A rocket is fired from the earth towards the sun. At what distance from the earths centre is the gravitational force on the rocket zero? Mass of the sun = 2×1030kg, mass of the earth = 6×1024kg. Neglect the effect of other planets etc. (orbital radius = 1.5×1011m).
Mass of the Sun, Ms=2×1030 kg
Mass of the Earth, Me=6×1024 kg
Orbital radius, r=1.5×1011 m
Mass of the rocket =m
Let x be the distance from the centre of the Earth where the gravitational force acting on satellite P becomes zero.
From Newton’s law of gravitation, we can equate gravitational forces acting on satellite P under the influence of the Sun and the Earth as:
GmMs(r−x)2=GmMex2
[(r−x)x]2=Ms/Me
(r−x)/x=(2×103060×1024)1/2=577.35
1.5×1011−x=577.35x
578.35x=1.5×1011
x=1.5×1011/578.35=2.59×108m.