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 x 10³⁰ kg, mass of the Earth = 6 x 10²⁴ kg. Neglect the effect of other planets etc. (orbital radius = 1.5 x 10¹¹ m)

Answer 1

Mass of the sun, M = 2 x 10³⁰ kg

Mass of the earth, m = 6 x 10²⁴ kg

Mass of the rocket = m_r

Distance between sun and the earth,

r = 1.5 x 10¹¹ m

Let at the point P, the gravitational force on the rocket due to Earth = gravitational force on the rocket due to sun

Let x = distance of the point P from the earth