1. The problem statement, all variables and given/known data A comet revolves around the sun in a closed elliptical trajectory. Ignore any force acting upon it besides gravity. Prove that the angle between the position vector (sun in the origin) and the velocity vector of the comet at its perihelion and aphelion is 90º. 3. The attempt at a solution I tried to approach this problem by writing down the motion equations for a body on an elliptical orbit under the action of gravity. But it is a second order differential equation, that I later found out has no analytic solution. So I just thought: when the comet is nearest and furthest from the sun, position r(t) must have a maximum/minimum, hence dr(t)/dt = 0, at those points. That also works for the r(t)^2, so dr(t)^2/dt = 0 <=> r(t)[itex]\cdot[/itex]v(t) = 0 and this happens (since none of them is zero) only when they are both perpendicular. However, by assuming dr(t)/dt = 0, I'm assuming that v(t) = 0 for some time t. But as we know that is never true, has the comet never stops moving. Is my solution valid? If so, why? If not, could you give me an hint? Does this all come down to the geomtry of the elipse ( because I never studied the equations that describe ellipses)?