Hello! I think it's a bit unnecessary to describe the whole problem, so I'll just focus on my question: There's an astroid moving in an hyperbolic orbit due to Earth's gravity (I found that)... I have been asked to find the minimal distance between the astroid and the Earth. It looks pretty obvious that this minimal distance is at the vertex (I hope I'm right with the word) of the hyperbula. If I'm right - how do I prove this? The velocity there isn't 0 or anything and I've wondered for some time what's special about that point and came to no cunclusion. If I'm wrong - I'm in even bigger trouble :) I'd really appreciate a nudge :) Thanks, Tomer.