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

5.6 x 10^9 J

Step-by-step 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 ( (1)/(r_(1))-(1)/(r_(2)) \right )`

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

`W=GMm\left ( (1)/(2R)-(1)/(3R) \right )=(GMm)/(6R)`

`W=(6.67*10^(-11)*7.76*10^(24)* 571)/(6* 8.8*10^6)`

W = 5.6 x 10^9 J