Question

A satellite of mass 5570 kg orbits the Earth and has a period of 6600 s .

determine the radius of its circular orbit.

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

r =

Determine the magnitude of the Earth's gravitational force on the satellite.

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

Fgrav =

Determine the altitude of the satellite.

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

h =

Answer 1

1.

Using force balance on satellite

Fg = Fc

G*M*m/R^2 = m*V^2/R

V = sqrt (G*M/R)

Time period is given by

T = 2*pi/w = 2*pi*R/V

T = 2*pi*sqrt (R^3/GM)

R^3 = G*M*T^2/(4*pi^2)

R = [G*M*T^2/(4*pi^2)]^(1/3)

Using given values

M = Mass of earth = 5.98*10^24 kg

T = time period = 6600 sec

G = 6.67*10^-11

So,

R = [6.67*10^-11*5.98*10^24*6600^2/(4*pi^2)]^(1/3)

R = 7.61*10^6 m

Part B.

Now gravitation force on satellite will be

Fg = G*M*m/R^2

m = mass of satellite = 5570 kg

So,

Fg = 6.67*10^-11*5.98*10^24*5570/(7.61*10^6)^2

Fg = 38363.0 N

Fg = 3.84*10^4 N

Part C.

Altitude of satellite = Radius of orbit - Radius of earth

Altitude of satellite = R - Re

Altitude of satellite = 7.61*10^6 - 6.37*10^6

Altitude of satellite = 1.24*10^6 m

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