__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 ×10

^{30}kg, mass of the earth = 6 × 10^{24}kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10^{11}m).

__Solution__:Mass of the Sun,

*M*

_{s}= 2 × 10

^{30}kg

*M*

_{e}= 6 × 10

^{24}kg

Orbital radius,

*r*= 1.5 × 10

^{11}m

Mass of the rocket =

*m*

*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:

GmM

_{s}/ (r - x)

^{2}= GmM

_{e}/ x

^{2}

[ (r - x) / x ]

^{2}= M

_{s}/ M

_{e}

(r- x) / x = [ 2 X 10

^{30}/ 60 X 10

^{24}]

^{1/2}= 577.35

1.5 X 10

^{11}- x = 577.35x

578.35x = 1.5 X 10

^{11}

x = 1.5 X 10

^{11}/ 578.35 = 2.59 X 10

^{8}m

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