- #1
rizumu
- 1
- 0
I am getting stuck trying to solve a differential equation describing the gravitational relationship between two celestial bodies.
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!
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!