Hohmann Orbit, PLanet Transfer (Energy)

[cirrith]

Homework Statement

The most energy-efficient method of getting a spaceship from one planet to another is via a Hohmann (transfer) orbit. The ship's launch is aimed in such a way that the perihelion and aphelion of the ship's orbit is tangent to the circular orbits of the two planets and timed so that its arrival at the destination planet's orbit coincides with the arrival of that planet at the same point. Let us use an example of a launch from Earth, which orbits the sun (Mass M_s) at distance R_E, into a Hohmann orbit designed to reach planet P that orbits the Sun at distance R_p. A rocket of mass m needs to add additional speed it already as by way of the orbital motion of the Earth.

Express all answers to the following questions in terms of relevant system parameters. (R_p M_s R_E)

a) What total energy must the spaceship have for this rendezvous? (Hint: ship's semi major axis)

b) What minimal amount of fuel energy expenditure is needed to achieve this?

c) What kinetic energy will the spaceship have after launch with this expenditure of rocket fuel?

d) How long will the trip take? (Hint: Kepler's Third Law)

Homework Equations

E_f - E_i = (W_other)_i-f

The Attempt at a Solution

 

[gneill]

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