Question

Consider a satellite (mass = 6.10 kg) in a circular orbit about Earth. Calculate the following properties of the satellite given a radius r of its orbit of 1.40×10⁷m. Its period:

Its kinetic energy:

Its angular momentum:

Its speed:

Answer 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)

KInetic energy is given by:

KE = 0.5*m*V^2 = 0.5*G*M*m/r

Angular momentum is given by:

L = mvr = m*r*sqrt (GM/r) = sqrt (G*M*m^2*r)

Now using given values:

G = 6.67*10^-11

M = 5.98*10^24 kg

m = 6.10 kg

r = radius of its orbit = 1.40*10^7 m

Part A

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

T = 2*pi*sqrt ((1.40*10^7)^3/(6.67*10^-11*5.98*10^24))

T = 16480.04 sec = 4.58 hr

Part B

KE = 0.5*G*M*m/r

KE = 0.5*6.67*10^-11*5.98*10^24*6.10/(1.40*10^7)

KE = 8.69*10^7 J

Part C

L = sqrt (G*M*m^2*r)

L = sqrt (6.67*10^-11*5.98*10^24*6.10^2*(1.40*10^7))

L = 4.55*10^11

Part D

v = sqrt (GM/r)

v = sqrt (6.67*10^-11*5.98*10^24/(1.40*10^7))

v = 5337.64 m/sec

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