Question

22. A rocket is fired from the earth towards the Sun. At
what distance from the ear5th's centre is the
gravitational force on the rocket zero? (Mass of the
sun - 2 x 10 kg, mass of the earth = 1.5 x 10"m).
(a) x-26 x 10 km (b)x=2.6 x 10 km
(c)x -2.6 x 104 km (d) x -2.6 x 10 km​

Answer 1

Explanation:

Mass of the Sun, M

s

=2×10

30

kg

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.