Question

A satellite of mass 5450 kg orbits the Earth and has a period of 6520 s . A)Determine the radius of its circular orbit. Express your answer using three significant figures and include the appropriate units. B)Determine the magnitude of the Earth's gravitational force on the satellite. Express your answer using three significant figures and include the appropriate units. C)Determine the altitude of the satellite. Express your answer using three significant figures and include the appropriate units.

Answer 1

The following equation is called Kepler’s third law.

T^2 = (4 * π^2 ÷ G * M) * r^2

a) Determine the radius of its circular orbit.
Express your answer using three significant figures and include the appropriate units.
Vo^2*(r+h) = M*G
{(r+h) = M*G/Vo^2 = 4*10^14/Vo^2
{2*PI*(r+h)/Vo = 6520
6.28*4*10^14/Vo^3 =6520
Vo = ³√6.28*4*10^14/6520 = 7276.525 m/sec
(r+h) = M*G/Vo^2 = 4*10^14/7276.525^2 = 7.555*10^6 m

b) Determine the magnitude of the Earth's gravitational force on the satellite.
Express your answer using three significant figures and include the appropriate units.
g' = g*r^2/(r+h)^2 = 9.8*(6.37/7.555)^2 = 6.967 m/sec^2
F = m*g' = 5450*6.967 ≈ 37.969 kN

c)Determine the altitude of the satellite.
Express your answer using three significant figures and include the appropriate units.
h = (r+h)-r = (7.555-6.37)*10^6 = 1.185*10^6 m (≈ 1185 km)