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).
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Explanation:
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 ...
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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
Answered by
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Mass of the Earth, M
e
=6×10
24
kg
Orbital radius, r=1.5×10
11
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:
(r−x)
2
GmM
s
=
x
2
GmM
e
[
x
(r−x)
]
2
=M
s
/M
e
(r−x)/x=(
60×10
24
2×10
30
)
1/2
=577.35
1.5×10
11
−x=577.35x
578.35x=1.5×10
11
x=1.5×10
11
/578.35=2.59×10
8
m.
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