Question

A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 104 m/s, and the radius of the orbit is 5.30 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.70 106 m. What is the orbital speed of the second satellite?

Answer 1

A = v^2/r
A = (1.70*10^4)^2/(5.30*10^6)
A = 54.53
A = G(m/r^2)
m = A*r^2/G
G = 6.67*10^-11
m = 54.53*(5.30*10^6)^2/6.67*10^-11
m = 2.30*10^25
------------------------------------
A = G(m/r^2)
A = 6.67*10^-11(2.30*10^25/(8.70*10^6)^2)
A = 20.27
A = v^2/r
(A*r)^(1/2) = v
v = 13279.6 m/s^2

Answer 2

V = sqrt[µ/r]
µ = V^2(r) = (1.7x10^4)^2(5.3x10^6) = 1.5317x10^15

V2 = sqrt[1.5317^15/8.7x10^6] = 1.3268x10^4m/s