soln_HW4_S10_transfers_AE313

soln_HW4_S10_transfers_AE313 - Due Wednesday March 3 2010...

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Due: Wednesday, March 3, 2010 Name: ANSWERS/SOLUTIONS Embry-Riddle Aeronautical University AE 313 – Space Mechanics Homework 4 Transfers 1. Consider the Earth and Mercury to be in coplanar circular orbits about the sun with radii of 1 and 0.4 AU, respecitively. a) What is the semimajor axis for the minimum energy transfer. (AU) ANS: 0.7 AU {} 10 . 4 0.7 22 ap rr aA U + + === b) What is the transfer time (TU and days) for the value calculated in a) ANS: 0.7948 TU = 46.2 days Soln: from the equations in class 33 0.4 0.7948 21 t Period a TT U ππ μ == = = c) What is the relative velocity of the transfer orbit with respect to Earth. ANS: 0.2441 AU/TU Soln: 1 1 1 Earth AU V TU a = 2 1 . 7 5 5 9 . 7 AU V TU ra ⎛⎞ =− = = ⎜⎟ ⎝⎠ d) What is the relative velocity of the transfer orbit with respect to Mercury. ANS: 0.3088 AU/TU Soln: 1 1.581 0.4 Mercury AU V TU a = 1 1.8898 0.4 0.7 AU V TU = =
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2. A satellite on a circular Earth orbit at an altitude of 800 km is predicted to have a
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soln_HW4_S10_transfers_AE313 - Due Wednesday March 3 2010...

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