This question already has an answer here:
Well known Kepler laws state that earth revolve around sun in an elliptical path with sun at one of the focii. My question is rather simple. Why so?
I mean for an equilibrium of earth that is it is not accelerated towards or away from sun its gravitational force must be balanced by centrifugal force (pseudo force as frame corresponding to earth)
But following an elliptical path it distance from sun won't be same and hence the gravitational force and hence how is this?
I suspect may be it is due to presence of other celestial bodies but that seems too vague and escaping from the truth
Also maximum of derivations in gravitation are done by assuming circular path of earth around sun. (atleast at my level)
Please give me the real physics behind it?