Question

For a lanet moving around the sun in an elliptical orbit , why the total energy of the 'sun plus planet' system remain constant?

Answer 1

As a Planet moves around Sun on the elliptical path,both its speed,which fixes its kinetic energy,and its distance from the centre of sun,which fixes its gravitational potential energy U,fluctuate with fixed period. however, the mechanical energy E of the Planet remains constant.since the planet mass is so much smaller than sun, we assign U and E for the Sun