(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 (MassM_{s}) at distanceR_{E}, into a Hohmann orbit designed to reach planetPthat orbits the Sun at distanceR_{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)

2. Relevant equations

E_{f}-E_{i}= (W_{other})_{i-f}

3. The attempt at a solution

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# Homework Help: Hohmann Orbit, PLanet Transfer (Energy)

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