Question

Six artificial satellites complete one circular orbit around a space station in the same amount of time. Each satellite has mass m and radius of orbit L. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible. Rank the net force acting on each satellite from their rockets.

Answer 1

1) For uniform circular motion, Centripetal Force is given by either of two equations:

F = mv^2/r
F = w^2rm

m = mass
r = radius
w = "omega" = angular velocity
v = tangential velocity

All of these satellites have the same angular velocity, so you just need to order them by decreasing mL to get the list in order from highest to lowest.

I get: A B C E F D. (C, E and F are all the same.)

Answer 2

A) m = 800kg, L = 5000m
B) m = 300kg, L = 7500m
C) m= 400kg. L = 2500m
D) m = 200kg, L = 5000m

assumed time to circulate the orbit = 1

A) v = (2pi*5000) / 1 = 31,416
Fg = GMm / (R^2)
= (6.673E-11*5.98E+24*800) / (6.37E+6)^2
= 9.83*800 = 7,867
Fs = (m)(v^2) / (R + L)
Fs = (800)(31416 ^ 2) / (6.37E+6plus 5000)
Fs = 123,854
net = 123854 - 7867 = 115,987 N

B) v = (2pi7500) / 1= 47,124
Fg = 9.83 * 300 = 2950
Fs = 104,457
net = 104457 - 2950 = 101,507 N

C) v = (2pi2500) /1 = 15,708
Fg = 9.83 * 400 = 3934
Fs = 15,488
net = 15488 - 3934 = 11,554 N

D) v = (2pi5000) = 31,416
Fg = 9.83 * 200 = 1967
Fs = 30,964
net = 30964 - 1967 = 28,997 N

A) largest net thrown out the space first
B) 2nd
D) 3rd
C) last