Motion of planets around the sun is not circular, even though sun is the central force causing planets to move (Refer previous mantra 10.149.1)
2. The motion of planets is such that Velocity of planets is in inverse relation with the distance between planet and sun.
It can be easily shown with the help of Newton’s Second Law that, for a planet revolving around sun in an elliptical orbit, having distance ‘r’ with sun and angle ‘θ’ made between length ‘r’ and any fixed axis, at any instant, following holds true
From the above, it can be easily shown that derivative of the product of square of distance between sun and planet and rate of change of angle θ, with respect to time, is zero. And thus following relation is obtained (with h as a constant)