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

Let the distance from the earth to the point where gravitational force is to zero be x

Given that, 

Mass of sum = M_s = 2 × 10³⁰ kg 

Mass of Earth = M_e = 6 × 10²⁴kg 

Orbital radius = r = 1.5 × 10¹¹ m

Now, We know that, gravitational force ∝ M/R²

Since, gravitational force of Earth = Gravitational force of Sun

x = 2.594 × 10⁸ m

At a distance of about 2.6 × 10⁵ km gravitational force is zero.