Gravity Simulator 2D: Calculating Trajectories

[Pink panther]

I want to create a simple 2d Gravity simulator where I have a large body i.e. A circle which could be a planet or the sun. I then want to simulate small comets or asteroids traveling past it, crashing into or being pulled into orbit. I know the gravitational force formula but that seems the simple part. What I want to know is how to calculate the trajectories for objects flying past. I guess speed and angle of approach determine whether a smaller object will crash, go past or go into orbit around the larger body. Any explanations or sources would be appreciated.

 

[BvU]

Hello Pinky,

Your gravitational force formula is most likely something like $\vec F = - {GMm\over |\vec r|^2} \, \hat r$. The equation of motion is $\vec F = m\vec a$ where $\vec a = {d\vec v \over dt}$ and $\vec v = {d\vec r \over dt}$.
If you want it in x, y coordinates you will need a coordinate transformation at some suitable moment.
That's really all there's to it !

Things become more complicated if you want to can no longer ignore the influence of the smaller m on the big M. Maybe that comes later; for now I interpret your large/small as a permit to ignore the motion of the large body.​