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PhyneasPhysicsPhrog t1_iwurph2 wrote

What you’re wanting to learn about is Hohmann Transfer Orbits. This is the process by which an object departs the Hill Sphere/Orbit of one object and enters that of another. In the case of interplanetary motion it accounts for the planets and host star’s gravity.

This is a good explanation with calculations: http://jwilson.coe.uga.edu/EMAT6680Fa05/Bacon/hohmanntransfers.html

I can also give you a Matlab and STK file with this built in.

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lawblawg t1_iwvgd9l wrote

Hohmann Transfers are an important (and very interesting) topic but they're not relevant to ballistic capture, which is what the OP is asking about.

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PhyneasPhysicsPhrog t1_iwvgp0s wrote

I’ve generally seen ballistic capture done in terms of the final steps of a transfer orbit. It’s generally easier to explain gravity assist and ballistic capture (rendezvous) using the Hohmann framework.

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