麻省理工学院：《Satellite Engineering》Lecture 10 Electromagnetic Formation Flight

Electromagnetic Formation Flight NRO DI Final Review Friday, August 29, 2003 National Reconnaissance Office Headquarters Chantilly, VA LOCKHEED MARTIN Massachusetts Institute of Lockheed Martin Corporation Technology Advanced Technology Center Space Systems Laboratory

• Massachusetts Institute of Technology • Space Systems Laboratory • Lockheed Martin Corporation • Advanced Technology Center Electromagnetic Formation Flight Electromagnetic Formation Flight NRO DII Final Review Friday, August 29, 2003 National Reconnaissance Office Headquarters Chantilly, VA

大 Outline Motivation Fundamental principles MIT EMFFORCE Testbed Governing Equations Design Trajectory Mechanics Calibration Stability and Control Movie Mission Applicability Space Hardware Design Issues Sparse Arrays Thermal Control Filled Apertures Power System Design Other Proximity Operations High b-Field Effects Mission Analyses Conclusions Sparse Arrays Filled Apertures Other Proximity Operations DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Outline Outline • Motivation • Fundamental Principles – Governing Equations – Trajectory Mechanics – Stability and Control • Mission Applicability – Sparse Arrays – Filled Apertures – Other Proximity Operations • Mission Analyses – Sparse Arrays – Filled Apertures – Other Proximity Operations • MIT EMFFORCE Testbed – Design – Calibration – Movie • Space Hardware Design Issues – Thermal Control – Power System Design – High B-Field Effects • Conclusions

大 Motivation Traditional propulsion uses propellant as a reaction mass Advantages ability to move center of mass of spacecraft (Momentum conserved when propellant is included) Independent (and complete) control of each spacecraft Disadvantages Propellant is a limited resource Momentum conservation requires that the necessary propellant mass increase exponentially with the velocity increment(AV) Propellant can be a contaminant to precision optics DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Motivation Motivation • Traditional propulsion uses propellant as a reaction mass • Advantages – Ability to move center of mass of spacecraft (Momentum conserved when propellant is included) – Independent (and complete) control of each spacecraft • Disadvantages – Propellant is a limited resource – Momentum conservation requires that the necessary propellant mass increase exponentially with the velocity increment (∆V) – Propellant can be a contaminant to precision optics

大 Question Is there an alternative to using propellant? Single spacecraft Yes. If an external field exists to conserve momentum Otherwise. not that we know of Multiple spacecraft Yes, again if an external field exists OR, if each spacecraft produces a field that the others can react against Problem: Momentum conservation prohibits control of the motion of the center of mass of the cluster, since only internal forces are present DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Question I: Question I: • Is there an alternative to using propellant? • Single spacecraft: – Yes, If an external field exists to conserve momentum – Otherwise, not that we know of… • Multiple spacecraft – Yes, again if an external field exists – OR, if each spacecraft produces a field that the others can react against – Problem: Momentum conservation prohibits control of the motion of the center of mass of the cluster, since only internal forces are present

大 Question / Are there missions where the absolute position of the center of mass of a cluster of spacecraft does not require control? Yes! In fact most of the ones we can think of Image construction u-v filling does not depend on absolute position Earth coverage As with single spacecraft, Gravity moves the mass center of the cluster as a whole, except for perturbations Disturbance(perturbation) rejection The effort to control perturbations affecting absolute cluster motion(such as J2) is much greater than that for relative motion Only disturbances affecting the relative positions(such as differential J2) NEED controlling to keep a cluster together Docking Docking is clearly a relative position enabled maneuver DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Question II: Question II: • Are there missions where the absolute position of the center of mass of a cluster of spacecraft does not require control? • Yes! In fact most of the ones we can think of… – Image construction • u-v filling does not depend on absolute position – Earth coverage • As with single spacecraft, Gravity moves the mass center of the cluster as a whole, except for perturbations… – Disturbance (perturbation) rejection • The effort to control perturbations affecting absolute cluster motion (such as J2) is much greater than that for relative motion • Only disturbances affecting the relative positions (such as differential J2) NEED controlling to keep a cluster together – Docking • Docking is clearly a relative position enabled maneuver

大 Example: Image Construction Image quality is determined by the point spread function of aperture configuration πDsin0 π(1+cose)D 2 V exp π Dsin e (v n +vin) Aperture dependence Geometry dependence The geometry dependence can be expanded into terms which only depend on relative position 丌 I()=1A()N+cosy, (=x2))+cos/w, ( DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Example: Image Construction Example: Image Construction • Image quality is determined by the point spread function of aperture configuration ( ) 2 1 1 ( ) 2 exp sin sin (1 cos ) , ⎥⎥⎥⎥⎦⎤ ⎢⎢⎢⎢⎣⎡ ∑ ⎟⎠⎞ ⎜⎝⎛ ψ + ψ λπ − ⎟⎟⎟⎟⎠⎞ ⎜⎜⎜⎜⎝⎛ λ π θ ⎟⎠⎞ ⎜⎝⎛ λ π θ ⎟⎠⎞ ⎜⎝⎛ λ π + θ ψ ψ = =Nn i j i n j n x y i DD J D I • The geometry dependence can be expanded into terms which only depend on relative position Aperture dependence Geometry dependence I ψi ( ) = IAp ψi ( ) N + cos 2πλψi(x1 − x2) ⎛ ⎝ ⎞ ⎠ + cos 2πλψi(x1 − x3) ⎛ ⎝ ⎞ ⎠ + ... ⎡⎣ ⎢ ⎤ ⎦ ⎥

大 Comparison -Golay Configurations Ss 3 spacecraft Point Spread Function 6 spacecraft Point Spread Function 13.1 13.1 s0书 0 50 -13.1 13.1 50131013.1500 5013.1013.1 x(m 8. (arcmin) x(m) 8. ( arcmin) 9 spacecraft Point Spread Function 12 spacecraft Point Spread Function 50 13.1 50 13.1 0 ! 50 -13.1 -13.1 05013.1013150 5013.10 3.1 (arcmin) x(m) e, ( arcmin) PSFs for the golay configurations shown here will not change if the apertures are shifted in any direction DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Comparison Comparison - Golay Configurations Configurations PSFs for the Golay configurations shown here will not change if the apertures are shifted in any direction

大 Question /l What forces must be transmitted between satellites to allow for all relative degrees of freedom to be controlled? In 2-D, N spacecraft have 3N DOFS, but we are only interested in controlling(and are able to control)3N-2 (no translation of the center of mass For 2 spacecraft, that's a total of 4 All except case(4 )can be generated using axial forces(such as electrostatic monopoles)and torques provided by reaction wheels Complete instantaneous control requires a transverse force which can be provided using either electrostatic or electromagnetic dipoles DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Question III: Question III: • What forces must be transmitted between satellites to allow for all relative degrees of freedom to be controlled? – In 2-D, N spacecraft have 3N DOFs, but we are only interested in controlling (and are able to control) 3N-2 (no translation of the center of mass) – For 2 spacecraft, that’s a total of 4: • All except case (4) can be generated using axial forces (such as electrostatic monopoles) and torques provided by reaction wheels • Complete instantaneous control requires a transverse force, which can be provided using either electrostatic or electromagnetic dipoles 1 2 3 4

大 What is it Not good for? Orbit Raising Bulk Plane Changes De-Orbit All these require rotating the system angular momentum vector or changing the energy of the orbit None of these is possible using only internal forces DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 What is it NOT good for? What is it NOT good for? • Orbit Raising • Bulk Plane Changes • De-Orbit • All these require rotating the system angular momentum vector or changing the energy of the orbit • None of these is possible using only internal forces

大 Forces and Torques: Conceptual In the Far Field the dipole field structure for electrostatic and electromagnetic dipoles are the same The electrostatic analogy is useful in getting a physical feel for how the transverse force is applied Explanation B DIl EMFF Final review ug.29,2003

DII EMFF Final Review Aug. 29, 2003 Forces and Torques: Conceptual Forces and Torques: Conceptual S N S N S N S N B A A B • In the Far Field, the dipole field structure for electrostatic and electromagnetic dipoles are the same • The electrostatic analogy is useful in getting a physical feel for how the transverse force is applied • Explanation …