Trajectory Design For A visibl Geosynchronous Earth Imager Edmund m.c. Kor SSL Graduate Research Assistant Prof david w. miller ctor, MIT Space Systems Lab Dr Raymond J sedwick Postdoctoral Associate, MIT Space Systems Lab AIAA Space Technology conference Exposition Albuquerque, New Mexico 30 September, 1999
Trajectory Design For A Visible Trajectory Design For A Visible Geosynchronous Earth Imager Geosynchronous Earth Imager Edmund M. C. Kong SSL Graduate Research Assistant Prof David W. Miller Director, MIT Space Systems Lab Dr. Raymond J. Sedwick Postdoctoral Associate, MIT Space Systems Lab AIAA Space Technology Conference & Expositi o n Albuquerque, New Mexico 30 September, 1999
Introduction Objective: To compare the different imaging configurations for a Separated Spacecraft Interferometer operating from an Earths orbit Outline Interferometric requirements Orbit Selection Equations of Motions(Hill's Equations) Steered Planar Array Propellant Free Array: Collector S/C Results Summary Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Introduction Introduction Objective : To compare the different imaging configurations for a To compare the different imaging configurations for a Separated Spacecraft Interferometer operating from an Separated Spacecraft Interferometer operating from an Earth’s orbit Earth’s orbit Outline : – Interferometric requirements & Orbit Selection – Equations of Motions (Hill’s Equations) – Steered Planar Array – Propellant Free Array: Collector S/C – Results – Summary
Interferometric Requirements Orbit Selection /lo Interferometric Requirements Reqt 1. Equal science light pathlength for visible imaging Regt 2. Axi-symmetric angular resolution about LOS Far-field assumption Array sees planar wavefronts from targets Orbit Selection Geosynchronous Higher altitude, lower perturbative effects(eg J2) Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Interferometric Interferometric Requirements & Orbit Selection Requirements & Orbit Selection Interferometric Requirements: Reqt 1. Equal science light pathlength for visible imaging Reqt 2. Axi-symmetric angular resolution about LOS Far-field assumption • Array sees planar wavefronts from targets y x z Orbit Selection: Geosynchronous • Higher altitude, lower perturbative effects (eg. J2)
Equations of Motions assumption First order perturbation about natural circular Keplerian orbit Hills Equations x-3n'x-2ny = y+2nx n Total Spacecraft Velocity Increment △V m212, atat a Example: AV required to hold a spacecraft stationary at (x, y, z) Spacecraft instantaneous acceleration △ V required n X a.=n2 △V=nTmv9x2+z Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Equations of Motions Equations of Motions Assumption : First order perturbation about natural circular Keplerian orbit (cross-range) z x N y (zenith-nadir) (velocity vector) S a z n z a y nx a x n x ny z y x 2 2 2 3 2 = + = + = − − && && & && & a a a dt Tlife ∆ = ∫ x + y + z 0 2 2 2 V Hill’s Equations : Total Spacecraft Velocity Increment : Example : ∆V required to hold a spacecraft stationary at (x,y,z) 2 2 2 V n T 9x z ∆ = life + Spacecraft instantaneous acceleration : ∆V required : ay = 0 a n z z 2 ax n x = 2 = −3
DSS Architecture 1 Constraint collector spacecraft to a local horizontal circular trajectory with combiner spacecraft at the center(Regts. 1& 2) △ V Requirement No AV for stationary combiner spacecraft at(o,y, 0 y|=±Rsin(m+a) AV for collector spacecraft R, cos(nt+a) 100 0 y -siny 0x s-sinφ sin cos y0y sin o sin⊥0 y LEO Average collector s/C AV at geo altitude △V/n2RT=1.55 Collector AV/n".Tif Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology DSS Architecture 1 DSS Architecture 1 Constraint collector spacecraft to a local horizontal circular trajectory with combiner spacecraft at the center (Reqts. 1 & 2) V / 1.55 2 ∆ n RoTlife = ( ) ( ) ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ + α = ± + α ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ ′′′ R nt R nt zyx o ocossin x, a 0 z y LOS ψ φ x' b c, z' y' • No ∆V for stationary combiner spacecraft at (0,y,0) • ∆V for collector spacecraft ∆V Requirement Average collector s/c ∆V at GEO altitude : ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ ′′′ ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ ψ ψ ψ − ψ ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ φ φ = φ − φ ⎥⎥⎥⎦⎤ ⎢⎢⎢⎣⎡ zyx zyx Hill 0 0 1 sin cos 0 cos sin 0 0 sin sin 0 cos sin 1 0 0