The fact that the planets move around the Sun, not in circles but in ellipses, was first demonstrated by

Kepler?s  laws  of  planetary  motion state  that  (a)  All  planets  move  in elliptical orbits with the Sun at one of  the  focal  points  (b)  The  radius vector  drawn  from  the  sun  to  a planet  sweeps  out  equal  areas  in equal  time  intervals.  This  follows from  the  fact  that  the  force  of gravitation on the planet is central and  hence  angular  momentum  is conserved.  (c)  The  square  of  the orbital   period   of   a   planet   is proportional  to  the  cube  of  the semi  major  axis  of  the  elliptical orbit of the plane.