Design and Analysis of Satellite Orbits for the Garada Mission

Transcription

1 International Global Navigation Satellite Systems Society IGNSS Symposium University of New South Wales, Sydney, NSW, Australia 5 7 November Design and Analysis of Satellite Orbits for the Garada Mission Li Qiao School of Surveying and Spatial Information Systems, University of New South Wales, Australia 6() & 6()9749 l.qiao@unsw.edu.au Chris Rizos School of Surveying and Spatial Information Systems, University of New South Wales, Australia 6()98545 & 6()9749 c.rizos@unsw.edu.au Andrew Dempster School of Surveying and Spatial Information Systems, University of New South Wales, Australia 6() & 6()9749 a.dempster@unsw.edu.au ABSTRACT The Australia Centre for Space Engineering Research (ACSER) is presently investigating the design of an earth observation Synthetic Aperture Radar (SAR) satellite mission known as Garada, for flood monitoring and other applications using several small satellites flying in formation. In the initial feasibility study phase, satellite orbit design and analysis is one of the challenges. This paper describes the objectives of the mission and the methods that can be employed for orbit design. The main parameters determining the orbit relate to accessibility revisit requirements and mission lifetime. The requirements and considerations regarding the choice of orbit types and orbital elements for formation configuration designs are presented. Two satellites are the minimum formation; a leading satellite and a following satellite. The satellites fly in approximately 6km altitude circular orbits. Sun-synchronous and more equatorially inclined orbits are compared. The effect of altitude and satellite ballistic coefficient on orbit lifetime is analysed. The two satellites fly in a string of pearls formation (i.e. in line) with a separation of around 4km. The satellites use onboard GPS receivers for navigation. Predictions of GPS signal coverage on orbit are presented. Orbit lifetime, revisit frequencies, illumination time and GPS signal coverage are simulated using the Satellite Tool Kit (STK). KEYWORDS: Small Satellite, Orbit design, Lifetime,Coverage analysis, Synthetic Aperture Radar (SAR)

2 . INTRODUCTION Australian Centre for Space Engineering Research (ACSER) is presently investigating the design of an earth observation Synthetic Aperture Radar (SAR) satellite mission known as Garada. The objectives of the proposed mission are flood and disaster monitoring, and early warning deforestation detection for tropical forests. The disaster monitoring service requirement for space high-resolution ( metres), quick update ( hour for floods, and day for forest monitoring) imagery has generated considerable interest during the last few years. This paper describes the requirements and considerations regarding the choice of the orbits. The orbit modelling is mainly driven by the SAR imaging performance, the lifetime of the satellites, and coverage requirements such as revisit time. The area of interest is the Australian region, which covers all of Australia and most of New Zealand. In order to achieve a fast revisit time, a constellation is proposed in order to increase the coverage performance. The process of orbital parameter determination and constellation design is described. Two kinds of orbits were compared: sun-synchronous orbits and inclined orbits. Since the mission requirements cannot be formulated easily, numerical techniques performed with STK software are employed to obtain initial estimates that can meet the mission requirements. Section presents the mission requirements. Section presents orbit design for a single satellite unit and considerations regarding satellites constellation, are discussed in Section 4.. MISSION REQUIREMENTS. SAR imaging performance In contrast to optical imaging, illumination conditions are not the major factor impacting on SAR imaging quality (Bar-Lev M et al. ). Furthermore, weather conditions such as haze, fog and clouds are not obstacles to SAR imaging. Instead, the altitude is the key factor for imaging performance. For this reason, a close to zero value of eccentricity is desired and the semi-major axis is fixed as a constraint on perigee altitude. An approximate relationship between radar RF power, radar amplitude, and the resultant signal to noise ratio (SNR) is: SNR~ Power Altitude () Equation () shows that when the orbit altitude varies from 5km to 8km, the power needed will increase by a factor of four to keep the same SNR on the ground. This can represent a large increase in the scale of the RF power amplifiers required (Skolnik, 8). A reasonable upper limit altitude therefore is 7km, which requires treble the power compared to a 5km altitude.. Lifetime requirement The proposed Garada satellite is in a Low Earth Orbit (LEO). Satellites in such orbits have lifetimes determined almost entirely by their interaction with the atmosphere (Kennewell 999). The semi-major axis and eccentricity are changed due to the drag effect (Jacchia 97; King-Hele 987). Hence the lifetime is an important factor in determining the altitude. Plans for future flights require accurate estimates of earth orbital lifetimes. However to calculate lifetime a number of factors must be considered, such as satellite atmospheric density, solar cycle effects, orbit configuration (primarily altitude), the drag coefficient and the mass of the

3 spacecraft.. Coverage requirements The coverage requirements are: coverage area and required revisit period. The area of interest is Australia region. The revisit period is defined as the time interval between two imaging opportunities of any site in the coverage area. The objective of this analysis is to design a constellation capable of day to hour revisit time over the Australian region. The physical coverage area of the satellites lies between the north and south parallels with latitude equal to the orbit inclination angle (Bar-Lev M et al. ). For instance, with 6 inclination orbits, the coverage of the satellite ground track is 6 S ~ 6 N. The actual coverage area is determined by the orbit inclination and the maximal imaging pointing angle of the radar. In this paper a 47 inclined orbit, which covers most of Australian region, and a sun-synchronous orbit are considered and compared in relation to revisit performance and illumination time. Though the illumination time is not the primary requirement, it potentially affects the orbit choice as the solar cells are the main power source. As a result, the period the satellite is in the full sun is important.. Orbit definition The laws of planetary motion, which were determined empirically by Kepler about 4 years ago, equally apply to a satellite s orbit around the Earth (Montenbruck and Gill 5). The satellite orbit can be defined by the classical set of Keplerian parameters, referred to the vernal equinox inertial coordinates axes. In fact, the orbit modelling task is to find the optimal set of orbital parameters to meet the mission requirement. The six Keplerian parameters are (Vallado 7): a The semi-major axis e The eccentricity i The inclination angle Ω The right ascension of ascending node (RAAN) ω The argument of perigee M The mean anomaly. ORBIT DESIGN FOR GARADA MISSION. GARADA satellite The Garada project has adopted a bistatic SAR configuration, i.e. two satellites, one with a transmitter and the other equipped with a receiver. These two satellites fly in line with an approximate km separation. Each satellite is assumed to have similar physical and orbital parameters. These two satellites share the same orbit except that the mean anomaly angles are different. Atmospheric drag has a large impact on the lifetime of the satellite. The drag equation (below) (Jacchia 96) illustrates how the drag acceleration Fd on any object is proportional to the density of the fluid ρ, the drag coefficient C d, the area and mass ratio A / m and the square of the relative speed v between the object and the fluid: v Cd A v ρ F d = m ()

4 The drag coefficient C d is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment. A lower value of drag coefficient indicates that the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area usually called the drag area, defined as the mean cross-sectional area of the satellite perpendicular to its direction of travel. Figure and Figure show change in drag coefficient and drag area with satellite life. It can Cd be seen that when changes from. to. (for satellite drag coefficient, Cd usually taken to be between. and.), the lifetime reduces from to 4 years. When the drag area varies from.m to.5m, lifetime reduces from to years. These results confirm that there is a strong relationship between drag and orbit lifetime. Figure to Figure 4 depict the change in reflect coefficient Cr and sun area with satellite lifetime. The reflect coefficient and sun area determine the value of satellite solar radiation press. Normally the satellite reflect coefficient is around. and it shows that when the Cr changes in a range from. to.5, it does not affect the lifetime significantly. Sun area barely affects the lifetime of the satellite as can be seen in Figure 4. This indicates that radiation pressure effects can be neglected in orbit lifetime calculations. Mass to area ratio (mass to cross-sectional area in the direction of travel) directly affects the drag magnitude. Figure 5 shows that as the satellite mass changes from to 5kg, the lifetime changes from less than year to.4 year. The lifetime increase with the mass as the area and mass ratio and the atmospheric drag acceleration reduce accordingly. In actuality the mass will vary as a function of time due to fuel consumption. Note that the change of mass is not considered in this paper. The impacts of density model on lifetime calculation are different (shown in Figure 6) as they have differences in modelling the whole atmosphere response to solar cycle changes in radiative and geomagnetic forcing (Marsh 7). Density model may results in serious errors in the predicted position of satellites especially those orbiting below 6km (Storz ). In the following test, NRLMSISE is adopted as the density model in the following test for its improvement over other models (Picone.et al ). x 4 Satellite life ime vs. DragCoeff x 4 Satellite life ime vs. Drag Area DragCoeff Drag Area(m ) Figure. Lifetime versus drag coefficient Figure. Lifetime versus drag area

5 x 4 Satellite life ime vs. ReflectCoeff 688 Satellite life ime vs. Sun Area ReflectCoeff Sun Area(m ) Figure. Lifetime versus reflect coefficient Satellite life ime vs. Sun Area.4 Figure 4. Lifetime versus sun area Satellite life ime vs. DensityModel.Jacchia7.Jacchia7.MSIS86 4.MSISE9 5.MSIS 8. 6.HarrisPriester 7.Jacchia7Lifetime Mass(kg) Density Model Figure 5. Lifetime versus mass Figure 6. Lifetime versus density model According to the lifetime sensitivity study (Note that the orbit altitude is set to 5km for these tests.), the calculated lifetime is mainly affected by the atmospheric drag and a small drag area is therefore vital for the satellite platform design. In the following discussion it is assumed that the physical parameters of the satellites are as indicated in Table. Table. Physical parameters of the Garada satellites Mass 4kg Drag area. m Drag coefficient C d. Area exposed to sun. m Solar radiation pressure coefficient Cr.. Orbit inclination There are two candidate orbits for the project: sun-synchronous and inclined circular orbits. The major difference between the two orbits is the inclination angle, and inclination impacts the surface coverage area. Though the real coverage of a satellite should be determined by both the sub-satellite track and the swath of the radar, the former can roughly represent the Earth coverage as the swath of SAR is of the order of a few hundreds of kilometres. The subsatellite track defines an imaginary line on the Earth s surface. Figure 7 and Figure 8 show the sub-satellite tracks of a sun-synchronous orbit (97.79 inclination) and a 47 inclined orbit, respectively. 47 is chosen so as to optimise Australian region coverage. The final type of satellite orbit was chosen to provide the best revisit coverage.

6 Figure 7. Earth coverage area for sun-synchronous orbit of inclination Orbit altitude and eccentricity Figure 8. Earth coverage area for 47 inclined orbit The preliminary orbit altitude of 5 to 7km was derived from the SAR imaging and the lifetime requirements. It is observed from Figure 9 and Figure that the two types of orbits have similar lifetime and satellite altitude plots. Table present some lifetime data in a year of Figure. The lifetime varies significantly with initial orbit altitude. When the orbit altitude is less than 6km the orbit decay is within 5 years. When the orbit altitude is great than 6km, the lifetime is longer than years. Therefore the altitude of orbits should not be lower than 6km for a 4kg satellite. The actual value of the satellite orbit was chosen to provide the best revisit coverage. In the following analyses the altitude of the orbit was assumed to be 6km. x 5 4 x Satellite Altitude (km) Figure 9. Sun-synchronous orbit lifetime versus satellite altitude Satellite Altitude (km) Figure. 47 inclination orbit lifetime versus satellite altitude

7 Table. Lifetime of 47 inclination orbits Satellite altitude (km) Lifetime (year) Satellite altitude (km) Lifetime (year) Satellite illumination and orbit RAAN As the solar cell panels are the main power source for the satellite it is necessary to estimate the periods when the satellite is in full solar illumination. Consider two orbits, one is a 6km altitude 47 inclined circular orbit and the other is at the same altitude but in a sunsynchronous (97.79 inclined) orbit. Figure and Figure show four statistic results of the sun lighting duration: maximum, minimum, mean value and standard deviation (std) respectively. In order to compare the different orbits, Figure b) zoom the plots in a) when lighting duration less than 6 seconds. Where, the mean value x and std definition s are: x n xi n i = n s = ( ( x x) ) = () i (4) n i = It can be seen from Figure and Figure that the statistics of sun lighting duration shows considerable variation with RAAN. The static results variation of sun-synchronous orbits shows a better consistency and its standard deviation is comparatively even (Figure b) in comparison to 47 inclined orbits. For 47 inclined orbits, while its average lighting duration increases to the maximum, its standard deviation is also increased. Figure shows total sun lighting duration per day of sun-synchronous orbits and 47 inclined orbits, depicted by the broken and solid lines respectively. Sun-synchronous orbits have an obvious advantage over the 47 inclined orbit, especially when the RAAN is varied from to 6 degree. Apart from this section, the mean lighting duration of the two orbits is of the same order of magnitude, varying from 4s to 5s. 6 x Max lighting duration Max lighting duration Lighting Duration(s) 4 Lighting Duration(s) 4 Mean lighting duration Min lighting duration Mean lighting duration Min lighting duration Satellite RAAN(deg) Min lighting duration Std lighting duration Satellite RAAN(deg) a). Max, min, mean and std b) Zoom in the sun illumination duration less than 6s Figure. Sun illumination duration vs. RAAN for 6km sun-synchronous orbit

8 6 5 Max lighting duration.6 x 5.4 Max Lighting Duration Min Lighting Duration Lighting Duration(s) 4 Mean lighting duration Min lighting duration Total Lighting Duration(s)..8 Std lighting duration Satellite RAAN(deg) Figure. Sun illumination duration vs. RAAN for 47 6km circular orbit Satellite RAAN(deg) Figure. Comparison of the total illumination duration The final orbit type and RAAN will be chosen according to whether the illumination time qualifies the solar battery. Illumination time analyses are useful for estimating the mission power budgets. Among the orbital element, the altitude and inclination are the two parameters influenced by imaging and coverage requirements. Eccentricity is considered to be close zero. The initial values of argument of perigee and mean anomaly are not important..5 Orbital revisit performance.5. Revisit time definition and SAR modelling As the GARADA mission is a disaster monitoring system the design is driven by coverage area and revisit time. The index to evaluate the coverage performance is the average revisit time. Revisit time measures the intervals during which coverage is not provided (also known as the gaps ). The computed average revisit time is the average of the durations of all the gaps in coverage over the entire coverage interval. If there are N gaps, then the average revisit time can be determined as: N i= GapDuration N A SAR sensor is defined as a rectangular sensor. Fixed sensor pointing type is used to model a SAR antenna attached to a satellite in the STK software. The swath width on the ground is controlled by the beamwidth of the sensor. Figure 4 shows the model of a SAR sensor attached to the satellite. The point angle and beamwidth are calculated according to the geometry between satellite and the ground. Assuming a 6km altitude orbit, for a 55 grazing angle and a 5km swath width on the ground, the sensor beamwidth is required to be.88. A right-look sensor is defined by specifying a 9 azimuth. Actually a 5km swath is very large. The constellation is designed using this assumed value. i (5)

9 .5. Revisit time by single satellite Figure 4. SAR sensor model in STK The revisit time varies with the latitude of the target, where the target could be one location, specified by the latitude or longitude, or a region of interest on the Earth s surface (Sengupta ). For the Australian mainland the northernmost point is Cape York ( 4'S, 4 'E ) and the southernmost point is Wilsons Promontory ( 9 8' S 46 'E ), while Sydney ( 4 S, 4 'E ) is approximately in the middle. The location which is closer to the latitude boundary determined by the obit inclination has a shorter revisit time. Figure 5 and Figure 6 plot the average revisit time in a day for three different latitude lines in a 47 inclined and sun-synchronous orbit, respectively. It is observed that in the case of the 47 inclined orbit, revisit of the 4 S and 4.5 S latitude line in less than day, however the revisit of the.68 (i.e. 4'S ) latitude line is less frequent. The revisit is not even to a specific latitude line due to the SAR being a side-looking sensor rather than nadir pointing. In comparison to Figure 5, sun-synchronous orbits have less diversity with different latitude due to the high inclination (see Figure 6). However, sunsynchronous orbits meet the day revisit in part for all latitudes, and have much more diversity in a specific latitude line..5.5 Lat =.68 S.5 Lat =.68 S.5 Lat = 4 S.5.5 Lat = 4.5 S Lat = 4.5 S Longitutde(deg) Figure orbit average revisit time vs. longitude for different latitude Lat = 4 S Longitutde(deg) Figure 6. sun-synchronous orbit average revisit time vs. longitude for different latitude Extending the analyses from the case of several latitude lines to the whole Australian region, with latitude varying from S to 47 S and longitude varying from E to 8 E.

10 Figure 7 and Figure 8 show the average revisit time for the Australian region for the 47 inclined and sun-synchronous orbit, respectively. 6oS 6 os.5.5 4oS 4 os os.5.5 os 4oS 4 os.5 Figure 7. revisit time by 47 inclined orbit for the Australian region 8oW 65oE 5oE 5oE oe 8oW 65oE 5oE 5oE oe.5 Figure 8. revisit time by sunsynchronous orbit for the Australian region Figure 9 and Figure show the statistical values of revisit time by sun-synchronous and 47 inclined orbits, respectively. The revisit times are periodic by longitude. 47 orbit revisit times reach the minimal value close to the latitude boundary, and within the boundary its revisit times increase when moving closer to the equator. However no access exists outside of the boundary. (As the simulation duration is days, hence if revisit time value equal to, it means no access to this location.) In a comparison of the two figures, the 47 orbit has a shorter revisit time than the sun-synchronous orbit Longitude(deg) Latitude(deg) - - Figure 9. Sun-synchronous orbit revisit time by longitude and latitude Longitude(deg) Latitude(deg) Figure. 47 inclined orbit revisit time by longitude and latitude - -

11 .6 GPS signal coverage on orbit The satellite platform will be equipped with the Namuru v GNSS receiver developed by UNSW. Spaceborne applications of GPS for LEO missions have become commonplace (Bauer 998). Consequently, the GPS coverage performance at the satellite in orbit is vital to its navigation performance. The number of GPS satellites in view can be predicted in advance. Figure and Figure show the number of available GPS satellites (assuming the current GPS constellation) for the sun-synchronous and 47 inclined orbits, respectively. The test assumes the receiver only tracks the GPS main lobe signal and the off-boresight angle is 7. Figure shows the percentage of time when satellites are tracked. It is observed that for more than 8% of the time the receiver can track 6 to 8 GPS satellites, which ensures there are enough measurements for good navigation performance. These results are similar to what would be expected in the case of ground-based GPS receivers. This is due to the fact that the altitude of the orbit is just 6 km, relevantly low compared to the GPS satellite altitude of about km. 9 9 Num of GPS signals Num of GPS signals Time(hour) Figure. Number of GPS satellites visible for 6km sun-synchronous orbit Time(hour) Figure. Number of GPS satellites visible for 6km inclined 47 orbit 5 47 inclined Sun synch 5 # Percent of time Number of N satellites Figure. Percentage of time different GPS satellites are visible 4. ORBITAL CONSTELLATION DESIGN The coverage area provided by a single satellite is comparatively small and it moves as the satellite travels at the high angular velocity needed to maintain its orbit, hence these LEOs are often deployed in satellite constellations. A constellation is a group of satellites working in

12 concern, i.e. considered to have coordinated ground coverage, operating together under shared control, synchronised so that they overlap well in coverage. The constellation performance profile is mainly driven by the number of orbital planes, the number of satellites per plane, the inclination angle and the instrument swath (Cornara et al. ). 4. Revisit time of sun-synchronous orbit satellite constellation The single sun-synchronous orbit revisit time plots (see Figure 9 and Figure ) illustrates the requirement of different orbital planes with a wide range of local times of the ascending nodes, varying from morning hours till afternoon. The satellite constellation consists of 9 separate sun-synchronous orbital planes with the following local times: from 9:, 9:, :, :, :, :, :, :, and :. Figure 4 and Figure 5 show the revisit statistics (minimum, maximum and average) by latitude and longitude. It can be seen that the requirement of hour revisit time is fulfilled in the Australian region (see Figure 6) Longitude(deg) Figure 4. 9 sun-synchronous satellite constellation revisit time by longitude Latitude(deg) Figure 5. 9 sun-synchronous satellite constellation revisit time by latitude 6 o S.5. 4 o S.5 o S. 4 o S.5 o E 5 o E 5 o E 65 o E 8 o W Figure 6. revisit time by 9 sun-synchronous satellite constellation 4. Revisit time by 47 inclined satellite constell ation

13 As a single satellite already almost satisfies the service requirements, a lower number of satellites would be required than for the sun-synchronous constellation. A four 47 inclined satellite constellation is designed in the Walker pattern, i.e. the four satellites are in four orbital planes and the RAAN are spread evenly about the equator (Walker 97). Figure 7 and Figure 8 show the revisit time performance by latitude and longitude. Figure 9 shows the average revisit time value for the Australian region. With the constellation, the requirement on day revisit time is fulfilled for latitudes less than 47, while the revisit time performance is significantly worse for values of latitude greater than this Latitude(deg) Figure inclined orbit revisit time by latitude for the Australian region Longitude(deg) Figure inclined orbit revisit time by longitude for the Australian region 6 o S.5 4 o S.5 o S 4 o S.5 o E 5 o E 5 o E Figure 9. revisit time for the 47 inclined Walker 4// constellation for the Australian region 65 o E 8 o W 5. CONCLUDING REMARKS Satellite orbit modelling is a complex process as it involves trade-offs between different parameters. The designed orbit has to meet the largest number of mission requirements at the least possible cost. In fact, the task is to determine the classical orbital parameters, and these parameters will define the mission lifetime, the flying environment, viewing geometry, payload performance and cost. This paper presents a primary analysis of the orbit design for the Garada project. The Garada mission should be a 6km circular orbit, and its candidate orbit types are sun-synchronous or

14 47 inclined orbit. The 6km sun-synchronous circular orbit and the 47 circular orbit were assessed in terms of their lifetime, solar illumination time, revisit time and GPS signal coverage. Since the user requirement is for a day to hour revisit of the interest area, the constellation is required to meet this criterion. With a 5km swath capability, a 9 sunsynchronous satellite constellation and a four 47 inclined satellite constellation can meet one day revisit time requirement in the Australian region. To meet user requirements and satisfy the cost budget, the orbit modelling studies will continue and the primary orbit design characteristics such as altitude may change. For constellation design, mixed constellations which consist not only of sun-synchronous orbits but also small-inclination circular LEOs will also be investigated. ACKNOWLEDGEMENTS Research for this paper was funded by the Australian Space Research Program. The authors acknowledge the support by the Australian Centre for Space Engineering Research (ACSER). REFERENCES Bar-Lev M, Shcherbina L, Levin V () Eros system-satellite orbit and constellation design, Processings of the nd Asian Conference on Remote Sensing, 5-9 November, Singapore: 5-58 Bauer F, Hartman K, Lightsey E (998) Spaceborne GPS: Current status and future sisions. Proceedings of ION GPS 998, September 5-8, Nashville, Tennessee, USA: Cornara S, Beech TW, Bello-Mora M, Jann G () Satellite constellation mission analysis and design, Acta Astronautica 48(5): Jacchia LG (96) Variations in the earth s upper atmosphere as revealed by satellite drag, Reviews of Modern Physics 5(4): Jacchia LG (97) New Static Models of the Thermosphere and Exosphere with Empirical Temperature Profiles, Special Report, Smithsonian Astrophysical Observatory, May 97. Kennewell J (999) Satellite Orbital Decay Calculations. IPS Radio and Space Service, Sydney Austrlian. King-Hele DG (987) Satellite Orbits in an Atmosphere: Theory and Applications, Blackie and Son, London, 4pp. Marsh DR, Garcis RR, Kinnison DE, Boville BA, Sassi F, Solomon SC and Matthes K (7) Modeling the whole atmosphere response to solar cycle changes in radiative and geomagnetic forcing, Journal of Geophysical Research,,D6 Montenbruck O, Gill E (5) Satellite Orbit: Models Methods and Application, Springer, 69pp. Picone, JM., Hedin AE, Drob DP, and Aikin AC (), NRLMSISE- empirical model of the atmosphere: Statistical comparisons and scientific issues, J. Geophys. Res., 7(A), 468 Sengupta P, Vadali SR, Alfriend KT () Satellite orbit and maintenance for terrestrial coverage, Journal of Spacecraft and Rockets 47(): Skolnik MI (8) Radar Handbook (third edition), McGraw-Hill, 8pp. Storz MF, Bowman BR, Branson J, High accuracy satellite drag model (HASDM), proceedingos AIAA/AAS Astrodynamics Specialist Conference, Montery, CA, USA, : 4886 Vallado DA (7) Fundamentals of Astrodynamics and Applications (third edition), Microcosm Press Springer, 55pp. Walker JG (97) Circular Orbit Patterns Providing Whole Earth Coverage, Royal Aircraft Establishment, Technical Report No. 7, November 97.