure will typically result in an acceleration of micro g for a microsatellite. There is little variation between orbit types except when the spacecraft enters eclipse. 4.4 Earth radiation and albedo pressure modelling Earth radiation pressure on a spacecraft is dependent on the Earth s albedo and infra-red radiation. It can be a significant term in low Earth orbit, rising to levels of comparable order to solar radiation pressure. Earth infra-red radiation approximates a black body spectrum, with a temperature of 288K. Average infra-red radiation emitted is 230 W/m 2, but over short time scales can vary from 150 to 350 W/m 2.

27 Page 27 of 126 For a high inclination orbit, the following table shows the running mean over 90 minutes, for different percentage probabilities that the radiation value is not exceeded. Probability: 3% 50% 97% Radiation: This is a factor of approximately 6 between Solar and Earth radiation magnitudes. Earth albedo effect also exerts a radiation pressure force on the spacecraft. The mean Earth albedo is 0.3, but significant short term variations can be observed. The albedo effect experienced by the spacecraft is principally dependent on the solar zenith angle over the region visible to the spacecraft, falling to zero in non-sunlit areas. Short term effects are observed due to variations in vegetation and atmospheric water vapour. For a high inclination orbit, the following table shows the running mean over 90 minutes, for different percentage probabilities that the albedo value is not exceeded. (Note that these values are corrected to zero zenith angle). Probability: 3% 50% 97% Albedo: In the case of a dawn-dusk orbit, where the spacecraft is generally moving close to the terminator, the solar zenith angle will be low. This then substantially reduces the albedo values effective at the spacecraft. In some instances, the spacecraft view of the Earth will include non-sunlit areas. The maximum zenith is approximately 30 degrees. This means that the above albedo values are effectively at least halved 4.5 Gravitational perturbations from other major bodies. The Sun and Moon perturb satellites in Earth orbit. It should be noted, however, that these perturbations contribute to the free fall environment, simply distorting the Earth dependent gravity field. The effect of these terms is therefore in accurate prediction of orbit evolution. The Earth relative perturbation from Sun and Moon is due to the gradient of the perturbing gravity field and the distance from the Earth s centre. Its magnitude is small. In Low Earth orbit, the effect is typically 0.05 micro g from the Sun and 0.12 micro g from the Moon. The acceleration has a cyclic nature with orbital frequency. It s magnitude increases linearly with orbital distance from the Earth. The gravity gradients experienced are : Solar gradient: Lunar gradient: 8*10-14 /s/s 1.8*10-13 /s/s 4.6 Atmospheric effects The atmospheric density is relevant to LEO spacecraft, in determining the magnitude of atmospheric drag. Atmospheric density is predominantly dependent on altitude. Numerous mathematical models have been developed that describe this dependence. However, the upper atmosphere, in particular, is dependent upon a number of other factors.

28 Page 28 of 126 The most comprehensive high altitude atmospheric model is the MSIS86 model. The Mass-Spectrometer- Incoherent-Scatter model describes the neutral temperature and densities in the upper atmosphere. It is based on data compilation and analysis, with measurements from rockets, satellites and incoherent scatter radars. This model is more detailed than the later MSIS90 model at higher altitude (above 250km) and therefore is well suited to most LEO satellites (MSIS86 lacks detail below 250km altitude). Solar radiation heats the lower atmosphere, causing an expansion into the higher altitude zones. Therefore the current activity within the eleven year solar cycle is of considerable importance. In particular, the key parameter is the solar radiation flux count: F10.7. This gives a long period density dependence. This term also exhibits shorter term variations, with significant variations over periods of several days. Figure 4-13 Recent and Predicted Solar Flux F10.7 Variation (taken from NOAA website) The atmosphere is also effected by seasonal variations. These are predominantly driven by the position of the Sun. The extent of the seasonal variation is dependent on the latitude. Variations over a 24 hour period (local solar time) are also significant. The variation is predominantly diurnal; however, semidiurnal and terdiurnal terms are present. The extent of this LST dependent density variation is also a factor of latitude. Magnetic activity has an effect on the atmosphere. The effect is significantly greater at the poles than at the equator. Section 6.3.1, Figure 6-15, shows atmospheric drag profiles that are a direct consequence of atmospheric density variations. The orbit altitude used was 1000km, in a dawn-dusk, sun-synchronous orbit. The difference between Summer and Winter cases is apparent. As a result of the atmospheric density, the spacecraft will experience a deceleration due to atmospheric drag. The resulting direction of the drag is nominally assumed to lie in a direction opposing the Earth relative velocity (ie the speed relative to a rotating atmosphere). This is close to opposing the inertial velocity but does apply a small out of orbit plane component. The drag is proportional to the atmospheric density and will, therefore, at any given altitude, exhibit all of the variations previously discussed. Therefore assessment of suitable orbits must take into account the range of possible drag values over the intended mission epochs.

29 Page 29 of 126 The air density is thought to contain higher frequency components in addition to the nominal behaviour described previously. Typical variations of up to 10% w.r.t. the local d.c. value over a distance of the order of the density scale height, 80 km, are thought to exist. These effects have not been measured at high orbital altitudes and so are extrapolations from lower altitude data. A representative power spectral density is shown in the figure below (this profile was used for the recent ESA STEP study). This effect will be of significance to Hyper, as the perturbation occurs within the critical frequency range Frequency (Hz) Figure 4-14 Example of high Frequency atmospheric density variation expressed as PSD. The plot shows single sided PSD of density variations (vertical axis in normalised density 2 / Hz). The 3 density variation is approx. 10%,of the d.c value. The magnitude of density in the PSD is varied with the prevailing d.c. value at a given altitude or solar activity level. In this context, normalised density is the factor by which the nominal, steady state atmospheric density is multiplied to generate the frequency dependent component, or: DensityPSD NormalisedDensityPSD * ( DensityDC ) 2 This is equivalent to: Mean square amplitude of frequency dependent component: Where: Then mean square value of the density factor (ie one sigma): 2 f * f DC = Atmospheric density and atmospheric drag modelling for Hyper Atmospheric density varies considerably over the range of possible altitudes for Hyper. The mean atmospheric density per orbit can be obtained from reference data regarding atmospheric density. This data is evaluated at different levels of solar activity, varying between solar minimum and solar maximum. The period for such variations is the eleven-year solar cycle. However, there are also shorter term variations in solar activity on a daily basis, such that the actual maximum values are the worst case daily variations at the solar maximum. The density as evaluated above is also averaged over an orbit. However, the density will also vary over the orbit. Two effects are apparent. One is a noise component associated with the molecular mean free path.

30 Page 30 of 126 The upper frequency associated with such a noise term is given by the speed of the spacecraft divided by mean free path. The second term is a low frequency effect caused principally by atmospheric density variations with latitude and local solar time. The period of such effects is typically that of the orbit period, but effects at twice orbit period are also apparent. The following discussion shows the effect on atmospheric drag caused by the variation in the averaged (per orbit) atmospheric density at mean and maximum levels of solar activity. Drag is proportional to atmospheric density. The characteristics of the noise component of drag due to molecular mean free path effects are also evaluated. It should be noted that the spectral analysis of this noise component does not include the variations in the dc drag force term during the course of the orbit. Such variations will add components at low frequency (in general very much lower than the upper frequency of the molecular free path noise components). The following baseline assumptions were made: For Hyper, Area/Mass is typically 3.3/750 = m 2 /kg A drag coefficient of 2.2 is assumed. DC forces DC Deceleration due to drag is given by: 1.00E E Deceleration (m/s/s) 1.00E E E E E E-09 MSIS Max MSIS Mean 1.00E-10 Orbit altitude (km) Figure 4-15 Deceleration due to drag Vs orbit altitude This assumes Area/Mass in the above plot and table below is m 2 /kg. The deceleration scales linearly with both Area/Mass and drag coefficient.

31 Page 31 of 126 Altitude (km) Density (kg/m^3) Max case Deceleration (m/s/s) Max case Density (kg/m^3) Mean case Deceleration (m/s/s) Mean case E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-10 For a 750 kg spacecraft with the previously declared Area/Mass this translates to a DC force shown in the following plot. 1.00E E Force (N) 1.00E E E E E-06 MSIS max MSIS mean 1.00E-07 Altitude (km) Figure 4-16 Force due to drag Vs orbit altitude Using the previous tables for acceleration vs altitude, the values for Hyper, at an altitude of 1000km, then the DC force values are: 3.35e-5 N at MSIS max 5.0e-7 N at MSIS mean assuming a 750 kg spacecraft

32 Page 32 of 126 The DC acceleration at 4.48e-8 m/s/s, at an altitude of 1000km under maximum conditions, exceed the maximum allowed acceleration (1.7e-8 m/s/s, Reference 1, R1-ENL-02) and therefore requires compensation by the drag free system. Force noise components The assumption regarding the atmospheric density noise characteristics are that the 3 sigma variations are no more than 10% of the DC value. Therefore in terms of PSD, the following characteristic is seen: FactorPSD fcorner This can be converted to a Drag force PSD as follows: 2 DragPSD ( Drag DC ) * FactorPSD The following analyses assume a spacecraft projected area of 3.3 m^2 Also a drag coefficient of 2.2 is assumed. The force scales linearly with both projected area and drag coefficient. Therefore using these values given previously for DC force at an altitude of 1000km gives: -5 2 DragPSD (3.35*10 ) * FactorPSD at max 7 2 DragPSD (5.0*10 ) * FactorPSD at mean where FactorPSD is determined by the upper frequency assumption. The upper frequency ( corner frequency) on the PSD plots is related to the atmospheric scale height and orbital speed. The scale height varies with altitude and solar activity. At 1000 km and mean solar activity, the scale height is approx 189km, giving an upper frequency of approx 0.04Hz

33 Page 33 of 126 At 1000km and max solar activity, the scale height is approx 126 km, giving an upper frequency of approx 0.06Hz The following results show the variation in Force noise with altitude at mean and maximum atmospheric conditions, assuming a 750kg spacecraft. 1.00E E Force PSD (N/Hz) 1.00E E E E E E-14 Maximum Mean 1.00E-16 Altitude (km) Figure 4-17 Force noise PSD Vs Altitude for mean and maximum atmospheres rms noise Force (N) 1.00E E E E E E E E E E E Altitude (km) Max Mean Figure 4-18 RMS Force noise Vs Altitude for mean and maximum atmospheres

34 Page 34 of 126 Altitude (km) rms force (N) Frequency (Hz) force PSD (N^2/Hz) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-07 Figure 4-19 Force noise data for maximum atmospheric density case Altitude (km) Frequency force PSD (N^2/Hz) rms force (N) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-09 Figure 4-20 Force noise data for mean atmospheric density case. The corner frequency data is shown in the following figure.

35 Page 35 of 126 Upper frequency (Hz) Altitude (km) Max Mean Figure 4-21 Variation in maximum frequency for drag force Vs altitude Therefore the two PSDs for Drag force at an altitude of 1000km become: At MSIS max 2.11e-11 N Hz

36 Page 36 of 126 At MSIS mean 7.22e-15 N Hz Therefore the PSDs have the above values, depending on the prevailing DC atmospheric density which varies over the 11 year solar cycle. The rms noise force at solar maximum and an altitude of 1000km is 1.5e-9 m/s/s. This is below the allowed maximum of 1.7e-8 m/s/s (Reference 1, R1-ENL-02) but the frequency content is closer to the sample frequency, being higher than other source of perturbation. This aspect is considered in reference High altitude Winds The upper atmosphere also experiences winds. These are principally locally horizontal and are caused by Coriolis force induced pressure gradients. Wind speeds tend to be greatest at high latitudes and at dawn and dusk. The model: HWM-93 is the standard model that predicts wind speed. At high altitudes, such as the Hyper proposed mission, the maximum wind speeds for the expected orbital configuration are typically less than 200 m/s in along and cross track directions (using HWM-93 predictions). However, peak values at approximately 350 m/s can be experienced at time of peak solar activity. Therefore the effect of such an along track wind can factor the drag by up to approximately 5% in mean atmospheric conditions. In high solar activities this can increase to 10%. This drag will vary over the orbit with the mainly latitude dependent wind speed. When compared with nominal atmospheric density variations over the orbit of typically 50% (again principally a latitude dependent term and partially correlated with wind speed which is a result of pressure gradients) the wind effect represents a small perturbation. The following figure shows a typical distribution over the Earth s surface for a fixed local solar time.

37 Page 37 of 126 Figure 4-22 Global Wind Speeds for a 1000km orbit with a 6am local time The drag forces, at 10% of the nominal, are, even at solar maximum, below the allowed maximum at 1000km altitude. 4.8 Radiation environment The radiation environment in low Earth orbit results from the presence of magnetically trapped ions and electrons. Near polar, low Earth orbits encounter the inner proton and electron belts, particularly due to the so called South Atlantic anomaly and also at latitudes above 50 degrees. Also, at high latitudes, the higher fluxes of cosmic rays and solar energetic particles will be experienced, as attenuation by the Earth s magnetic field here is very limited.

38 Page 38 of 126 Figure 4-23 Contour plots of the electron and proton radiation belts

39 Page 39 of 126 The figures shows the significantly increasing flux above approximately 1.2 Earth radii (ie altitude of approximately 1300km). As one of the main trade-off parameters is orbital altitude, it is important to assess the effect of the increase in exposure. Radiation effects are best calculated in terms of the integral of the flux experienced by the spacecraft. This principally includes the effects of trapped protons and electrons in the Van Allen belts. The flux integral, or fluence, can be translated to a dose in terms of rads. This is often expressed in terms of the radiation dose experienced after passage through a defined thickness of aluminium. The effect is shown in the following figure: 4PI Total Dose in Si at centre of Al Spheres for various Sun- Synchronous altitudes for a 06:00 Ascending Node 1.00E E+07 Dose (Rads) 1.00E E E km 900km 1100km 1300km 1500km 1.00E E Z (mm) Figure PI Total Dose in Si at centre of Al Spheres for various Sun-Synchronous altitudes for a 06:00 Ascending Node The variation with altitude can be seen. It assumed that the orbit is a dawn/dusk, sun synchronous case (although the variation with LST of the ascending node is relatively small). The details of the analysis are contained in the Appendices. A further radiation effect to be considered is the charging if the Inertial Sensor Unit. This is considered further in reference Effect of orbital debris Low Earth orbit is populated by clouds of debris, ranging from dead satellites to the residuals of explosions. In addition the micro-meteorite environment must be considered.

40 Page 40 of 126 Particle fluxes (per year) vary between 10-6 (large catalogue objects) to 10 4 (Aluminium oxide particles). The higher fluxes are associated with very low mass particles (mg). The effect of such an impact is a very short period transient force. The transmission of this vibration to the instrument will be significantly damped by the satellite structure. Therefore some acceleration may be experienced by the instrument but the effect is transitory and is not expected to significantly degrade the total number of measurements Summary of orbital perturbations The following table shows the acceleration effects due to the various perturbations discussed. The required maximum acceleration to be experienced by the ASU is 1.7e-8 m/s/s (Reference 1, R1-ENL-02) Perturbation Acceleration at 700km Acceleration at 1000km Relationship to requirements Central spherical gravity field J2 (contributes to free fall, does not require compensation) Higher order gravity harmonics (contributes to free fall, does not require compensation) Lunar gravity (contributes to free fall, does not require compensation) Solar gravity (contributes to free fall, does not require compensation) Solar radiation pressure (A/M at ) Differential over 1 m radial: 2.2e-6 m/s/s Differential over 1 m radial: 1.0e-8 m/s/s Differential over 1 m radial: 1.0e-10 m/s/s 1.2e-6 Differential over 1 m radial: 1.0e-13 m/s/s 5.5e-7 Differential over 1 m radial: 1.0e-13 m/s/s Differential over 1 m radial: 2.0e-6 m/s/s 0.02 Differential over 1 m radial: 1.0e-8 m/s/s Differential over 1 m radial: 1.0e-10 m/s/s 1.3e-6 Differential over 1 m radial: 1.0e-13 m/s/s 5.9e-7 Differential over 1 m radial: 1.0e-13 m/s/s Differential acceleration over 1m is two orders of magnitude above requirement at 1.7e-8 m/s/s (Reference 1, R1-ENL-02). Compensation is therefore required. Free fall acceleration not covered by requirement. Differential acceleration over 1m is below requirement. Free fall acceleration not covered by requirement. Differential acceleration over 1m is below requirement Free fall acceleration not covered by requirement. Differential acceleration over 1m is below requirement Free fall acceleration not covered by requirement. Differential acceleration over 1m is below requirement 2.0e-8 m/s/s 2.0e-8 m/s/s Acceleration exceeds requirement of 1.7e-8 m/s/s (Reference 1, R1-ENL-02). Requires compensation via drag free control

41 Page 41 of 126 Earth radiation pressure (A/M at ) 3.4e-9 m/s/s 3.4e-9 m/s/s Acceleration below requirement of 1.7e-8 m/s/s (Reference 1, R1-ENL-02) Earth albedo radiation pressure (A/M at ) Atmospheric drag at 700km altitude (A/M at ) Atmospheric drag due to winds at 700km altitude (A/M at ) 3.4e-9 m/s/s 3.4e-9 m/s/s Acceleration below requirement of 1.7e-8 m/s/s (Reference 1, R1-ENL-02) 6.2e-7 to 1.1e-8 m/s/s (max and mean solar cycle values) 6.2e-8 to 0.6e-9 m/s/s (max and mean solar cycle values) 4.5e-8 to 6.7e-10 m/s/s (max and mean solar cycle values) 4.5e-9 to 3.4e-11 m/s/s (max and mean solar cycle values) Acceleration exceeds requirement of 1.7e-8 m/s/s (Reference 1, R1-ENL-02). Requires compensation via drag free control Magnetic field 1.0e-13 m/s/s 8e-14 m/s/s Less than requirement of 1.7e-8 m/s/s (Reference 1, R1-ENL-02). Not significant Table 4-2 Accelerations due to non-keplerian perturbations The above accelerations are expressed in m/s/s The requirements relating to allowable acceleration are given in Reference 1, R1-ENL-02. Acceleration nano m/s/s k m km km 1000km 1 = J2 2 = Higher harmonics

42 Page 42 of = Lunar gravity 4 = Solar gravity 5 = SRP 6 = ERP 7 = Albedo 8 = Max Drag 9 = Mean Drag Figure 4-25 Effect of orbital perturbations for 700 and 1000km altitude orbits

43 Page 43 of Operational orbit issues Selection of the baseline orbit requires consideration of many issues, including observation needs and spacecraft implications. The ideal orbital altitude for observation is a trade-off between minimising disturbances and achieving a high level signal. Further implications from the baseline orbit choice are thermal stability, available satellite injection mass and de-orbit considerations. 5.1 Orbit dynamics This section on orbital dynamics is included to relate the possible orbital motions to equipotential surfaces, which are of interest for their effect on the payload. A spacecraft in an orbit about a spherical gravity field can move in a variety of motions. The possible motions are described by Kepler in terms of conic sections. These motions range from circular orbits to hyperbolae, depending on the energy and angular momentum Orbital energy is the sum of kinetic and potential terms, and can therefore be described as: 2 V E 2 r where V is velocity and r radial position. The angular momentum is given by: L rv cos where Γ is the angle between the normal to the radial vector and the velocity vector (often referred to as flight path or elevation). Both quantities are conserved. This analysis can be extended as follows by expressing velocity as radial and transverse components: E 2 Vr 2 L 2r 2 2 r The modified potential energy term: L 2r 2 2 r is plotted in the following figure. The solution clearly that for a given orbital energy, a number of motions are possible.

44 Page 44 of 126 Potential Energy Circular orbit case: Motion over Equipotential surface Orbital energy Extremes of radial motion Radius The minimum modified potential energy value corresponds to motion in a circle. In only this scenario does the spacecraft move along an equipotential surface. In all other configurations, there is an exchange between kinetic and potential energies. 5.2 Orbit options Orbits considered for Hyper are Low Earth orbits in order to obtain an effect of observable magnitude. Use of circular orbits means that the measured LT effect signals will have sinusoidal profiles, without any radial modulation terms that would result from an eccentric orbit. Previous assessments have also proposed use of Sun-synchronous orbits to enable a relatively stable thermal environment to be achieved. A dawn dusk orbit means that eclipse is avoided for most of the year. One consequence of a Sun-synchronous orbit is that the LT effect axis of rotation will contain a small out of orbit plane component that will vary in direction with location in the orbit. A polar orbit ensures that the effect always lies in plane. However, a polar orbit means that nodal regression rate reduces to zero. As a consequence, the Sun moves around the orbit plane by 360 deg in the course of a year and significant eclipse phases will be experienced. The main orbit design parameters can be summarised in the following table:

45 Page 45 of 126 Parameter Semi-major axis (or altitude in circular case) Eccentricity Inclination Longitude of ascending node (Local solar time for sun-synchronous orbits) Argument of Perigee Trade-off High altitude reduces perturbations due to atmospheric drag. High altitude gives greater exposure to radiation. High altitude requires greater effort to deorbit Non zero eccentricity gives option to have increased altitude over the ground station J2 causes rotation of the argument of perigee therefore regular control required to maintain benefit from ground station coverage Variable altitude causes modulation of LT signal. In standard sun-synchronous LEO missions, eccentricity chosen to yield frozen orbit (implies mean eccentricity typically If sun-synchronicity is required, inclination fixed by orbit altitude. Non sun-synchronous orbits experience regular eclipse. In sun-synchronous case, node crossing is fixed at require local solar time. For non-synchronous case, LST of ascending node varies. LST at dawn/dusk avoids eclipse for most of the year. LST at dawn/dusk or noon/midnight prevents inclination drift and therefore need for out of plane corrections. Argument of perigee rotates in general case (except for Molnya orbit) Mean argument of perigee can be frozen for near circular orbits. Requires location at the orbit anti-node. Gives repeatable altitude/latitude profile. Table 5-1 Selection issues for orbital elements In the case of a dawn/dusk, synchronous orbit, eclipse occurs during a given period of the year. The duration of this period varies with orbit altitude, Similarly, the maximum length of the eclipse experienced during such periods is also dependent on the orbit altitude. These effects are shown in the following figures.

46 Page 46 of Eclipse duration (min) Number of Days with eclipse Orbital altitude (km) Orbital altitude (km) Figure 5-1 The effect of orbital altitude on eclipse duration and season duration Increasing the orbit altitude reduces the number of days spent in eclipse. No measurements will be taken when eclipse occurs during the orbit. Therefore the number of measurements within the nominal two year mission lifetime increases with orbit altitude. Measurement ratio Orbit altitude (km) Number of measurements Number of orbits Figure 5-2 Effect of orbital altitude on number of measurements. The ratio in the above plot is relative to the previously used value of 700km, taken over two eclipse free seasons within a two year period. Increase of the altitude to 1000km gives nearly a 10% increase in the number of direct measurements (at 3 sec intervals), or a 3.3% increase in the number of orbits over which measurements are taken. The Hyper experiment requires that the spacecraft must maintain an inertialy fixed attitude during observations. The spacecraft will point a sensor to a guide star which should in general lie close to the orbit normal, whilst maintaining a fixed inertial rotation about this reference direction. Therefore a spacecraft in a dawn-dusk, Sun synchronous orbit will select a guide star in a near anti-sun direction, as discussed in section 2.

47 Page 47 of 126 The following figures show the evolution of the Sun direction with respect to the nominal orbit plane. The spacecraft is assumed to lie in a 1000km, Sun synchronous orbit, with a 6.00am ascending node. Summer Autumn

48 Page 48 of 126 Winter Spring Figure 5-3 Yearly evolution of Sun-Synchronous dawn-dusk orbit at Equinox Eclipses occur around the Winter solstice

49 Page 49 of Availability of guide stars A guide star is required to maintain accurate attitude pointing during the LT experiment measurement phase. A number of requirements exist for the selection of the guide star, as follows: It should lie in the anti-sun direction, within a cone angle of 30 deg The angle between guide star and orbit normal should be less than 20 deg Therefore only a limited set of stars are needed, as the spacecraft orbit normal moves in right ascension through the course of the year. The Hyper assessment study report concludes that a set of 10 stars should be selected for the year (with no measurements during eclipse season), giving continuous observation periods of approximately 25 days between slewing to acquire a new star. In fact the minimum set would be 6 stars, but this increased number allows greater choice in the selection of the star. Guide star selection will be considered in Reference Orbit maintenance The spacecraft will nominally fly in a drag-free mode, with drag make-up via continuous propulsion. This will also compensate for radiation pressure effects. Therefore there will be no requirements for periodic station keeping manoeuvres to maintain orbit altitude or ground track due to semi-major axis drift. If the drag-free point does not correspond with the centre of mass, then the overall effect is for the spacecraft to fly in a slightly non-keplerian orbit, with its natural motion under gravity continuously augmented by thrust from the FEEPs. Furthermore, if the spacecraft is in a nominal dawn-dusk orbit, then secular out of plane perturbations from Lunar-Solar gravity (causing inclination drift) will be zero. Inclination drift is a maximum for 9.00am and 9.00pm orbits, with the inclination drift rate reducing to zero for dawn-dusk orbits and noon-midnight orbits. Hence the nodal regression rate (which is predominantly dependent on the orbital inclination) will remain at Sun-synchronous rate. 5.5 Thrust requirements There is an associated minimum thrust requirement associated with each perturbation if drag free control is to be maintained. The full thrust envelope is determined by the control system analysis given in reference 2. Here the baseline levels are given. The thrust calculations assume a spacecraft mass of 750 kg.

50 Page 50 of 126 Perturbation Thrust at 700km Thrust at 1000km Comment Central spherical gravity field gradient J2 field gradient Higher order gravity harmonics Gradient compensation over 1m: 1.65 mn Gradient compensation over 0.1m: 165 micron Gradient compensation over 1m: 7.5 micron Gradient compensation over 0.1m: 0.75 micron Gradient compensation over 1m: 0.22 micron Gradient compensation over 0.1m: micron Lunar gravity gradient Negligible Negligible Gradient compensation over 1m: 1.5 mn Gradient compensation over 0.1m: 150 micron Gradient compensation over 1m: 7 microµn Gradient compensation over 0.1m: 0.7 micron Gradient compensation over 1m: 0.2 micron Gradient compensation over 0.1m: 0.02 micron Force related to choice of drag free point, ie close to centre of mass or centre of ASU. Force related to choice of drag free point, ie close to centre of mass or centre of ASU. Force related to choice of drag free point, ie close to centre of mass or centre of ASU. Solar gravity gradient Negligible Negligible Solar radiation pressure 15 micron 15 micron (A/M at ) Earth radiation pressure 2.5 micron 2.5 micron (A/M at ) Earth albedo radiation 2.5 micron 2.5 micron pressure (A/M at ) Atmospheric drag at 700km altitude (A/M at ) 460 micron to 8 micron (max and mean solar cycle values) cycle values) Atmospheric drag due to 46 micron to 0.8 micron winds at 700km altitude (max and mean solar (A/M at ) cycle values) Magnetic field Negligible Negligible 34 micron to 0.4 micron (max and mean solar 3.4 micron to 0.04 micron (max and mean solar cycle values) The dominant thrust requirements arise from two main sources: Gravity gradient compensation in maintaining the drag free point offset from the centre of mass Atmospheric drag compensation The selection of the location of the drag free control point (or points) therefore is very significant in FEEP system design. This choice is related to the chosen method of gravity compensation: active dynamic control or electronic compensation within the ASU. This point is raised in section Ground stations A sun-synchronous implies use of a high latitude ground station to maximise communications links. A station such as Kiruna (68deg latitude) gives on average a 12.7% link time for a 1000km Sun-synchronous orbit.

51 Page 51 of 126 Figure 5-4 Example of ground station visibility to Kiruna for a 1000km SSO The above plot shows coverage over a five day nominal repeat period. 5.7 End of life de-orbit The spacecraft will nominally be required to re-enter within a period of 25 years after the end of operation. For higher altitude orbits (typically above 600km), this means a dedicated perigee lowering manoeuvre, as the natural lifetime is too great. To ensure re-entry within the allowed period, the perigee should lowered to typically 550km for the higher altitude orbits (above 700km). This implies a DeltaV of between 50 and 70 m/s for orbital altitudes of 700 and 1000 km respectively. This is in fact the largest DeltaV component for the mission. However, such a manoeuvre implies the availability of a moderately high thrust system. In practice, Hyper may not have the use of such a system at the end of life, having vented any standard propulsion system propellants to prevent unwanted perturbations due to fuel motion. An alternative scenario involves the use of the drag-free control system. Continuously supplied low thrust can be used to spiral inwards. The result of such a transfer is that the orbit remains nearly circular. It is only necessary to lower the altitude to approximately between 500 and 600km. Atmospheric drag may then be used to complete the natural orbit decay within the prescribed time limit. The decay time from a 600km altitude is typically 15 years for a spacecraft with Area/Mass of For lower area/mass ratios, such as as currently projected for Hyper, the decay time more than doubles. To achieve 15 years with Hyper implies an altitude of approximately 550km. This then allows 10 years for orbit altitude reduction. The following figure shows that using 500 micron of thrust, the spacecraft would take approximately 10 years to lower its altitude from 1000km to below 600km. Such a strategy would therefore be consistent with the 25 year maximum time requirement. Even a 100km altitude reduction takes over 2 years of thrust time. There are therefore serious operational considerations for the spacecraft making such extended, controlled manoeuvres. The de-orbit manoeuvre implies constant thrust vector control.

52 Page 52 of 126 Comparison of re-entry times for circular orbits MSIS-86 mean density MSIS-86 max density Altitude (km) Figure 5-5 De-orbit times assuming a nominal Area/Mass of 0.01 m 2 /kg The effects of different assumptions about the prevailing atmospheric density are shown in the plot. Over long periods, the mean atmosphere curve should be assumed as several solar cycles will pass Time for manoeuvre (days) Orbital altitude (km) 500 micron 250 micron 100 micron Figure 5-6 Duration of Low Thrust de-orbit manoeuvre for 750kg spacecraft The above plot shows the manoeuvre duration for different assumptions about available thrust. 5.8 Launch options

53 Payload mass, kg HYPER Feasibility Page 53 of 126 The launch mass for Hyper is likely to be in the region of kg into the required orbit (ie typically km). There are currently several low cost launchers available, with differing capacities into such an orbit. A number of these are based on ICBM technology and as such may be phased out after Launchers in this category include Rockot and DNEPR Rockot Eurockot offers the possibility of a dedicated launch into low Earth orbit for a launch price of ~ 13 MEUR. Eurockot is expected to phase out about 2008, but will be replaced by the European Vega launcher that will have at least the same capability (though a higher price ~ 20 MEUR.) The following figure illustrates launch mass capabilities for Rockot. Injection dispersions are typically: Altitude +- 2% Inclination 0.05 deg This translates to a total DeltaV requirement of approximately 14 m/s, in a combination of in plane apogee/perigee and out of plane inclination correction manoeuvres i=97 i=94 i=100 i=63 i=73 i=82 i=86 Performance of a launch vehicle generally decreases with required circular orbit altitude. However, the presence of azimuth constraints on the launch direction means that for a launcher such as Rockot, an intermediate high inclination parking orbit is used, followed by a plane change manoeuvre. The final injection mass capability is then related also to the plane change required. Rockot reaches SSO via 94 or 100 deg inclination parking orbits. Therefore higher altitude SSO with inclination approaching 100 degrees require no further plane change i=98.1 SSO Consequently, there is little performance variation in the altitude range 600 to 1000km via the 100 deg inclination orbit. If restricted to the 94 deg inclination transfer orbit, payload drops from just under 1000kg to 600kg Circular orbit altitude, km Rockot Performance from Plesetsk (from reference (Rockot) Figure 5-7 Rockot injection capabilities in LEO.

54 Page 54 of DNEPR Figure 5-8 DNEPR injection mass capacity with altitude COSMOS Figure 5-9 COSMOS injection mass capacity with altitude

55 Page 55 of PSLV India s PSLV, or Polar Satellite Launch Vehicle, has a capacity of 1000kg into a 904 km altitude, sunsynchronous inclination orbit Summary Typical DeltaVs required for medium altitude, circular orbit dispersion correction are given in the following table: LAUNCHER TOTAL DELTA V REQUIRED (M/S) EUROCKOT 14.1 PSLV 44.7 COSMOS 59.9 DNEPR 7.3 Figure 5-10 Dispersion correction DeltaVs The injection mass requirements are met by Rockot. COSMOS can achieve approximately 750 kg at 700km altitude. DNEPR can achieve approximately 800 kg at 700km altitude However, both of these launchers show a significant reduction in injected mass with increasing altitude. Of the set considered, Rockot offers the most attractive option. However, the consequence of a projected end of service in 2008 must be considered. In such a scenario, launchers such as PSLV offer a possible alternative, or the more expensive VEGA option can be used. Soyuz has a high injection mass capability but is likely to be more expensive.

56 Page 56 of Orbit selection The major factors contributing to orbit selection are shown in the table below. Orbit Type Circular Elliptical Sun-synchronous Polar Low altitude High altitude Observation implications LT effect periodic in magnitude and direction LT effect periodic but magnitude modulated by altitude dependent effect LT effect rotation axes have a component out of the orbit plane LT effect rotation axis contained in orbit plane LT effect amplitude high LT effect amplitude reduces slowly with altitude. Disturbances For sun-synchronous orbit, major disturbance (drag) has small variation over orbit. Significant drag variations over orbit period. High atmospheric drag disturbances Low atmospheric drag disturbances Spacecraft implications Relatively constant environment over orbit period (true for sun-synchronous) Good ground station links for Molnya orbits. SSO inclination will experience apse rotation. Possibilities for near constant solar illumination geometries out of eclipse season. (select dawn-dusk orbit) Variable solar illumination geometry due to zero nodal regression. Generally higher available spacecraft mass at orbit injection. Limited or no de-orbit effort required. Higher gravity gradients. Spacecraft mass at orbit injection generally reducing with orbit altitude. Improved ground station links. Longer de-orbit times. Reduced gravity gradient. Increased radiation dosage. Table 6-1 Orbit selection factors The previous assessment studies recommended the use of a Sun-synchronous, 700 km circular orbit. This orbit represents a good compromise. A limiting factor was the injection mass achievable using Eurockot.

57 Page 57 of 126 However, the availability of greater injection mass via the alternative launch azimuth option means that the use of higher altitudes can be considered. Preliminary indications suggest that as the science signal only decreases slowly with altitude, then the drag free control system could be simplified by selection of a greater orbital altitude. Although solar radiation pressure must be compensated at this altitude, this perturbation shows less variation than atmospheric drag, which may also contain significant higher frequency noise components. However, launcher performance must be considered, but there appears to be no penalty with Rockot used in orbits up to 1000km. De-orbit times using the baselined 500 micron FEEPs are still acceptable from 1000km altitude, but there are operational implications for this extended operation. The preceding discussions have indicated that a number of orbit parameters are effectively pre-selected, ie: Low Earth orbit Sun synchronous Near circular Local solar time of ascending node (dawn dusk) However, orbit altitude is the critical parameter for this mission. Issues relating to orbital altitude are the following: Injection mass from the launcher Atmospheric drag Gravity gradient knowledge Scientific observability Radiation End of mission de-orbit

58 Page 58 of 126 Parameter 700km 1000km 1200km Comment Injection mass from the launcher 1000 kg 1000kg Estimated 800 to 850 kg No distinction between 700 and 1000km. Reduction at altitudes greater than Atmospheric drag Max at 6.2e-7 m/s/s Max at 4.5e-8 m/s/s Max at 7.8e-9 m/s/s 1000km Order of magnitude reduction at higher altitude.(700 to 1000km) Drag at solar maximum is the dominant non-gravitational perturbation at 700 and 1000km Gravity gradient knowledge Scientific observability Implies model at order 30 Implies model at order 20 LT effect magnitude reduced by 12%.c.f. 700km (Figure 2-2) Implies model at order 13 LT effect magnitude reduced by 19%.c.f. 700km (Figure 2-2) At 1200km Solar Radiation Pressure (SRP) at 2e-8 m/s/s exceeds atmospheric drag Higher altitude allows simplification of the modelling process Increasing altitude increases number of observations but reduces magnitude of the measured effect. Number of observations due to decrease in eclipse time increased by 9.9% (Figure 5-2 ) Number of observations due to decrease in eclipse time increased by 17% (Figure 5-2 ) Radiation De-orbit Dose with 5mm Al shield over 2 years: 8500 Rads Controlled Deorbit periods with 500 micron thrust typically 3 years Dose with 5mm Al shield over 2 years: Rads Controlled Deorbit periods with 500 micron thrust typically 10 years Dose with 5mm Al shield over 2 years: Rads Controlled Deorbit periods with 500 micron thrust typically 15 years Steeply increasing radiation dose at higher altitude De-orbit from higher altitude orbits required extended low thrust periods. Figure 6-1 Orbital altitude trade-offs Three cases covering the range of altitude interest are evaluated in greater detail.

59 Page 59 of Baseline option 1: 700km orbit category This option benefits from A lower radiation dosage (below the Van Allen belts) Acceptable launch mass (from Rockot) The fine detail of the orbit altitude is determined by ground track repeat requirements, which minimise the ground contact cycle times. A one day repeat period implies orbit altitudes of: Mean radius: Mean radius: 7265 km (mean altitude above 6378 km sphere = 887 km) 6940 km (mean altitude above 6378 km sphere = 562 km) Both of these are significantly removed from 700km, therefore a two day repeat was investigated. This implies: Mean radius: 7098 km (mean altitude above 6378 km sphere = 720 km) This was therefore adopted. The orbit features incorporated were: Sun synchronous: Dawn/dusk: Frozen orbit: Inclination = 98 deg Local solar time of ascending node = 6.00 am Mean perigee placed at the orbit antinode (latitude of approx 82 deg) The following illustrations show these features:

60 Page 60 of 126 Figure 6-2 Repeating ground track for 700 km orbit with 2 day repeat The track spacing is approximately 12.5 deg in longitude at the equator

61 Page 61 of 126 Figure 6-3 Sun-synchronous Nodal regression for 700 km orbit with 2 day repeat over 10 day period The orbit node rotates through 10 degrees in the above illustration. The Sun initially lies to the left of the figure, rotating through 10 degrees in an anti-clockwise direction. The ground station coverage is shown in the following figure:

62 Page 62 of 126 Figure 6-4 Ground station visibility for 700 km orbit with 2 day repeat The ground station patterns rise and fall on a daily basis but repeat exactly over a two days period. Ground station mean coverage times are 10.1% and 9.3% for these two Northerly ground stations. The altitude behaviour is also of interest. The Frozen orbit feature is shown in the following figure (ie repeatable altitude with latitude) Figure 6-5 Orbit altitude history for 700 km orbit with 2 day repeat

63 Page 63 of 126 Altitude is evaluated over a uniform sphere of radius 6378 km 6.2 Baseline option 2: 900km orbit category This option benefits from A lower atmospheric drag perturbation Lower earth radiation pressure perturbation Acceptable launch mass (from Rockot) The fine detail of the orbit altitude is determined by ground track repeat requirements, which minimise the ground contact cycle times. A one day repeat period implies orbit altitudes of: Mean radius: Mean radius: 7265 km (mean altitude above 6378 km sphere = 887 km) 7443 km (mean altitude above 6378 km sphere = 1065 km) In fact, the 887 km case is also a one day repeat period case This was therefore adopted. The orbit features incorporated were: Sun synchronous: Dawn/dusk: Frozen orbit: Inclination = 99 deg Local solar time of ascending node = 6.00 am Mean perigee placed at the orbit antinode (latitude of approx 81 deg) The following illustrations show these features:

64 Page 64 of 126 Figure 6-6 Repeating ground track for 900 km orbit with 1 day repeat The track spacing is approximately 25 deg in longitude at the equator

65 Page 65 of 126 Figure 6-7 Ground station visibility for 900 km orbit with 1 day repeat The ground station patterns but repeat exactly over a one days period. Ground station mean coverage times are 11.7% and 10.8% for these two Northerly ground stations. The altitude behaviour is also of interest. The Frozen orbit feature is shown in the following figure (ie repeatable altitude with latitude). Figure 6-8 Orbit altitude history for 900 km orbit with 1 day repeat Altitude is evaluated over a uniform sphere of radius 6378 km

66 Page 66 of Baseline option 3: 1000km orbit category This option benefits from A further reduced atmospheric drag perturbation Lower earth radiation pressure perturbation Acceptable launch mass (from Rockot) The fine detail of the orbit altitude is determined by ground track repeat requirements, which minimise the ground contact cycle times. For a target of 1000km, then a one day repeat period implies the nearest orbit altitudes of: Mean radius: Mean radius: 7265 km (mean altitude above 6378 km sphere = 887 km) 7443 km (mean altitude above 6378 km sphere = 1065 km) In fact, the 1065 km case is also a two day repeat period case A three day repeat period gives: Mean radius: 7387 km (mean altitude above 6378 km sphere = 1009 km) The three day case was therefore adopted. The orbit features incorporated were: Sun synchronous: Dawn/dusk: Frozen orbit: Inclination = 99.5 deg Local solar time of ascending node = 6.00 am Mean perigee placed at the orbit antinode (latitude of approx 80.5 deg) The following illustrations show these features:

67 Page 67 of 126 Figure 6-9 Repeating ground track for 1000 km orbit with 3 day repeat The track spacing is approximately 8 deg in longitude at the equator Figure 6-10 Ground station visibility for 1000 km orbit with 3 day repeat

68 Page 68 of 126 The ground station patterns but repeat exactly over a one days period. Ground station mean coverage times are 12.7% and 11.8% for these two Northerly ground stations. The altitude behaviour is also of interest. The Frozen orbit feature is shown in the following figure (ie repeatable altitude with latitude). Figure 6-11 Orbit altitude history for 1000 km orbit with 3 day repeat Altitude is evaluated over a uniform sphere of radius 6378 km

69 Page 69 of 126 Figure 6-12 Orbit altitude history for 1000 km orbit with 3 day repeat Altitude is evaluated over the WGS84 ellipsoid. The following plot shows the evolution of eclipse duration during a year, evaluated from a starting day at the Summer solstice. The orbit has a 6.00am ascending node. Eclipse duration (secs) Day from Summer Solstice Figure 6-13 Eclipse durations over an operational year, for a 1000km altitude orbit

70 Page 70 of 126 A typical mission scenario would be to achieve operational status at the end of the eclipse season, so that the maximum uninterrupted period is experienced. In this scenario the mission timeline would be approximately as follows: Orbit injection: December 19 Year 1 Commence operations: January 19 Year 2 Start of Eclipse season 1: November 23 Year 2 End of Eclipse season 1: January 19 Year 3 Start of eclipse season 2 and end of operational mission: November 23 Year 3 This assumes a nominal 30 day check-out period after injection before commencing operations Simulation A more detailed simulation of this orbit has been performed to assess the evolution of environmental effects. Gravity gradient knowledge is required at two levels: Results processing Real time compensation The real time compensation should reduce the effect of gravity gradient on the instrument to the order of 10-8 /s/s (by possibly electronic compensation in the instrument or localised compensation placing the drag free point close to the centre of the ASU) (see Reference 1, R1-ENL-02). The variation of the gravity gradient to this resolution should be understood. The following simulation results show this over an orbit E E-06 Radial Gradient E E E E Time (secs)

71 Page 71 of 126 Perpendicular gradient E E E E E E E E E E E E Time (secs) Figure 6-14 Gravity gradient evolution in 1000km SSO. The radial and perpendicular contributions are in phase. The dominating effect is the inverse square field, but the effect of J2 gradient also modulates the profile. The major variation is caused by the change in orbit altitude due to the low eccentricity of the frozen orbit and the effect of J2. If active compensation of the gradient within the ASU is intended, ie to place the drag free point possibly at the centre of the ASU, then the distance from the centre of mass of the spacecraft must be considered. The force required for compensation, assuming a nominal 1m displacement, would be the above gradients multiplied by the spacecraft mass, ie typically 1.5mN continuous thrust. The associated DeltaV would be approximately 70 m/s per year. Atmospheric drag is the most influential non gravitational perturbation. Simulations have been performed to observe its evolution.

72 Page 72 of Drag (m/s/s) Summer Winter Time (secs) Figure 6-15 Drag deceleration in 1000km orbit at maximum in Summer and Winter

73 Page 73 of Baseline option 4:1200km orbit category This option benefits from A further reduced atmospheric drag perturbation Lower earth radiation pressure perturbation At this altitude, available launch mass from Rockot (and all other launchers) is degraded. The fine detail of the orbit altitude is once again determined by ground track repeat requirements, which minimise the ground contact cycle times. A one day repeat period implies orbit altitudes of: Mean radius: Mean radius: 7265 km (mean altitude above 6378 km sphere = 887 km) 7642 km (mean altitude above 6378 km sphere = 1263 km) To achieve an altitude closer to 1200km, a 6 day repeat period was adopted. This has the properties: Mean radius: 7573 km (mean altitude above 6378 km sphere = 1195 km) This was therefore adopted. The orbit features incorporated were: Sun synchronous: Dawn/dusk: Frozen orbit: Inclination = deg Local solar time of ascending node = 6.00 am Mean perigee placed at the orbit antinode (latitude of approx 79.6 deg) The following illustrations show these features:

74 Page 74 of 126 Figure 6-16 Repeating ground track for1200 km orbit with 6 day repeat The track spacing is approximately 4 deg in longitude at the equator Figure 6-17 Ground station visibility for 1200 km orbit with 6 day repeat

75 Page 75 of 126 The ground station patterns but repeat exactly over a one days period. Ground station mean coverage times are 14.5% and 13.3% for these two Northerly ground stations. The altitude behaviour is also of interest. The Frozen orbit feature is shown in the following figure (ie repeatable altitude with latitude). Figure 6-18 Orbit altitude history for 900 km orbit with 1 day repeat Altitude is evaluated over a uniform sphere of radius 6378 km

76 Page 76 of Summary of orbit altitude features Mean altitude 720 km / 2 day repeat 887 km / 1 day repeat 1009 km / 3 day repeat 1195 km / 6 day repeat Inclination 98 deg 99 deg 99.5 deg deg Ground station coverage at Kiruna 10.2 % 11.7 % 12.7% 14.5% From an operational viewpoint, there is little to choose between this range of orbit altitudes. The discussion at the beginning of the section outlined a benefit from the reduced perturbation. Also, at the higher altitude, earlier discussions showed limitations in launcher performance and increase in radiation dosage. Therefore on balance, the 1000km altitude shows the most advantage.

77 Page 77 of Conclusions Orbit selection must consider a number of key issues: Scientific observability Orbital environment Spacecraft design implications and operations A number of parameters are effectively pre-selected for the mission in order to ensure a feasible spacecraft design and scientific observability: Low Earth orbit Sun synchronous orbit Near circular Local solar time of ascending node at dawn/dusk The main issue is the selection of orbit altitude. The associated issues are: Launcher injection mass Orbit perturbation environment and drag-free control Gravity gradient compensation and knowledge Reduction of LT effect with altitude Radiation environment De-orbit The key orbit selection options are outlined in Table 5-1. The main orbit perturbations are shown in Table 4-2 The reduced perturbation environment, acceptable launch mass and acceptable radiation environment give a preference for a 1009km altitude orbit over the original 700km. The magnitude of the LT effect is still acceptable at this higher altitude. Although a 1200km orbit allows even further reduction of perturbation effects, the reduction in available injection mass and also the more severe radiation environment count against this orbit. Therefore 1009km altitude is recommended as the best compromise. The precise altitude at 1009km is obtained from consideration of the features of a near 1000km altitude environment and downlink repeat considerations. The change of the nominal altitude to 1009km (from the previous 700km) means: Atmospheric drag perturbations reduced by one order of magnitude Gravity gradient modelling simplified Eclipse reduced increasing number of observations Radiation increased by factor of 2 but shielding implications acceptable LT effect magnitude still acceptable Launcher injection mass with Rockot unaffected This orbit choice, with a compatible spacecraft design, is compliant with the mission requirements. The issues associated with straylight and guide star selection are considered separately under Reference 3. A number of key points arise from these considerations. They apply generally irrespective of the orbit altitude choice.

78 Page 78 of 126 The De-Sitter rotation is an order of magnitude larger than the LT effect, but only applies in a direction normal to the orbit plane. The dominant LT effect takes place in the orbit plane and therefore there is a good argument to focus the measurement axes in this plane. Drift of the axes out of this plane (for example because the spacecraft is only re-oriented after typically 30 day intervals) will means that the De-Sitter effect will be observed by the ASU in addition to the LT effect. However, the signals can be separated by the difference in frequency content. The ASU requires the effective acceleration gradients to be at /s/s. (Reference 1, R1- ENL-03). Typical gravity gradients in LEO are 2*10-6 /s/s. Active compensation of the gradient effect, by placing the drag free point at the centre of the individual ASUs, implies continuous thrust of 1.5 mn per metre displacement from the centre of mass. This can lead to large thrust requirements. Alternatively electronic compensation could be applied to reduce the effective gradient experienced by the ASU to 3.4*10-8 /s/s. This allows the placing the drag free point at a location closer to the centre of mass (ie no longer performing active compensation) and therefore reduces the thrust requirement on the thrusters. Gravity gradient knowledge is required to high accuracy (2.4*10-11 /s/s). This is exceeded with the latest state of the art models by approx 1 order of magnitude, but requires high order modelling (order 20) The dominant non-gravitational perturbation is atmospheric drag at Solar maximum. This will be compensated by the drag-free control.

79 Page 79 of Consequences of baseline orbit modification The initial baseline orbit selected for Hyper during the CDF study utilised an altitude of 700km. This represents a good compromise between a number of conflicting factors. The result of a detailed evaluation of orbit options has shown that it would be beneficial to raise the orbit altitude to approximately 1000km. The consequences of this change in baseline can be summarised as follows: The spacecraft experiences a more benign, non-gravitational perturbation environment. In particular, the disturbance caused by atmospheric drag is reduced by approximately an order of magnitude. There is a reduction in magnitude of the Lense-Thirring effect of approximately 12%. (see Figure 2-2) The number of days spent in eclipse reduces, with the consequence that over a two year operational period, the number of days that are eclipse free (and so can be devoted to continuous observation) increases by nearly 10% (see Figure 5-2 ) The radiation dose almost doubles, but over the two year period, the total dose is still low (15krads). (See Figure 4-24 ) Launcher injection mass with Rockot is almost unchanged (due to adoption of different intermediate orbits for the two launch cases). Other launchers would experience a significant injection mass reduction at the higher altitude. (see section 5.8 ) Gravity gradient decreases in magnitude by approximately 12%. This has an implication for thrust requirements in maintaining the drag free point offset from the centre of mass. Thrust requirement scales with gravity gradient, therefore higher altitude allows thrust reduction. See section 5.5 The reduction in gravity gradient with altitude also means that the problem of obtaining high accuracy knowledge of the field is alleviated to some extent. The order of the gravity field model required to accurately predict the gradient to the required accuracy reduces from order 30 to 20, allowing simplification of processing requirements. See section The time required for a de-orbit manoeuvre using FEEPs is significantly increased from 3 to 10 years. However, there is currently no firm requirement for de-orbit. See section 5.7.

80 Page 80 of Summary of baseline orbit features The baseline orbit lies close to 1000km altitude, with a 3 day repeat period. The orbit is placed in a stable frozen configuration, with perigee at the orbit antinode. This implies a low eccentricity of approximately The nodes and inclination are such that a dawn-dusk, sun-synchronous orbit results. Orbit mean altitude (wrt spheroid radius 6378km): Orbit mean radius Orbit period (node crossing): Orbit eccentricity and perigee: Orbit inclination: Orbit ascending node: Longitude motion per rev: Max eclipse period: Eclipse season: 1009 km 7387km secs = mins Frozen orbit, perigee at antinode 99.5 deg Dawn-dusk configuration deg 822 secs 57 days

81 Page 81 of REFERENCES 1. Performance Requirements breakdown HYP-2-05-V HYPER Feasibility Activity 2 3. HYPER Feasibility Activity 3

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83 Page 83 of 126 APPENDICES

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85 Page 85 of 126 Appendix 1 The Lense Thirring effect on satellite orbits The presence of a rotating central mass induces a frame drag. The effect can be measured not only as a precession of gyroscopic devices, but also as a Coriolis like term on moving objects. As a consequence, Newton s standard equations for motion under the influence of a central sphere are modified as follows: GM r 2 r where r r GM 2 r l r 2 4 r d 5 GM l r is the gravitational parameter of the planet is the angular velocity is the radius of the planet (assumed to be spherical in this analysis) is the geocentric position vector also the vector d is constructed as follows: d r 2 x 3r r 2 r 3r r r r 2 2 y r 2 x y z z 2r 2 z The first term is standard Newtonian gravitation The second term is a perturbation, represented by the vector P, ie Px P Py P z This can be converted to terms in an orbit referenced frame, where: S is radial T is transverse in the orbit plane W is normal to the orbit plane Then: P P P S T W cosu *cos sin u *sin * cosi sin u * cos cosu *sin *cosi sin *sin i cosu *sin sin u * cos *cosi sin u *sin cosu *cos * cosi cos *sin i sin u *sin ipx cosu *sin i Py cosi P z Then the perturbing forces are expressed as:

86 Page 86 of 126 Px P Py P z 2 4GMl C cosi 4 5 r 2 4GMl C * e *cosi *sin a(1 e ) r 2 4GMl C sin i r * e *sin *cosu 2sin u r a(1 e ) Lagrange s planetary equations can be expressed in terms of the perturbing accelerations da dt 2 n(1 e ) P * e *sin S PT a(1 e r 2 ) de dt 2 (1 e ) na 0.5 P S r a *sin PT e cos a di dt 1 C P W * r * cos d dt C 1 sin i P W *sin d dt 2 1 e ) nae r PS P * cos T 1 sin a e * 2sin 2 (1 ) 0.5 ( 2 i d 2 dt dl dt (1 e ) sin na 2 e PS * r * 2 1 (1 e ) d dt i d 2 dt Then assuming the orbital elements remain approximately constant over an orbit period, with the exception of the anomaly, yields secular rates of change of the elements as follows a 0 4GMl e 3 5na 2 cosi 2 (1 e ) 0.5 cos

87 Page 87 of 126 i (2 * e * cos * cos 1.5 GMl 3 5na sin i 2 2(1 e ) u cos 2u) 4GMl 3 5na 2 1 (1 e 2 ) 1.5 ( e *(sin 0.5sin 2u *cos ) 0.5sin 2u) 2 2 4GMl cosi 1 e 2 ((2 *sin ) 2sin na (1 e ) e i ) 2 This gives non zero secular terms in node and longitude or perigee 1 2 c c 4GMl 5 4GMl * 3 2 a (1 e ) 2 * 3 2 a (1 e ) 1.5 * t * 1 3sin i t 2 where GM is the gravitational parameter of the Earth is the angular velocity l is the radius of the Earth (assumed to be spherical in this analysis) a is the semi-major axis, e the eccentricity and i the inclination if the orbit c is the speed of light The Lense-Thirring rotation therefore influences the evolution of a satellite orbit about the Earth. The effect was predicted in Ref 1. The recent Lageos experiments have attempted to measure the effect. Observations have been found to lie close to the predicted effects. The two principal effects observed are: Rotation of the orbital right ascension of ascending node. Rotation of the orbital argument of perigee. Further details of this are given in appendix 1. For Lageos 1, the node is predicted to rotate by approximately 31 mas/year and 31.5 mas/year for Lageos 2. For Lageos 1, the perigee is predicted to rotate by approximately 32 mas/year and -57 mas/year for Lageos 2. The main sources of error are in the knowledge of J2 and J4, but by using the combined measurements from the two satellites, these uncertainties can be eliminated. The results are in agreement with the Lense-Thirring predictions to within 10% with an uncertainty of 20%.

88 Page 88 of 126 Appendix 2 Gravity gradients Gravity gradients are evaluated for different harmonic orders. The difference in the gravity gradient is evaluated over two order differences at a series of orders. Therefore the results show the gradients pertaining to different orders of modelling. Appendix 1.1 Case 1 Altitude = 1000 km Gravity gradient at order 10 Gravity gradient at order Longitude (deg) E-11 5E-11 4E-11 3E-11 2E-11 1E-11 0 Lat Figure 10-1Gravity gradient increment due to orders 8 to10 with 1000km altitude Astrium Limited owns the copyright of this document which is supplied in confidence and which shall not be used for any purpose other than that for which it is supplied and shall no

89 Page 89 of 126 Gravity gradient at order 20 Gravity gradient at order E E-11 1E-11 8E E-12 4E-12 2E-12 0 Longitude (deg) Lat Figure 10-2Gravity gradient increment due to orders 18 to20 with 1000km altitude At this order the gradients drop below the knowledge requirement threshold.

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91 Page 91 of 126 Figure 10-3 Gravity gradient increments due to orders 18 to 20 at altitude 1000km part be reproduced, copied, or communicated to any person without written permission from the owner.

92 B Page 92 of 126 Appendix 1.2 Case 2 Altitude = 500 km Gravity gradient at order 10 Gravity gradient at order 8 1.4E E-10 1E-10 8E E-11 4E-11 2E-11 0 Longitude (deg) Lat Figure 10-4Gravity gradient increment due to orders 8 to10 with 500km altitude These gradients exceed the threshold

93 Page 93 of 126 Gravity gradient at order 20 Gravity gradient at order E-11 6E-11 5E-11 4E E-11 2E-11 1E Longitude (deg) Lat Figure 10-5Gravity gradient increment due to orders 18 to20 with 500km altitude These gradients exceed the threshold TechnicalNoteV4.doc

94 Page 94 of 126 Gravity gradient at order 30 Gravity gradient at order 28 5E-11 Longitude (deg) E-11 3E-11 2E-11 1E Lat Figure 10-6Gravity gradient increment due to orders 28 to30 with 500km altitude These gradients exceed the threshold TechnicalNoteV4.doc

95 Page 95 of 126 Gravity gradient at order 40 Gravity gradient at order E-11 3E E-11 2E-11 0 Longitude (deg) E-11 1E-11 5E Lat Figure 10-7Gravity gradient increment due to orders 38 to40 with 500km altitude These gradients exceed the threshold TechnicalNoteV4.doc

96 Page 96 of 126 Gravity gradient at order 48 Gravity gradient at order 46 2E E-11 Longitude (deg) E-11 5E Lat 80 Figure 10-8Gravity gradient increment due to orders 46 to 48 with 500km altitude These gradients fall below the threshold TechnicalNoteV4.doc

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98 Page 98 of 126 part be reproduced, copied, or communicated to any person without written permission from the owner. TechnicalNoteV4.doc

99 B Page 99 of 126 Appendix 3 Radiation analysis This appendix reviews radiation fluence and total dose at various circular sun-synchronous orbits, which may be applicable to the ESA HYPER mission. References RD/1 SPENVIS (Space ENVironment Information System) - The aim was to analyse the variation of radiation fluence for a 1 year mission duration at stepped energy bins for circular LEO sun-synchronous orbits with: Varying altitude, and Varying LST (Local Solar Time) The range of orbit cases under scrutiny is shown in Figure This will allow us to see how both Altitude and LST affect the radiation fluence and total dose for a particular orbit. Figure 10-9 Range of Orbit Cases LST Altitude (km) 06:00 hours 12:00 hours 18:00 hours

100 Page 100 of 126 Appendix 1.3 Methodology The ESA web-based tool SPENVIS was used to generate fluences, with the in-built SHIELDOSE model. The following assumptions were made within SPENVIS Choose Radiation Analysis Run Orbit Generator o Select Heliocentric orbit o Orbit epoch selected 01 Jan h 00min 00s o Orbit Duration select 1 day o Satellite orientation One axis parallel to the velocity vector o Set Orbit parameters Altitude x km Local time of ascending node [hr]: x Evaluate trapped proton and electron fluxes o Trapped radiation models select AP-8 (for trapped proton model) and AE-8 (for trapped electron model) o Report File Select level of detail every sixtieth orbital point o Set model parameters Model selection; Protons: AP-8 MAX omnidirectional, Electrons: AE-8 MAX Energy thresholds for output; Protons: 0.1MeV 300MeV, Electrons: 0.04MeV 7MeV Other parameters; Include local time variation, Confidence level for not exceeding fluxes: % Evaluate trapped proton flux anisotropy o Trapped proton anisotropy model: Badhwar and Konradi 1990 MAX Evaluate Solar Proton Fluence o Solar proton model: JPL-91 o Geomagnetic shielding: Apply Shielding o Magnetosphere condition: Quiet o Set model parameters Mission duration: 1year The mission duration will be converted to time during solar active years. The offset in the solar activity cycle (from the start of solar maximum) can be calculated or forced: Calculated from orbit epoch Confidence level: 95% Apply the radiation shielding and effects models: dose and other parameters in aluminium-shielded components: define the shielding thickness and mission duration o Mission duration for trapped particle fluences: days o Shield depth values: mm o Enter values in the table (in increasing order) and click on the last value required: Nr 25, Depth 20.0, min depth o Run SHIELDOSE Detector material: Silicon Run and look in generated report file for the ionising doe model SHIELDOSE TechnicalNoteV4.doc

101 Page 101 of 126 Appendix 1.4 Varying the Altitude for a LST 06:00 Ascending node Trapped Proton Fluence Trapped Proton Fluences at various Sun-synchronous altitudes for a 06:00 LST ascending node 1.00E+14 Fluence (/cm^2/mev) 1.00E E E E E E E E E Energy (MeV) 500km 700km 900km 1100km 1300km 1500km 1800km Figure Trapped Proton Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node TechnicalNoteV4.doc

102 B Page 102 of 126 Altitude (km) Energy Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence (MeV) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+07 Figure Trapped Proton Differential Fluxes and 1 year Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node

103 B Page 103 of 126 Trapped Electron Fluence Trapped electron Fluences at various Sun-synchronous altitudes for a 06:00 LST ascending node Fluence (/cm^2/mev) 1.00E E E E E E E E E E E Energy (MeV) 500km 700km 900km 1100km 1300km 1500km 1700km Figure Trapped Electron Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node

104 B Page 104 of 126 Altitude (km) Energy Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence (MeV) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+07 Figure Trapped Electron Differential Fluxes and 1 year Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node

105 B Page 105 of 126 Solar Proton Fluence Solar Proton Fluences at various Sun-synchronous altitudes for a 06:00 LST ascending nod 1.00E+11 Fluence (/cm^2/mev) 1.00E E E E E km 700km 900km 1100km 1300km 1500km 1800km 1.00E Energy (MeV) Figure Solar Proton Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node

106 B Page 106 of 126 Altitude(km) Energy Mission fluence Mission fluence Mission fluence Mission fluence Mission fluence Mission fluence Mission fluence (MeV) (/cm2/mev) (/cm2/mev) (/cm2/mev) (/cm2/mev) (/cm2/mev) (/cm2/mev) (/cm2/mev) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+05 Figure Solar Proton 1 year Fluence at various Sun-synchronous altitudes for a 06:00 LST ascending node

107 B Page 107 of 126 Radiation Dose 4PI Total Dose in Si at centre of Al Spheres for various Sun- Synchronous altitudes for a 06:00 Ascending Node 1.00E+08 Dose (Rads) 1.00E E E E E km 700km 900km 1100km 1300km 1500km 1800km 1.00E Z (mm) Figure PI Total Dose in Si at centre of Al Spheres for various Sun-Synchronous altitudes for a 06:00 Ascending Node

108 Page 108 of 126 Altitude (km) Z(MM) Z(MILS) Z(G/CM2) Total Dose (Rads) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+03 Figure PI Total Dose in Si at centre of Al Spheres for various Sun-Synchronous altitudes for a 06:00 Ascending Node TechnicalNoteV4.doc

109 Page 109 of 126 Appendix 1.5 Varying the LST Ascending node for a 700km circular Sun-Synchronous orbit Trapped Proton Fluence Trapped Proton Fluences for various LST ascending nodes for a 700km Sun-synchronous altitude 1.00E+12 Fluence (/cm^2/mev) 1.00E E+10 06:00 Hours 12:00 Hours 18:00 Hours 1.00E Energy (MeV) Figure Trapped Proton Fluence for various LST ascending nodes for a 700km Sunsynchronous altitude TechnicalNoteV4.doc

110 B Page 110 of 126 LST 06:00 06:00 12:00 12:00 18:00 18:00 Energy Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence (MeV) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+06 Figure Trapped Proton Differential Fluxes and 1 year Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude

111 B Page 111 of 126 Trapped Electron Fluence Trapped electron Fluences for various LST ascending nodes for a 700km Sun-synchronous altitude 1.00E+15 Fluence (/cm^2/mev) 1.00E E+13 06:00 Hours 12:00 Hours 18:00 Hours 1.00E Energy (MeV) Figure Trapped electron Fluence for various LST ascending nodes for a 700km Sunsynchronous altitude

112 B Page 112 of 126 LST 06:00 06:00 12:00 12:00 18:00 18:00 Energy Differential flux Mission fluence Differential flux Mission fluence Differential flux Mission fluence (MeV) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) (/cm2/s/mev) (/cm2/mev) 1.47E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+07 Figure Trapped Electron Differential Fluxes and 1 year Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude

113 B Page 113 of 126 Solar Proton Fluences Solar Proton Fluences for various LST ascending nodes for a 700km Sun-synchronous altitude 1.00E E+10 Fluence (/cm^2/mev) 1.00E E E E+06 06:00 Hours 12:00 Hours 18:00 Hours 1.00E Energy (MeV) Figure Solar Proton Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude

114 B Page 114 of 126 LST 06:00 12:00 18:00 Energy Mission fluence Mission fluence Mission fluence (MeV) (/cm2/mev) (/cm2/mev) (/cm2/mev) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+05 Figure Solar Proton 1 year Fluence for various LST ascending nodes for a 700km Sun-synchronous altitude

115 B Page 115 of 126 Radiation Dose 4PI Total Dose in Si at centre of Al Spheres for various LST Ascending Nodes for a Sun-Synchronous orbit of altitude 700km 1.00E E+06 Dose (Rads) 1.00E E+04 06:00 Hours 12:00 Hours 18:00 Hours 1.00E E Z (mm) Figure PI Total Dose in Si at centre of Al Spheres for various LST Ascending Nodes for a Sun- Synchronous orbit of altitude 700km TechnicalNoteV4.doc

116 Page 116 of 126 LST (Hours) 06:00 12:00 18:00 Z(MM) Z(MILS) Z(G/CM2) Total Dose (Rads) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+02 Figure PI Total Dose in Si at centre of Al Spheres for various LST Ascending Nodes for a Sun- Synchronous orbit of altitude 700km TechnicalNoteV4.doc

117 Page 117 of 126 Appendix 1.6 Conclusions The following conclusions can be drawn from the analysis: Varying the Altitude for a LST 06:00 Ascending node Maximum factor of several hundred difference in Fluence between 500km (lowest) and 1800km (highest) for Trapped Protons. Maximum Factor of 10 in Fluence between 500km (lowest) and 1800km (highest) for Trapped Electrons. Very little difference in Fluence between 500km (lowest) and 1800km (highest) for Solar Protons. For lower shielding thickness (~<5mm), the maximum factor difference in Total Dose is 10 between 500km (lowest) and 1800km (highest). For shielding thickness > 5mm this factor increases to almost 100 for a shielding thickness of 20mm. Varying the LST Ascending node for a 700km circular Sun-Synchronous orbit Very little difference in Fluence for Trapped Protons, Trapped Electrons or Solar Protons by varying LST at 700km altitude. Very little difference in Total Dose by varying LST at 700km altitude. TechnicalNoteV4.doc

118 Page 118 of 126 Appendix 4 Atmospheric wind effects The reference model is HWM-93 Nominal Model Parameters are: Day number: 1 F 10.7 [10-22 W m -2 Hz -1 ]: 140 F 10.7 (3-hour average) [10-22 W m -2 Hz -1 ]: 140 A p [2 nt]: 15 Local time 6 or 12 Altitude 700 or 1000km LST 6 am case Variation of total wind speed with latitude, for various orbit altitudes with a 6am local time, and fixed longitude of 0deg 300 Total Wind Speed (m/s) km 700km 1000km Latitude (deg) Figure Variation of total wind speed with latitude for various orbit altitudes with a 6am/pm local time, and a fixed longitude of 0deg TechnicalNoteV4.doc

119 Page 119 of 126 Lat. (deg) Total wind speed at 300km altitude (m s-1) Total wind speed at 700km altitude (m s-1) Total wind speed at 1000km altitude (m s-1) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+02 LST 12 pm case TechnicalNoteV4.doc

120 Page 120 of 126 Variation of total wind speed with latitude, for various orbit altitudes with a 12pm local time, and fixed longitude of 0deg 300 Total Wind Speed (m/s) km 700km 1000km Latitude (deg) Figure Variation of total wind speed with latitude for various orbit altitudes with a 12pm local time, and a fixed longitude of 0deg TechnicalNoteV4.doc

121 Page 121 of 126 Lat. (deg) Total wind speed at 300km altitude (m s-1) Total wind speed at 700km altitude (m s-1) Total wind speed at 1000km altitude (m s-1) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+02 TechnicalNoteV4.doc

122 Page 122 of 126 Figure Global Wind Speeds for a 700km orbit with a 6am local time Figure Global Wind Speeds for a 700km orbit with a 12pm local time TechnicalNoteV4.doc