Question

A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.95 x 104 m/s, and the radius of the orbit is 3.72 x 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 7.51 x 106 m. What is the orbital speed of the second satellite?

Answer 1

Orbital speed of a satellite is given by:

V = sqrt (G*M/R)

M = mass of planet around which satellite is orbiting

G = Gravitational constant,

Since M and G are constant, So Orbital speed is inversely proportional to the square root of orbital radius

So,

V2/V1 = sqrt (R1/R2)

V2 = V1*sqrt (R1/R2)

Now given that

for R1 = 3.72*10^6 m, V1 = 1.95*10^4 m/sec

So, when R2 = 7.51*10^6 m

then

V2 = (1.95*10^4)*sqrt (3.72*10^6/(7.51*10^6))

V2 = 13724.17 m/sec

V2 = 1.37*10^4 m/sec

Let me know if you've any query.