PS4%202010

# PS4%202010 - AAE 532 Orbit Mechanics Problem Set 4 Due...

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AAE 532 – Orbit Mechanics Problem Set 4 Due: 9/22/10 Problem 1: Assume that a system is comprised of two particles that interact only gravitationally. Define ˆ e as a unit vector in the direction of e . Define ˆ p as a unit vector 90 D from ˆ e such that ˆ ˆˆ × ep=h (where ˆ h is a unit vector parallel to orbital angular momentum). (a) Demonstrate that the velocity can be written sin ( cos ) e p μ θθ ∗∗ ⎡⎤ −+ + ⎣⎦ v= e p (b) In an elliptical orbit, the general expression to relate flight path angle and true anomaly is tan sin re p γ θ = Prove that this expression is correct. Problem 2: A satellite is in motion about the Earth. Assume that it is reasonable to model the problem in terms of the relative two-body problem (Earth and satellite). The orbit is characterized such that 10 aR = and .6 e = . It is currently located ( o t ) at the point in the orbit such that 60 o = D . (a) Determine the following orbit parameters and satellite state information: ,, ,,,;,, , pao o o o php e r iod r r r v E E . [List time in hours and all angles in degrees.]

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PS4%202010 - AAE 532 Orbit Mechanics Problem Set 4 Due...

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