The smallest and greatest distances a planet travels around the sun are r and R, respectively. If the planet’s minimum speed on its journey is v0, its maximum speed is :

\(\frac{v_o R }{r}\)

By Kepler's law, the areal velocity = \(\frac{L}{2m}\)​ is a constant and hence L (angular momentum) is constant.

mvr = constant (at any point of trajectory)

Minimum speed (v₀​) is possible at the maximum distance (R) from sun and maximum speed (v′) is possible at the minimum distance (r) from the sun.

mv_o​R=mv′r  

\(v' = \frac{v_o R}{r}\)