Gravitation NCERT Solutions Class 11 Physics - Solved Exercise Question 8.12

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).
Solution:
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 X 1030 / 60 X 1024]1/2  =  577.35
1.5 X 1011 - x = 577.35x
578.35x = 1.5 X 1011
x = 1.5 X 1011 / 578.35  =  2.59 X 108 m

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