1. The problem statement, all variables and given/known data The earth travels in an elliptical path with the sun at one of its foci. Is the acceleration of the earth directed towards the sun or towards the centre of the ellipse? 2. Relevant equations The earth's elliptical path can be parametrized as: [itex]x=acos (pt)[/itex] [itex]y=bsin (pt)[/itex] 3. The attempt at a solution Using the above parametrizations and differentiating twice, I get that the earth's acceleration is directed towards the centre of the ellipse. However the force on the earth is due to the sun, and so I feel the earth's acceleration must be directed towards the sun. Please help.