hw12_FA05 - R.G Melton Fall 2005 AERSP 309 HW#12(Practice...

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R.G. Melton AERSP 309 HW #12 Fall 2005 (Practice Problems only – not to hand in) 1. A satellite in low Earth orbit is oriented as shown. The s/c is oriented such that its 2 1 ˆ ˆ b b plane coincides with the orbital ( θ i i r ˆ ˆ ) plane. a. Develop an expression for the gravity gradient torques in terms of the angle . b. For the case of small librations (oscillations) about only the 3-axis and I 3 >I 2 >I 1 , and assuming that remains small, show that 0 2 3 = + k I ± ± , where k is a constant. c. The equation above describes simple harmonic motion about the 3-axis. Find an expression for the period of this librational motion, and evaluate it for the case of R = 7000 km, I 1 = 3000, I 2 = 5000, I 3 = 7500 kg m 2 . d. Suppose that this satellite were placed into an elliptical orbit with period equal to that of the librational motion. What is the consequence? (Hint: don’t ever do this) 2. If the specific impulse of a given propellant combination is I sp = 450 s. and the s/c has initial mass
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hw12_FA05 - R.G Melton Fall 2005 AERSP 309 HW#12(Practice...

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