Hopefully you can make out the situation below, but that's what I'm looking for. I'm assuming that ##v_0## is small so that it doesn't orbit. I figure the path will fit an ellipse. I'm just wondering what the equation of motion is for this situation.
Basically I'm assuming that gravity points towards the planet's centre i.e. ##\vec{a}=-g\hat{r}##. You know what, let's the situation and assume that the projectile is shot tangentially to the planet's surface. The reason why I haven't posted any work is that I'm still working on it. I just want...
I figured this would be a problem in some classical mechanics book but so far I can't find an answer anywhere. Assume there is no drag or lift, and since the planet is not rotating we don't have to worry about Coriolis effects. I'm working on a solution but I want to see if my work is correct...