I was trying to solve this problem myself but i dont know how to work out certain variables like gravity, centripetal force and the changing impact point due to the curve of a planet (any planet).
So i wondered if you guys could try and help me giving out some of the intuition to get the result and i also wondered if its possible to describe the motion of a projectile over a planet using polar coordinates.
So yeah, we have a initial launching point from the surface of a circle, and then a initial velocity and initial angle of launch, how do i know what will the distance over the surface up until the impact point be for that projectile accounting for the planetary body circular shape and the changing gravitational force?
Best Answer
If you are happy to ignore atmospheric drag and the rotation of the planet then the projectile is in orbit as soon as it is launched. As long as it’s launch speed is lower than the planet’s escape velocity then it will follow an elliptical path until the ellipse intersects the surface of the planet again. The orbital parameters are determined by the speed and direction of launch.
If your planet has an atmosphere and/or is rotating then the solution will be more complex.