Question:
8.12 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:
Mass of the Sun, Ms = 2 × 1030 kg
Mass of the Earth, Me = 6 × 10 24 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 = GmMe / x2
[ (r - x) / x ]2 = Ms / Me
(r - x) / x = [ 2 × 1030 / 60 × 1024]1/2 = 577.35
1.5 × 1011 - x = 577.35x
578.35x = 1.5 × 1011
x = 1.5 × 1011 / 578.35 = 2.59 × 108 m.
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