Question

Six artificial satellites circle a space station at constant speed. The mass m of each satellite, distance L from the space station, and the speed v of each satellite are listed below. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible.

Six artificial satellites circle a space station at constant speed. The mass m of each satellite, distance L from the space station, and the speed v of each satellite are listed below. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible.

Answer 1

Answer 2

1) 2pi*(2500)/T1=80 --> multiply both sides by T1, then divide by120 to get T1.
T1=196.375 sec...


2) T2=2*pi*10000/40=1571 sec....

3) T3=2*pi*2500/160=98.1875 sec..

4) T4=2*pi*10000/80=785.5 sec...

5) T5=2*pi*5000/120=261.84 sec...
6)T6=2*pi*5000/160=196.375 sec ....

so rank order is T2>T4>T5>T1=T6>T3

Answer 3

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

•