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hw07_FA05

# hw07_FA05 - v TOTAL = |∆ v 1 | |∆ v 2 | b Calculate the...

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R.G. Melton AERSP 309 HW #7 Fall 2005 (due Friday Oct. 28 at beginning of class) 1. (20 points) Consider a Hohmann transfer from Mars to Earth. As a first approximation, we typically ignore the two planets’ gravitational effects and consider only the effects of the Sun. The problem then consists of transferring from a circular orbit at Mars’ distance ( r Mars ) from the Sun to a circular orbit at Earth’s distance ( r ) from the Sun. µ Sun = 1.327 × 10 11 km 3 /s 2 r = 1.496 × 10 8 km r Mars = 2.279 × 10 8 km a. Calculate the total impulsive v needed for the transfer (note:
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Unformatted text preview: v TOTAL = |∆ v 1 | + |∆ v 2 | ) b. Calculate the time required for the transfer (in days). 2. (15 points) A s/c is presently orbiting Earth on a path with a 1 = 15000 km, and e 1 = 0.45. a. Calculate the flight-path angle when the s/c reaches a true anomaly of 258 o . b. Calculate the ∆ v needed to circularize the orbit at θ 1 = 258 o . where the radius is r 1 (that is, to execute an impulsive maneuver onto a circular orbit with radius r 1 ). c. Calculate the ∆ v needed to circularize the orbit at perigee on the original orbit....
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