Question

Two planets of equal mass orbit a much more massive star (figure). Planet m₁ moves in a circular orbit of radius 1 x 10⁸ km with period 2 yr. Planet m₂ moves in an elliptical orbit with closest distance r₁ = 1 x 10⁸ km and farthest distance r₂ = 1.8 x 10⁸ km, as shown.

(a) Using the fact that the mean radius of an elliptical orbit is the length of the semi-major axis , find the period of m₂ orbit.

(b) Which planet has the greater speed at point P ? which has the greater total energy ?

(c) Compare the speed of planet m₂ at P with that at A.

Answer 1

(a) Mean radius of planet,

(b) For m₂, point P is perigce position. So speed at this greater than orbital speed for circular orbit.