hw10_FA05 - At some instant in time the angular...

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Aersp 309 HW #10 R.G. Melton (practice problems only – not to hand in) 1. For a satellite in Earth orbit with r p = 8000 km and r a = 15400 km, i 1 = 12 deg, and ω = 0 deg, calculate a. the v required to increase the inclination to i 2 = 28.5 deg. if the maneuver is performed at perigee b. the v required to decrease the inclination to i 2 = 0 deg. if the maneuver is performed at apogee 2. Determine the eccentricity and inclination needed for a sun-synchronous Earth orbit with fixed perigee and with a period of 10800 sec. Remember that sun- synchronous means that year deg/ 360 + = avg dt d and that fixed perigee requires that 0 = avg dt d 3. A satellite with inertia matrix ) m (kg 10320 0 0 0 7000 0 0 0 4200 2 = B I is undergoing rotational motion.
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Unformatted text preview: At some instant in time, the angular velocity (rotational rate) is (rad/s). ˆ 2 . ˆ 7 . ˆ 6 . 3 2 1 b b b + − = K For that instant, calculate the a) angular momentum vector b) angle between G K and H c) rotational kinetic energy T . 4. A satellite with principal MOIs I 1 = I 2 = 5000 kg ⋅ m 2 and I 3 = 8000 kg ⋅ m 2 is being forced to rotate with constant angular velocity (rotational rate) (rad/s) ˆ 8 . ˆ 4 . ˆ 3 . 3 2 1 b b b + + = G , where the b i are unit vectors along the principal axes. a. Calculate the torque required to maintain this motion. b. A torque is acting on the satellite, so why isn’t the rotational rate increasing in magnitude?...
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