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- TL;DR Summary
- I would like to model the motion of a single celestial body with initial velocity v a distance r from a mass fixed in place . For the purpose of the question let's just say that the mass appeared r meters away from our celestial body perpendicular to its velocity. There are no outside forces or other orbits acting on these bodies and they will act as spherical point-masses. Where should I start with this modeling? Which equations will be most relevant to me? Should this be done on a polar plane?

I have yet to decide on values for the mass of the fixed object, M, the mass of the moving celestial body, m, the initial velocity, v, and the distance between the two objects, r. I will most definitely decide on a larger mass M because I would like the celestial body to spiral in towards the mass rather than be deflected slightly or fall into a stable orbit. I have attached an image illustrating the concept of my problem. This is for a calculus class, so I plan to preform this task primarily through the use of calculus.

Thank you for your time,

William B

Thank you for your time,

William B