Question

Answer in m/s

A satellite is in a circular orbit about the earth (M_E = 5.98 times 10^24 kg). The period of the satellite is 2.38 times 10^4 s. What is the speed at which the satellite travels?

Answer 1

V = Velocity
G = Universal Gravitational Constant
Mc = Mass of central object
R = Radius
T = Period

Mc = 5.98E+24 kg
T = 23800 s
G = 6.67428E-11 m^3/kg-s
pi = 3.14159

R^3 = [ (T^2 * G * Mc) / (4 * pi^2) ]
R^3 = { [ (23800 s)^2 * (6.67428E-11 m^3/kg-s) * (5.98E+24 kg) ] / (4 * pi^2 ) }
R^3 = { 5.7266*10^21 m^3 }
R = 1.8*10^7 m

V = SQRT (GMc/R)
V = SQRT { [ (6.67428E-11) * (5.98E+24) ] / (1.8*10^7 m) }
V = SQRT { 22173441.33 }
V = 4708.87 m/s