Calculate the velocity of the satellite

Question

A satellite orbits in circular motion at an altitude of 5000 kilometers above the surface of the Earth. Calculate the orbital (tangential) velocity of the satellite.
mEarth = 5.972 x 1024 kg rEarth = 6.371 x 106

Answer 1

Recall the orbital relation

 

v = √(GM/r)

 

G = 6.67 x 10^-11 Nm²/kg²

 

r =  (5 x 10⁶ m) + (6.371 x 10⁶ m) = 1.1371 x 10⁷ m

 

[By the way, you did not state the units of R_e.]

 

v = √[(6.67 x 10^-11)(5.972 x 10²⁴) / (1.1371 x 10⁷)] m/s ≅ 5919 m/s