A rocket is fired from the earth towards the Sun. At what distance from the earth’s center is the gravitational force on the rocket zero?

Question

A rocket is fired from the earth towards the Sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the Sun = 2 × 10³⁰ kg, Mass of the earth = 6 × 10²⁴kg. Neglect the effect of other planets etc. (Orbital radius = 1.5 × 10¹¹m).

Answer 1

Mass of Sun, M = 2 × 10³⁰ kg

Mass of Earth m = 6 × 10²⁴kg.

Distance between Sun and Earth, r= 1.5 × 10¹¹m

Suppose, at the point P, the gravitational force on the rocket due to earth = gravitational force on the

rocket due to Sun

Let x be the distance of the point P from the earth