Kinematics equations

Question

If a satellite orbits the earth at an altitude of 300 km at a speed of 6.95 km/s, what is the period, in hours, of the satellite's orbit? (Radius of the earth is 6.38 x 10^6 m)

Answer 1

v = orbital speed = 6.95 km/s

h = height of orbit above surface of earth = 300 km

R_e = radius of earth = 6.38 x 10⁶ m = 6.38 x 10³ km

r = orbital radius = h + R_e = (300 + 6380) km = 6680 km

T = orbital period

 

v = 2πr / T

 

T = 2πr / v

 

T = 2π (6680 km) / ( 6.95 km/s) ≅ 6039 s = (6039/3600) hrs ≅ 1.678 hrs