Question

A planet of mass m moves around the sun of mass M in an eliptical orbit the maximum and minimum distance of the planet from the sun are r1 and r2 respectively the time period of the planet is proportional to

Answer 1

Given the perihelion = r2 = shortest distance of a planet from Sun

                aphelion = r1 = longest distance of planet from Sun

                mass of planet = m.

                mass of Sun = M

So the length of the major axis of the Elliptical orbit of the planet

   = r1 + r2.

Semimajor axis = R = (r1 + r2)/2.

According to Kepler's laws:

   The square of time period T of a planet revolving around Sun is proportional to the cube of semi major axis R of the elliptical orbit of the planet.

   T² ∞ R³

   T ∞  R³/²

   T  ∞ [ (r1 + r2) / 2 ] ³/²   

Answer 2

The answer is provided in the attachment.

PLEASE MARK AS BRAINLIEST