Question

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 x 10³⁰kg, mass of the earth = 6 x 20²⁴ kg. Neglect the effect of other planets etc. (orbital radius = 1.5 x 10¹¹ m).

Answer 1

Solution:

30

s

24

e

11

of sun,M 2 10 kg

Mass of earth,M 6 10 kg

Orbital radius,r=1.5 10 m

Let gravitational force on rocket becomes 0 at a distance of x from earth's centre.

At this point,

Electric field due to ear

Mass = ×

= ×

×

e s

2 2

0.5

30 0.5

24

8

th=Electric field due to sun

GM GM

( )

( )

2 10 1 ( )

6 10

3

1735

tting value of r and solving,

x=2.6 10 m