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.
-20 b1 ft, 10 b2 ft, -10b2 ft.
b) How should the spacecraft be oriented relative to the
Vector from bus c.m. to c.p.:
illustrated orbiting reference frame? Present your results in
the form: b1 aligned with f2, b2 aligned with f,, and b3
aligned with f,
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 =
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
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
f2 is perpendicular to orbit
notes. In the notes, T2 is the gravity gradient torque which
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
where r is the distance from the center of the earth to the satellite = 6378 +altitude in km
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