A satellite of mass 5470 kg orbits the Earth and has a period of 6590 s . Part A

ID: 1444529 • Letter: A

Question

A satellite of mass 5470 kg orbits the Earth and has a period of 6590 s .

Part A

Determine the radius of its circular orbit.

Express your answer using three significant figures and include the appropriate units

r =

Part 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

Part C

Determine the altitude of the satellite.

Express your answer using three significant figures and include the appropriate units

h = ?

G = 6.67 * 10-11, M = 6 * 1024 kg , P = 6590 s

F = m a = m v2 / r

a = v2 / r

v = 2 pi r / P , a = 4 pi2 r / P2

Gravitational force F = G M m / r2 = m a = m [4 pi2 r/ P2]

r = [ G M P2 / (4 pi2) ]1/3

r = [ 6.67 * 10-11 * 6 * 1024 * 65902 / (4 pi2) ]1/3

r = 7.61 * 106 m

---------------------------------------------------

R = radius of earth = 6.38 * 106 m

Altitude of satellite = r - R = (7.61 * 106) - (6.38 * 106)

= 1.23 * 106 m

------------------------------------------------

Magnitude of gravitational force = G M m / r2

= (6.67 * 10-11 * 6 * 1024 * 5470) / (1.23 * 106)2

= 1.45 * 106 N

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.