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 × 10³⁰ kg, mass of the earth = 6 × 10²⁴ kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10¹¹)

Answer 1

Hii dear,

◆ Answer-
2.6×10^8 m

◆ Explaination-
# Given-
M = 2×10^30 kg
m = 6×10^24 kg
r = 1.5×10^11 m

# Solution-
Let m' be mass of the rocket.
Suppose at distance x gravitational force acting on the rocket is zero.
That is-
GMm'/(r-x)^2 = Gmm'/x^2
(r-x)/x = √(M/m)
(r-x)/x = √(2×10^30/6×10^24)
(r-x)/x = 577.35
r/x = 577.35+1 = 578.35
x = r/578.35
x = 1.5×10^11/578.35
x = 2.6×10^8 m

Gravitational force will be zero when rocket is at 2.6×10^8 m from earth's surface.

Hope this is helpful...