Question

Calculate the work required to move a planet’s satellite of mass 571 kg from a circular orbit of radius 2R to one of radius 3R, where 8.8 × 106 m is the radius of the planet. The mass of the planet is 7.76 × 1024 kg. Answer in units of J]

Answer 1

Answer:

5.6 x 10^9 J

Explanation:

mass of satellite, m = 571 kg

r1 = 2 R

r2 = 3R

R = 8.8 x 10^6 m

mass of planet, M = 7.76 x 10^24 kg

The formula for the work done is given by

$W=GMm\left ( \frac{1}{r_{1}}-\frac{1}{r_{2}} \right )$

Where, G is universal gravitational constant, G = 6.67 x 10^-11 Nm^2/kg^2

$W=GMm\left ( \frac{1}{2R}-\frac{1}{3R} \right )=\frac{GMm}{6R}$

$W=\frac{6.67\times10^{-11}\times7.76\times10^{24}\times 571}{6\times 8.8\times10^6}$

W = 5.6 x 10^9 J