I'm afraid you'll have to wait until you take a course in upper division mechanics
to see an explanation of this one. If you solve
you find that
your result is either and ellipse, a parabola, or a hyperbola. It's straightforward
but involves a fair knowlege of differential equations. But wait why don't we
see hyperbolic motion for planets? Well if we did, they would stay around for very
long would they. That's why the planets have to have elliptical orbits.