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 = 6×1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10¹¹ m).

Answer 1

Given: The mass of the sun is 2× 10 30  kg, the mass of the earth is 6× 10 24  kg, the radius of orbit is 1.5× 10 11  m.

Let the distance from the center of the earth where the gravitational force is zero be x, then the distance from the sun will be r−x.

The gravitational force on the rocket will be zero when the gravitational force due to earth is equal to the gravitational force due to sun.

Gm M s ( r−x ) 2 = Gm M e x 2 ( r-x x ) 2 = M s M e

Where, the mass of the sun is M s , the mass of the earth is M e , the orbital radius is r, the mass of rocket is m.

By substituting the given values in the above expression, we get

( r−x x ) 2 =( 2× 10 30 6× 10 24 ) 1.5× 10 11 −x x =577.35 x=2.6× 10 8  m

Thus, the distance from the centre of the earth where gravitational force acting on rocket becomes zero is 2.6× 10 8  m.