Astrodynamics (AERO0024)
|
|
- Rebecca Maxwell
- 5 years ago
- Views:
Transcription
1 Astrodynamics (AERO0024) 5. Dominant Perturbations Gaëtan Kerschen Space Structures & Systems Lab (S3L)
2 Motivation Assumption of a two-body system in which the central body acts gravitationally as a point mass. In many practical situations, a satellite experiences significant perturbations (accelerations). These perturbations are sufficient to cause predictions of the position of the satellite based on a Keplerian approach to be in significant error in a brief time. 2
3 STK: Different Propagators 3
4
5 4. Non-Keplerian Motion 4.1 Dominant perturbations Atmospheric drag Third-body perturbations Solar radiation pressure 5
6 Different Perturbations and Importance? In low-earth orbit (LEO)? In geostationary orbit (GEO)? 4.1 Dominant perturbations 6
7 Satellite dependent! Montenbruck and Gill, Satellite orbits, Springer, 2000 Fortescue et al., Spacecraft systems engineering, 2003
8 Orders of Magnitude 400 kms 1000 kms kms Oblateness Drag Oblateness Sun and moon Oblateness Sun and moon SRP 4.1 Dominant perturbations 8
9 The Earth is not a Sphere 9
10 Mathematical Modeling r ' P r Satellite unit mass r x y z r ' U G M body dm 2 r r ' 2 2 r ' r cos U G body U=-V, potential, V, potential energy r U dm 2 r 1 2cos. ' cos rr rr. ' r ' r 1 10
11 Legendre Polynomials First introduced in 1782 by Legendre as the coefficients in the expansion of the Newtonian potential x r=norm(x) r =norm(x ) x' 11
12 Legendre Polynomials 12
13 Let s Use Them 1 1 l l P [cos ] 2 1 2cos 1 x l0 P[ ] 1 d 2 l! l l l l 2 d 1 l Legendre polynomials P P P 2 0[ ] 1, 1[ ], 2[ ] 3 1, etc
14 Summing up G l U Pl [cos( )] dm r body l 0 Geometric method (intuitive feel for gravity and inertia) U U0 U1 U2... Theory Spherical-harmonic expansion Experiments 14
15 Geometric Method: First Term U 0 G r dm r Two-body potential 15
16 Geometric Method: Second Term G G x y z U 1 cos dm dm 2 r r r G x dm y dm z dm 3 r 0 Center of mass at the origin of the coordinate frame 16
17 Geometric Method: Third Term U 2 2 G 2 3cos 1 dm r 2 G 2 G r ' dm 3 r ' sin dm 3 3 2r 2r G 3 3 A B C I 2r ' r dm dm dm dm A B C 2 2 r ' sin dm I Moments of inertia Polar moment of inertia 17
18 Geometric Method: MacCullagh s Formula Gm G U A B C I r 2r Some of the simplest assumptions are - the ellipsoidal Earth (oblate spheroid) with uniform density (a=b>c). - triaxial ellipsoid (a>b>c). 18
19 Geometric Method: Difficult to Go Further 19
20 Summing up G l U Pl [cos( )] dm r body l 0 Geometric method (intuitive feel for gravity and inertia) Spherical-harmonic expansion Experiments Theory 20
21 Fourier Series? Complete set of orthogonal functions. Circle representation. A square wave defined using 4 Fourier terms 21
22 The Earth Is a Sphere Spherical Harmonics Similar in principle as Fourier series. Complete set of orthogonal functions. They can be used to represent functions defined on the surface of a sphere Our objective! 22
23 Spherical Harmonics If you want to model the 2-body problem or Earth s oblateness, which spherical harmonics do you need? 23
24 Spherical Harmonics & Legendre Polynomials l l l l l 24
25 Spherical Trigonometry G l U Pl [cos( )] dm r body l 0? SphericalTrigonometry.html, geocentric latitude, longitude cos cos(90 )cos(90 )... P sin(90 )sin(90 ) cos( ) sat P sat P sat cos sin( )sin( ) cos( )cos( )cos( ) P sat P sat P sat 25
26 Addition of Spherical Harmonics l l m! P cos P sin P sin 2 ( A A' B B' ) l l P l sat l, m l, m l, m l, m m1 l m! with A P sin cos( m ), A' P sin cos( m ) l, m l, m P P l, m l, m sat sat B P sin sin( m ), B' P sin sin( m ) l, m l, m P P l, m l, m sat sat l, degree m, order 26
27 Associated Legendre Polynomials P m lm 2 m/ 2 d P[ ] 1 2 m/ 2 l d [ ] 1 1 d 2 l! d lm, m l lm 2 1 l P 1, P sin, P cos, etc. 0,0 1,0 sat 1,1 sat For m=0, the associated Legendre functions are the conventional Legendre polynomials. 27
28 Gravitational Coefficients ( l m)! C ' r ' 2 P sin cos( m ) dm l l, m l, m P P ( l m)! body ( l m)! S ' r ' 2 P sin sin( m ) dm l l, m l, m P P ( l m)! body (independent of satellite) C ' C R m, S ' S R m (nondimensionalization) l l l, m l, m l, m l, m 28
29 Normalization C S ( l m)! k(2l 1) C, S, P P, ( l m)! l, m l, m l, m l, m l, m l, m l, m l, m l, m l, m k 1 if m 0, k 2 if m 0 C C 4,0 70,61 (4 0)! (4 0)!1(2.4 1) 5 7 (70 61)! (70 61)!2(2.70 1)
30 End Result l l R U 1 Plm sinsat Cl, m cos( msat ) Sl, m sin( msat ) r l2 m0 r 30
31 Very Important Remark l l R U 1 Plm sin sat Cl, m cos( m sat ) Sl, m sin( m sat ) r l 2 m 0 r Many different expressions exist in the literature: V=±V P lm =(-1) m P lm Normalized or non-normalized coefficients Latitude or colatitude (sin or cos) Be always aware of the conventions/definitions used! 31
32 Determination of Gravitational Coefficients Because the internal distribution of the Earth is not known, the coefficients cannot be calculated from their definition. They are determined experimentally; e.g, using satellite tracking. Satellite-to-satellite tracking: GRACE employs microwave ranging system to measure changes in the distance between two identical satellites as they circle Earth. The ranging system detects changes as small as 10 microns over a distance of 220 km. 32
33 Gravitational Coefficients: GRACE EGM-2008 has been publicly released: Extensive use of GRACE twin satellites. 4.6 million terms in the spherical expansion ( in EGM-96) Geoid with a resolution approaching 10 km (5 x5 ). 33
34 EGM96 (Course Web Site) 0,1? 34
35 EGM96 (Course Web Site) C 4,0 (4 0)! (4 0)!1(2.4 1) 5 7 JGM-2 35
36 Zonal Harmonics (m=0) The zonal coefficients are independent of longitude (symmetry with respect to the rotation axis). l l R U 1 Plm sinsat Cl, m cos( msat ) Sl, m sin( msat ) r l2 m0 r J l C l,0 Sl,0 0 (definition) l l R U 1 JlPl sinsat Plm sinsat Cl, m cos( msat ) Sl, m sin( msat ) r l2 r m1 36
37 Zonal Harmonics (m=0) Each boundary is a root of the Legendre polynomial. Vallado, Fundamental of Astrodynamics and Applications, Kluwer,
38 First Zonal Harmonic: J2 It represents the Earth s equatorial bulge and quantifies the major effects of oblateness on orbits. It is almost a thousand times as large as any of the other coefficients. J 2.1.(2.2+1) C ,0=
39 First Zonal Harmonic: J2 Planet J 2 Mercury Venus Earth Moon Jupiter Saturn 60e e e e e e-2 39
40 Sectorial Harmonics (l=m) The sectorial coefficients represent bands of longitude. The polynomials P l,l are zero only at the poles. Vallado, Fundamental of Astrodynamics and Applications, Kluwer,
41 Tesseral Harmonics (lm0) Vallado, Fundamental of Astrodynamics and Applications, Kluwer,
42 Can You Recognize the Spherical Harmonics? sectorial tesseral zonal 42
43 Resulting Force 1 1 U with ˆ ˆ ˆ F r φ λ r r r cos 1 1 ˆ ˆ ˆ r φ θ r r r sin 43
44 Spherical Earth Gravitational force acts through the Earth s center. U r 1 1 ˆ ˆ ˆ r φ λ r r r cos 44
45 P Oblate Earth: J2 l l R U 1 JlPl sinsat Plm sinsat Cl, m cos( msat ) Sl, m sin( msat ) r l2 r m [ ] 3 1 U 1 J r 2 R r 3sin sat ˆ ˆ ˆ r φ λ r r r cos Perturbation of the radial acceleration Longitudinal acceleration that can be decomposed into an azimuth and normal accelerations 45
46 STK: Central Body Gravity (HPOP) 46
47 STK: Gravity Models (HPOP) 47
48 Atmospheric Drag Atmospheric forces represent the largest nonconservative perturbations acting on low-altitude satellites. The drag is directly opposite to the velocity of the satellite, hence decelerating the satellite. The lift force can be neglected in most cases Atmospheric drag 48
49 Mathematical Modeling Knowledge of attitude Velocity with respect to the atmosphere The atmosphere co-rotates with the Earth. vr vω r r 1 C 2 A v m 2 sat D r v v r r Inertial velocity Earth s angular velocity [1.5-3] Atmospheric density All these parameters are difficult to estimate! Atmospheric drag 49
50 Atmospheric Density The gross behavior of the atmospheric density is well established, but it is still this factor which makes the determination of satellite lifetimes so uncertain. There exist several models (e.g., Jacchia-Roberts, Harris- Priester). Dependence on temperature, molecular weight, altitude, solar activity, etc Atmospheric drag 50
51 Solar Activity Atmospheric drag 51
52 von Karman Institute for Fluid Dynamics An international network of 50 double CubeSats for multipoint, in-situ, long-duration (3 months) measurements in the lower thermosphere ( km) and for re-entry research
53 Atmospheric Density using CHAMP An accelerometer measures the non-gravitational accelerations in three components, of which the along-track component mainly represents the atmospheric drag. By subtracting modeled accelerations for SRP and Earth Albedo, the drag acceleration is isolated and is proportional to the atmospheric density. 53
54 CHAMP Density at 410 kms Atmospheric drag 54
55 Further Reading on the Web Site Atmospheric drag 55
56 Harris-Priester ( km) Static model (e.g., no variation with the 27-day solar rotation). Interpolation determines the density at a particular time. Simple, computationally efficient and fairly accurate Atmospheric drag 56
57 Harris-Priester ( km) Account for diurnal density bulge due to solar radiation Height above the Earth s reference ellipsoid Angle between satellite position vector and the apex of the diurnal bulge Atmospheric drag 57
58 Atmospheric Bulge The high atmosphere bulges toward a point in the sky some 15º to 30º east of the sun (density peak at 2pm local solar time). The observed accelerations of Vanguard satellite (1958) indicated that the air density at 665 km is about 10 times as great when perigee passage occur one hour after noon as when it occurs during the night! Atmospheric drag 58
59 Atmospheric Bulge Position Sun declination Sun right ascension Lag Atmospheric drag 59
60 Interpolation Between Altitudes Mean solar activity Atmospheric drag 60
61 STK Atmospheric Models (HPOP) Atmospheric drag 61
62 STK Solar Activity (HPOP) Atmospheric drag 62
63 Third-Body Perturbations For an Earth-orbiting satellite, the Sun and the Moon should be modeled for accurate predictions. Their effects become noticeable when the effects of drag begin to diminish Third-body perturbations 63
64 Mathematical Modeling (Sun Example) r r r sat r sat r Sat sat m r sat sat Gm m Relative motion is of interest r Gm m sat sat sat 3 3 r sat r sat r sat Inertial frame of reference r sat Gm r Gm r Gm r Gm r r r r sat sat sat sat sat sat sat r r Third-body perturbations sat direct indirect G m m r Gm r r sat sat sat rsat rsat r 64
65 STK: Third-Body Gravity (HPOP) 65
66 Solar Radiation Pressure It produces a nonconservative perturbation on the spacecraft, which depends upon the distance from the sun. It is usually very difficult to determine precisely. It is NOT related to solar wind, which is a continuous stream of particles emanating from the sun. Solar radiation (photons) Solar wind (particles) 800km is regarded as a transition altitude between drag and SRP Solar radiation pressure 66
67 Mathematical Modeling F p c Ae SR SR R sc / sun W/m psr N/m 3e8 m/s 6 2 The reflectivity c R is a value between 0 and 2: - 0: translucent to incoming radiation. - 1: all radiation is absorbed (black body). - 2: all radiation is reflected. The incident area exposed to the sun must be known. The normals to the surfaces are assumed to point in the direction of the sun (e.g., solar arrays) Solar radiation pressure 67
68 Mathematical Modeling: Eclipses Use of shadow functions: F 0 SR Dual cone Solar radiation pressure Cylindrical 68
69 STK: Solar Radiation Pressure (HPOP) 69
70 STK: Shadow Models (HPOP) 70
71 STK: Central Body Pressure (HPOP) 71
72 4. Non-Keplerian Motion 4.1 DOMINANT PERTURBATIONS Atmospheric drag Third-body perturbations Solar radiation pressure 72
73 Astrodynamics (AERO0024) 5. Dominant Perturbations Gaëtan Kerschen Space Structures & Systems Lab (S3L)
Astrodynamics (AERO0024)
Astrodynamics (AERO0024) 5. Dominant Perturbations Gaëtan Kerschen Space Structures & Systems Lab (S3L) Motivation Assumption of a two-body system in which the central body acts gravitationally as a point
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 4B. Non-Keplerian Motion Gaëtan Kerschen Space Structures & Systems Lab (S3L) 2. Two-body problem 4.1 Dominant perturbations Orbital elements (a,e,i,ω,ω) are constant Real satellites
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 5. Numerical Methods Gaëtan Kerschen Space Structures & Systems Lab (S3L) Why Different Propagators? Analytic propagation: Better understanding of the perturbing forces. Useful
More informationThird Body Perturbation
Third Body Perturbation p. 1/30 Third Body Perturbation Modeling the Space Environment Manuel Ruiz Delgado European Masters in Aeronautics and Space E.T.S.I. Aeronáuticos Universidad Politécnica de Madrid
More informationAPPENDIX B SUMMARY OF ORBITAL MECHANICS RELEVANT TO REMOTE SENSING
APPENDIX B SUMMARY OF ORBITAL MECHANICS RELEVANT TO REMOTE SENSING Orbit selection and sensor characteristics are closely related to the strategy required to achieve the desired results. Different types
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 3B. The Orbit in Space and Time Gaëtan Kerschen Space Structures & Systems Lab (S3L) Previous Lecture: The Orbit in Time 3.1 ORBITAL POSITION AS A FUNCTION OF TIME 3.1.1 Kepler
More informationAn Analysis of N-Body Trajectory Propagation. Senior Project. In Partial Fulfillment. of the Requirements for the Degree
An Analysis of N-Body Trajectory Propagation Senior Project In Partial Fulfillment of the Requirements for the Degree Bachelor of Science in Aerospace Engineering by Emerson Frees June, 2011 An Analysis
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 3. The Orbit in Space Gaëtan Kerschen Space Structures & Systems Lab (S3L) Motivation: Space We need means of describing orbits in three-dimensional space. Example: Earth s oblateness
More informationANNEX 1. DEFINITION OF ORBITAL PARAMETERS AND IMPORTANT CONCEPTS OF CELESTIAL MECHANICS
ANNEX 1. DEFINITION OF ORBITAL PARAMETERS AND IMPORTANT CONCEPTS OF CELESTIAL MECHANICS A1.1. Kepler s laws Johannes Kepler (1571-1630) discovered the laws of orbital motion, now called Kepler's laws.
More informationAS3010: Introduction to Space Technology
AS3010: Introduction to Space Technology L E C T U R E S 8-9 Part B, Lectures 8-9 23 March, 2017 C O N T E N T S In this lecture, we will look at factors that cause an orbit to change over time orbital
More informationExperimental Analysis of Low Earth Orbit Satellites due to Atmospheric Perturbations
Experimental Analysis of Low Earth Orbit Satellites due to Atmospheric Perturbations Aman Saluja #1, Manish Bansal #2, M Raja #3, Mohd Maaz #4 #Aerospace Department, University of Petroleum and Energy
More informationAstronomy 6570 Physics of the Planets
Astronomy 6570 Physics of the Planets Planetary Rotation, Figures, and Gravity Fields Topics to be covered: 1. Rotational distortion & oblateness 2. Gravity field of an oblate planet 3. Free & forced planetary
More informationLong-Term Evolution of High Earth Orbits: Effects of Direct Solar Radiation Pressure and Comparison of Trajectory Propagators
Long-Term Evolution of High Earth Orbits: Effects of Direct Solar Radiation Pressure and Comparison of Trajectory Propagators by L. Anselmo and C. Pardini (Luciano.Anselmo@isti.cnr.it & Carmen.Pardini@isti.cnr.it)
More informationSection 13. Orbit Perturbation. Orbit Perturbation. Atmospheric Drag. Orbit Lifetime
Section 13 Orbit Perturbation Orbit Perturbation A satellite s orbit around the Earth is affected by o Asphericity of the Earth s gravitational potential : Most significant o Atmospheric drag : Orbital
More informationAtmospheric Drag. Modeling the Space Environment. Manuel Ruiz Delgado. European Masters in Aeronautics and Space
Atmospheric Drag p. 1/29 Atmospheric Drag Modeling the Space Environment Manuel Ruiz Delgado European Masters in Aeronautics and Space E.T.S.I. Aeronáuticos Universidad Politécnica de Madrid April 2008
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) L04: Non-Keplerian Motion Gaëtan Kerschen Space Structures & Systems Lab (S3L) Non-Keplerian Motion 4 Dominant Perturbations Analytic Treatment Numerical Methods Concluding Remarks
More informationHYPER Feasibility Study
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
More informationHYPER Industrial Feasibility Study Final Presentation Orbit Selection
Industrial Feasibility Study Final Presentation Orbit Selection Steve Kemble Astrium Ltd. 6 March 2003 Mission Analysis Lense Thiring effect and orbit requirements Orbital environment Gravity Atmospheric
More informationA SEMI-ANALYTICAL ORBIT PROPAGATOR PROGRAM FOR HIGHLY ELLIPTICAL ORBITS
A SEMI-ANALYTICAL ORBIT PROPAGATOR PROGRAM FOR HIGHLY ELLIPTICAL ORBITS M. Lara, J. F. San Juan and D. Hautesserres Scientific Computing Group and Centre National d Études Spatiales 6th International Conference
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) L06: Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Motivation 2 Problem Statement? Hint #1: design the Earth-Mars transfer using known concepts
More informationFundamentals of Astrodynamics and Applications
Fundamentals of Astrodynamics and Applications Third Edition David A. Vallado with technical contributions by Wayne D. McClain Space Technology Library Published Jointly by Microcosm Press Hawthorne, CA
More informationLecture 2c: Satellite Orbits
Lecture 2c: Satellite Orbits Outline 1. Newton s Laws of Mo3on 2. Newton s Law of Universal Gravita3on 3. Kepler s Laws 4. Pu>ng Newton and Kepler s Laws together and applying them to the Earth-satellite
More informationastronomy A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times.
astronomy 2008 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. 5. If the distance between the Earth and the Sun were
More informationInfrared Earth Horizon Sensors for CubeSat Attitude Determination
Infrared Earth Horizon Sensors for CubeSat Attitude Determination Tam Nguyen Department of Aeronautics and Astronautics Massachusetts Institute of Technology Outline Background and objectives Nadir vector
More informationMODELLING OF PERTURBATIONS FOR PRECISE ORBIT DETERMINATION
MODELLING OF PERTURBATIONS FOR PRECISE ORBIT DETERMINATION 1 SHEN YU JUN, 2 TAN YAN QUAN, 3 TAN GUOXIAN 1,2,3 Raffles Science Institute, Raffles Institution, 1 Raffles Institution Lane, Singapore E-mail:
More informationChapter 5 - Part 1. Orbit Perturbations. D.Mortari - AERO-423
Chapter 5 - Part 1 Orbit Perturbations D.Mortari - AERO-43 Orbital Elements Orbit normal i North Orbit plane Equatorial plane ϕ P O ω Ω i Vernal equinox Ascending node D. Mortari - AERO-43 Introduction
More informationAnalytical Method for Space Debris propagation under perturbations in the geostationary ring
Analytical Method for Space Debris propagation under perturbations in the geostationary ring July 21-23, 2016 Berlin, Germany 2nd International Conference and Exhibition on Satellite & Space Missions Daniel
More informationABSTRACT 1. INTRODUCTION
Force Modeling and State Propagation for Navigation and Maneuver Planning for CubeSat Rendezvous, Proximity Operations, and Docking Christopher W. T. Roscoe, Jacob D. Griesbach, Jason J. Westphal, Dean
More informationThermal Radiation Effects on Deep-Space Satellites Part 2
Thermal Radiation Effects on Deep-Space Satellites Part 2 Jozef C. Van der Ha www.vanderha.com Fundamental Physics in Space, Bremen October 27, 2017 Table of Contents Mercury Properties & Parameters Messenger
More informationInfrared Earth Horizon Sensors for CubeSat Attitude Determination
Infrared Earth Horizon Sensors for CubeSat Attitude Determination Tam Nguyen Department of Aeronautics and Astronautics Massachusetts Institute of Technology Outline Background and objectives Nadir vector
More informationSpace Travel on a Shoestring: CubeSat Beyond LEO
Space Travel on a Shoestring: CubeSat Beyond LEO Massimiliano Vasile, Willem van der Weg, Marilena Di Carlo Department of Mechanical and Aerospace Engineering University of Strathclyde, Glasgow 5th Interplanetary
More informationORBITAL DECAY PREDICTION AND SPACE DEBRIS IMPACT ON NANO-SATELLITES
Journal of Science and Arts Year 16, No. 1(34), pp. 67-76, 2016 ORIGINAL PAPER ORBITAL DECAY PREDICTION AND SPACE DEBRIS IMPACT ON NANO-SATELLITES MOHAMMED CHESSAB MAHDI 1 Manuscript received: 22.02.2016;
More informationChapter 9 Circular Motion Dynamics
Chapter 9 Circular Motion Dynamics Chapter 9 Circular Motion Dynamics... 9. Introduction Newton s Second Law and Circular Motion... 9. Universal Law of Gravitation and the Circular Orbit of the Moon...
More informationC) D) 2. The model below shows the apparent path of the Sun as seen by an observer in New York State on the first day of one of the four seasons.
1. Which diagram best represents the regions of Earth in sunlight on June 21 and December 21? [NP indicates the North Pole and the shading represents Earth's night side. Diagrams are not drawn to scale.]
More informationFundamentals of Satellite technology
Fundamentals of Satellite technology Prepared by A.Kaviyarasu Assistant Professor Department of Aerospace Engineering Madras Institute Of Technology Chromepet, Chennai Orbital Plane All of the planets,
More informationORBITS WRITTEN Q.E. (June 2012) Each of the five problems is valued at 20 points. (Total for exam: 100 points)
ORBITS WRITTEN Q.E. (June 2012) Each of the five problems is valued at 20 points. (Total for exam: 100 points) PROBLEM 1 A) Summarize the content of the three Kepler s Laws. B) Derive any two of the Kepler
More information1. The bar graph below shows one planetary characteristic, identified as X, plotted for the planets of our solar system.
1. The bar graph below shows one planetary characteristic, identified as X, plotted for the planets of our solar system. Which characteristic of the planets in our solar system is represented by X? A)
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 10. Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Motivation 2 6. Interplanetary Trajectories 6.1 Patched conic method 6.2 Lambert s problem
More informationChapter 8 Part 1. Attitude Dynamics: Disturbance Torques AERO-423
Chapter 8 Part 1 Attitude Dynamics: Disturbance Torques AEO-43 Types of Disturbance Torques Solar Pressure Dominant torque for geosynchronous satellites Gravity Gradient Can be disturbance or control torque
More informationLecture Module 2: Spherical Geometry, Various Axes Systems
1 Lecture Module 2: Spherical Geometry, Various Axes Systems Satellites in space need inertial frame of reference for attitude determination. In a true sense, all bodies in universe are in motion and inertial
More informationInertial Frame frame-dragging
Frame Dragging Frame Dragging An Inertial Frame is a frame that is not accelerating (in the sense of proper acceleration that would be detected by an accelerometer). In Einstein s theory of General Relativity
More information(ii) Observational Geomagnetism. Lecture 5: Spherical harmonic field models
(ii) Observational Geomagnetism Lecture 5: Spherical harmonic field models Lecture 5: Spherical harmonic field models 5.1 Introduction 5.2 How to represent functions on a spherical surface 5.3 Spherical
More informationExam #1 Covers material from first day of class, all the way through Tides and Nature of Light Supporting reading chapters 1-5 Some questions are
Exam #1 Covers material from first day of class, all the way through Tides and Nature of Light Supporting reading chapters 1-5 Some questions are concept questions, some involve working with equations,
More informationEVALUATING ORBITS WITH POTENTIAL TO USE SOLAR SAIL FOR STATION-KEEPING MANEUVERS
IAA-AAS-DyCoSS2-14-16-03 EVALUATING ORBITS WITH POTENTIAL TO USE SOLAR SAIL FOR STATION-KEEPING MANEUVERS Thais C. Oliveira, * and Antonio F. B. A. Prado INTRODUCTION The purpose of this paper is to find
More informationA Senior Project. presented to. the Faculty of the Aerospace Engineering Department. California Polytechnic State University, San Luis Obispo
De-Orbiting Upper Stage Rocket Bodies Using a Deployable High Altitude Drag Sail A Senior Project presented to the Faculty of the Aerospace Engineering Department California Polytechnic State University,
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 5B. Orbital Maneuvers Gaëtan Kerschen Space Structures & Systems Lab (S3L) Previous Lecture: Coplanar Maneuvers 5.1 INTRODUCTION 5.1.1 Why? 5.1.2 How? 5.1.3 How much? 5.1.4 When?
More informationCOVARIANCE DETERMINATION, PROPAGATION AND INTERPOLATION TECHNIQUES FOR SPACE SURVEILLANCE. European Space Surveillance Conference 7-9 June 2011
COVARIANCE DETERMINATION, PROPAGATION AND INTERPOLATION TECHNIQUES FOR SPACE SURVEILLANCE European Space Surveillance Conference 7-9 June 2011 Pablo García (1), Diego Escobar (1), Alberto Águeda (1), Francisco
More informationEarth Science, 11e. Origin of Modern Astronomy Chapter 21. Early history of astronomy. Early history of astronomy. Early history of astronomy
2006 Pearson Prentice Hall Lecture Outlines PowerPoint Chapter 21 Earth Science 11e Tarbuck/Lutgens This work is protected by United States copyright laws and is provided solely for the use of instructors
More informationCHAPTER 3 PERFORMANCE
PERFORMANCE 3.1 Introduction The LM-3A performance figures given in this chapter are based on the following assumptions: Launching from XSLC (Xichang Satellite Launch Center, Sichuan Province, China),
More informationAstronomy I Exam I Sample Name: Read each question carefully, and choose the best answer.
Name: Read each question carefully, and choose the best answer. 1. During a night in Schuylkill Haven, most of the stars in the sky (A) are stationary through the night. (B) the actual motion depends upon
More informationOrbits for Polar Applications Malcolm Macdonald
Orbits for Polar Applications Malcolm Macdonald www.strath.ac.uk/mae 25 June 2013 malcolm.macdonald.102@strath.ac.uk Slide 1 Image Credit: ESA Overview Where do we currently put spacecraft? Where else
More informationEarth Science, 13e Tarbuck & Lutgens
Earth Science, 13e Tarbuck & Lutgens Origins of Modern Astronomy Earth Science, 13e Chapter 21 Stanley C. Hatfield Southwestern Illinois College Early history of astronomy Ancient Greeks Used philosophical
More informationSatellite Communications
Satellite Communications Lecture (3) Chapter 2.1 1 Gravitational Force Newton s 2nd Law: r r F = m a Newton s Law Of Universal Gravitation (assuming point masses or spheres): Putting these together: r
More informationChapter 1: Discovering the Night Sky. The sky is divided into 88 unequal areas that we call constellations.
Chapter 1: Discovering the Night Sky Constellations: Recognizable patterns of the brighter stars that have been derived from ancient legends. Different cultures have associated the patterns with their
More informationStatistical methods to address the compliance of GTO with the French Space Operations Act
Statistical methods to address the compliance of GTO with the French Space Operations Act 64 th IAC, 23-27 September 2013, BEIJING, China H.Fraysse and al. Context Space Debris Mitigation is one objective
More informationDynamics of the Earth
Time Dynamics of the Earth Historically, a day is a time interval between successive upper transits of a given celestial reference point. upper transit the passage of a body across the celestial meridian
More informationAttitude Determination using Infrared Earth Horizon Sensors
SSC14-VIII-3 Attitude Determination using Infrared Earth Horizon Sensors Tam Nguyen Department of Aeronautics and Astronautics, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge,
More informationSail-Assisted End-of-Life Disposal of High-LEO Satellites
4th International Symposium on Solar Sailing Kyoto, Japan, January 17-20, 2017 Sail-Assisted End-of-Life Disposal of High-LEO Satellites Sergey Trofimov Keldysh Institute of Applied Mathematics Russian
More informationBenefits of a Geosynchronous Orbit (GEO) Observation Point for Orbit Determination
Benefits of a Geosynchronous Orbit (GEO) Observation Point for Orbit Determination Ray Byrne, Michael Griesmeyer, Ron Schmidt, Jeff Shaddix, and Dave Bodette Sandia National Laboratories ABSTRACT Determining
More informationr( θ) = cos2 θ ω rotation rate θ g geographic latitude - - θ geocentric latitude - - Reference Earth Model - WGS84 (Copyright 2002, David T.
1 Reference Earth Model - WGS84 (Copyright 22, David T. Sandwell) ω spheroid c θ θ g a parameter description formula value/unit GM e (WGS84) 3.9864418 x 1 14 m 3 s 2 M e mass of earth - 5.98 x 1 24 kg
More informationCelestial Mechanics and Satellite Orbits
Celestial Mechanics and Satellite Orbits Introduction to Space 2017 Slides: Jaan Praks, Hannu Koskinen, Zainab Saleem Lecture: Jaan Praks Assignment Draw Earth, and a satellite orbiting the Earth. Draw
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 5B. Orbital Maneuvers Gaëtan Kerschen Space Structures & Systems Lab (S3L) Previous Lecture: Coplanar Maneuvers 5.1 INTRODUCTION 5.1.1 Why? 5.1.2 How? 5.1.3 How much? 5.1.4 When?
More informationPhysics Mechanics Lecture 30 Gravitational Energy
Physics 170 - Mechanics Lecture 30 Gravitational Energy Gravitational Potential Energy Gravitational potential energy of an object of mass m a distance r from the Earth s center: Gravitational Potential
More informationPropagation and Collision of Orbital Debris in GEO Disposal Orbits
Propagation and Collision of Orbital Debris in GEO Disposal Orbits Benjamin Polzine Graduate Seminar Presentation Outline Need Approach - Benefit GEO Debris Continuation of Previous Work Propagation Methods
More informationChapter 4. Motion and gravity
Chapter 4. Motion and gravity Announcements Labs open this week to finish. You may go to any lab section this week (most people done). Lab exercise 2 starts Oct 2. It's the long one!! Midterm exam likely
More informationOptimization of Orbital Transfer of Electrodynamic Tether Satellite by Nonlinear Programming
Optimization of Orbital Transfer of Electrodynamic Tether Satellite by Nonlinear Programming IEPC-2015-299 /ISTS-2015-b-299 Presented at Joint Conference of 30th International Symposium on Space Technology
More informationChapter 1 Solar Radiation
Chapter 1 Solar Radiation THE SUN The sun is a sphere of intensely hot gaseous matter with a diameter of 1.39 10 9 m It is, on the average, 1.5 10 11 m away from the earth. The sun rotates on its axis
More informationDesign and Implementation of a Space Environment Simulation Toolbox for Small Satellites
56th International Astronautical Congress 25 35th Student Conference (IAF W.) IAC-5-E2.3.6 Design and Implementation of a Space Environment Simulation Toolbox for Small Satellites Rouzbeh Amini, Jesper
More informationAST111, Lecture 1b. Measurements of bodies in the solar system (overview continued) Orbital elements
AST111, Lecture 1b Measurements of bodies in the solar system (overview continued) Orbital elements Planetary properties (continued): Measuring Mass The orbital period of a moon about a planet depends
More informationDeorbiting Upper-Stages in LEO at EOM using Solar Sails
Deorbiting Upper-Stages in LEO at EOM using Solar Sails Alexandru IONEL* *Corresponding author INCAS National Institute for Aerospace Research Elie Carafoli, B-dul Iuliu Maniu 220, Bucharest 061126, Romania,
More informationGravitation. Luis Anchordoqui
Gravitation Kepler's law and Newton's Synthesis The nighttime sky with its myriad stars and shinning planets has always fascinated people on Earth. Towards the end of the XVI century the astronomer Tycho
More informationAerodynamic Lift and Drag Effects on the Orbital Lifetime Low Earth Orbit (LEO) Satellites
Aerodynamic Lift and Drag Effects on the Orbital Lifetime Low Earth Orbit (LEO) Satellites I. Introduction Carlos L. Pulido Department of Aerospace Engineering Sciences University of Colorado Boulder Abstract
More informationSunlight and its Properties Part I. EE 446/646 Y. Baghzouz
Sunlight and its Properties Part I EE 446/646 Y. Baghzouz The Sun a Thermonuclear Furnace The sun is a hot sphere of gas whose internal temperatures reach over 20 million deg. K. Nuclear fusion reaction
More informationThe Orbit Control of ERS-1 and ERS-2 for a Very Accurate Tandem Configuration
The Orbit Control of ERS-1 and ERS-2 for a Very Accurate Tandem Configuration Mats Rosengren European Space Operations Centre Robert Bosch Str 5 D64293 Darmstadt Germany Email: mrosengr@esoc.esa.de Abstract
More information5.12 The Aerodynamic Assist Trajectories of Vehicles Propelled by Solar Radiation Pressure References...
1 The Two-Body Problem... 1 1.1 Position of the Problem... 1 1.2 The Conic Sections and Their Geometrical Properties... 12 1.3 The Elliptic Orbits... 20 1.4 The Hyperbolic and Parabolic Trajectories...
More informationlightyears observable universe astronomical unit po- laris perihelion Milky Way
1 Chapter 1 Astronomical distances are so large we typically measure distances in lightyears: the distance light can travel in one year, or 9.46 10 12 km or 9, 600, 000, 000, 000 km. Looking into the sky
More informationOn Sun-Synchronous Orbits and Associated Constellations
On Sun-Synchronous Orbits and Associated Constellations Daniele Mortari, Matthew P. Wilkins, and Christian Bruccoleri Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843,
More informationAST 2010 Descriptive Astronomy Study Guide Exam I
AST 2010 Descriptive Astronomy Study Guide Exam I Wayne State University 1 Introduction and overview Identify the most significant structures in the universe: Earth, planets, Sun, solar system, stars,
More informationPHYS 160 Astronomy Test #1 Fall 2017 Version B
PHYS 160 Astronomy Test #1 Fall 2017 Version B 1 I. True/False (1 point each) Circle the T if the statement is true, or F if the statement is false on your answer sheet. 1. An object has the same weight,
More informationControl of Long-Term Low-Thrust Small Satellites Orbiting Mars
SSC18-PII-26 Control of Long-Term Low-Thrust Small Satellites Orbiting Mars Christopher Swanson University of Florida 3131 NW 58 th Blvd. Gainesville FL ccswanson@ufl.edu Faculty Advisor: Riccardo Bevilacqua
More informationRECOMMENDATION ITU-R S Impact of interference from the Sun into a geostationary-satellite orbit fixed-satellite service link
Rec. ITU-R S.1525-1 1 RECOMMENDATION ITU-R S.1525-1 Impact of interference from the Sun into a geostationary-satellite orbit fixed-satellite service link (Question ITU-R 236/4) (21-22) The ITU Radiocommunication
More informationCHAPTER 3 PERFORMANCE
PERFORMANCE 3.1 Introduction The LM-3B performance figures given in this chapter are based on the following assumptions: Launching from XSLC (Xichang Satellite Launch Center, Sichuan Province, China),
More informationSEMI-ANALYTICAL COMPUTATION OF PARTIAL DERIVATIVES AND TRANSITION MATRIX USING STELA SOFTWARE
SEMI-ANALYTICAL COMPUTATION OF PARTIAL DERIVATIVES AND TRANSITION MATRIX USING STELA SOFTWARE Vincent Morand, Juan Carlos Dolado-Perez, Hubert Fraysse (1), Florent Deleflie, Jérôme Daquin (2), Cedric Dental
More information4. Which object best represents a true scale model of the shape of the Earth? A) a Ping-Pong ball B) a football C) an egg D) a pear
Name Test on Friday 1. Which diagram most accurately shows the cross-sectional shape of the Earth? A) B) C) D) Date Review Sheet 4. Which object best represents a true scale model of the shape of the Earth?
More informationEARTHS SHAPE AND POLARIS PRACTICE 2017
1. In the diagram below, letters A through D represent the locations of four observers on the Earth's surface. Each observer has the same mass. 3. Which diagram most accurately shows the cross-sectional
More information2) The number one million can be expressed in scientific notation as: (c) a) b) 10 3 c) 10 6 d)
Astronomy Phys 181 Midterm Examination Choose the best answer from the choices provided. 1) What is the range of values that the coordinate Declination can have? (a) a) -90 to +90 degrees b) 0 to 360 degrees
More informationis a revolution relative to a fixed celestial position. is the instant of transit of mean equinox relative to a fixed meridian position.
PERIODICITY FORMULAS: Sidereal Orbit Tropical Year Eclipse Year Anomalistic Year Sidereal Lunar Orbit Lunar Mean Daily Sidereal Motion Lunar Synodical Period Centenial General Precession Longitude (365.25636042
More informationCalculation of Earth s Dynamic Ellipticity from GOCE Orbit Simulation Data
Available online at www.sciencedirect.com Procedia Environmental Sciences 1 (1 ) 78 713 11 International Conference on Environmental Science and Engineering (ICESE 11) Calculation of Earth s Dynamic Ellipticity
More informationName Class Date. For each pair of terms, explain how the meanings of the terms differ.
Skills Worksheet Chapter Review USING KEY TERMS 1. Use each of the following terms in a separate sentence: year, month, day, astronomy, electromagnetic spectrum, constellation, and altitude. For each pair
More informationThe Earth, Moon, and Sky. Lecture 5 1/31/2017
The Earth, Moon, and Sky Lecture 5 1/31/2017 From Last Time: Stable Orbits The type of orbit depends on the initial speed of the object Stable orbits are either circular or elliptical. Too slow and gravity
More informationUseful Formulas and Values
Name Test 1 Planetary and Stellar Astronomy 2017 (Last, First) The exam has 20 multiple choice questions (3 points each) and 8 short answer questions (5 points each). This is a closed-book, closed-notes
More informationLecture 5. Motions of the Planets
Lecture 5 Motions of the Planets; Geometric models of the Solar System Motion of Planets Opposition, Conjunction Retrograde Motion Scientific Method and "Models" Size of the Earth Geocentric vs Heliocentric
More informationGEOID UNDULATIONS OF SUDAN USING ORTHOMETRIC HEIGHTS COMPARED WITH THE EGM96 ANG EGM2008
GEOID UNDULATIONS OF SUDAN USING ORTHOMETRIC HEIGHTS COMPARED Dr. Abdelrahim Elgizouli Mohamed Ahmed* WITH THE EGM96 ANG EGM2008 Abstract: Positioning by satellite system determine the normal height above
More informationMAHALAKSHMI ENGINEERING COLLEGE-TRICHY QUESTION BANK UNIT I PART A
MAHALAKSHMI ENGINEERING COLLEGE-TRICHY QUESTION BANK SATELLITE COMMUNICATION DEPT./SEM.:ECE/VIII UNIT I PART A 1.What are the different applications of satellite systems? *Largest International System(Intel
More informationOrbital and Celestial Mechanics
Orbital and Celestial Mechanics John P. Vinti Edited by Gim J. Der TRW Los Angeles, California Nino L. Bonavito NASA Goddard Space Flight Center Greenbelt, Maryland Volume 177 PROGRESS IN ASTRONAUTICS
More informationMicro-satellite Mission Analysis: Theory Overview and Some Examples
Micro-satellite Mission Analysis: Theory Overview and Some Examples Lars G. Blomberg Alfvén Laboratory Royal Institute of Technology Stockholm, Sweden March 003 KTH Report ALP-003-103 Abstract. Rudimentary
More informationScientists observe the environment around them using their five senses.
Earth Science Notes Topics 1: Observation and Measurement Topic 2: The Changing Environment Review book pages 1-38 Scientists observe the environment around them using their five senses. When scientists
More informationLecture D30 - Orbit Transfers
J. Peraire 16.07 Dynamics Fall 004 Version 1.1 Lecture D30 - Orbit Transfers In this lecture, we will consider how to transfer from one orbit, or trajectory, to another. One of the assumptions that we
More informationPrinciples of Global Positioning Systems Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 12.540 Principles of Global Positioning Systems Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 12.540
More informationChapter 13. Gravitation
Chapter 13 Gravitation e = c/a A note about eccentricity For a circle c = 0 à e = 0 a Orbit Examples Mercury has the highest eccentricity of any planet (a) e Mercury = 0.21 Halley s comet has an orbit
More information