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1) The illustrated gravity gradient stabilized spacecraft is placed in a 600 km, circular, Earth orbit. a) What are the spacecraft's moments and products of Vectors from bus (central box) inertia relative to its c.m. and b? Give results as a 3x3 c.m. to tip masses: 20b, ft, inertia matrix, with all 9 elements defined in sl-ft². a -20 b1 ft, 10 b2 ft, -10b2 ft. b) How should the spacecraft be oriented relative to the b2 b1 Vector from bus c.m. to c.p.: illustrated orbiting reference frame? Present your results in 03 1b, ft. the form: b1 aligned with f2, b2 aligned with f,, and b3 Rc.p. aligned with f, c.m. Bus mass properties: weight c) The center of pressure (c.p.) for aerodynamic drag is = 1,000 lb, I11 = I22 = 133 = 200 displaced 1 foot away from the center of the spacecraft's sl-ft², I1 = 113 = 123 = 0. bus in the b, direction, as illustrated. When the spacecraft is in its gravity gradient stable orientation, what is the Tip masses (treat as point disturbance torque applied by aerodynamic drag? Use the masses): weight = 32.2 lbs following parameters: air density = 2x10-1: kg/m³, area = each. 20 ft², coefficient of drag = 2.6. Express your answer in the Booms are massless. form Taero = Xb1 + Yb2, + Zb3 N-m. d) The aero torque will displace the gravity gradient spacecraft from the attitude defined in b). What is the Orbiting reference frame spacecraft's orientation relative to f, after it settles down to basis vectors: a new equilibrium, in which the aero torque is balanced by a gravity gradient torque? Assume Taero does not change f, is in direction of from its value computed in part c). Use the gravity gradient spacecraft velocity vector torque equations given at the bottom of page 7-10 of the f, f2 is perpendicular to orbit notes. In the notes, T2 is the gravity gradient torque which f2 plane resists displacement of the spacecraft from its ideal gravity gradient orientation due to rotation about the axis f3 is in direction from perpendicular to the orbit plane. Express your answer as an spacecraft to center of Earth angle(s) in degrees. Orbit frequency = 631.34816 rad/sec where r is the distance from the center of the earth to the satellite = 6378 +altitude in km

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Spacecraft Attitude Systems
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