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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Celestial Mechanics Question

**Physics Forums | Science Articles, Homework Help, Discussion**