I am getting stuck trying to solve a differential equation describing the gravitational relationship between two celestial bodies.(adsbygoogle = window.adsbygoogle || []).push({});

What I have so far is this:

a1 = G m2 (r2 -r1) / ||r2 -r1||^3

a2 = G m1 (r1 -r2) / ||r1 -r2||^3

where:

boldface denotes vectors in 3 dimensional Cartesian space

G for gravitational constant

m for mass

r for position

a for acceleration

I guess my question is where to go from here. I am assuming that the general solution will contain constants relating to initial position and initial velocity for both bodies. My goal is to arrive at a point where I can plot the trajectories of the two bodies using iterations. Essentially a system I can solve using numerical methods such as Euler's.

Anyway, any insight into how to solve this kind of problem would be great! Eventually I want to expand it to more than 2 bodies but I need to get comfortable with 2 first before taking the problem to N-bodies. This is for a numerical methods class, and possibly a final project/presentation.

Cheers!

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# Celestial Mechanics Question

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