## Six artificial satellites complete one circular orbit around a space station in the same amount of time. Each satellite has mass m and radiu

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. Rank from largest to smallest.

a. m=200 kg and L= 5000m
b. m=400 kg and L=2500m
c. m=100kg and L=2500m
d. m=100kg and L=10000m
e. m=800kg and L=5000m
f. m=300kg and L=7500m

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2 weeks 2021-07-19T06:21:18+00:00 1 Answers 4 views 0

b = e > a = c = f > d

Explanation:

Since the satellites complete one circular orbit in the same amount of time, their speed is the same.

The force needed to maintain the orbit is the centripetal force given by F = mv²/L where m = mass of artificial satellite and L = radius of orbit.

So, for artificial satellite a

a. m=200 kg and L= 5000m

F =  mv²/L

F =  200 kgv²/5000 m

F =  0.04v² N

So, for artificial satellite b

b. m=400 kg and L= 2500m

F =  mv²/L

F =  400 kgv²/2500 m

F =  0.16v² N

So, for artificial satellite c

c. m=100 kg and L= 2500m

F =  mv²/L

F =  100 kgv²/2500 m

F =  0.04v² N

So, for artificial satellite d

d. m=100 kg and L= 10000m

F =  mv²/L

F =  100 kgv²/10000 m

F =  0.01v² N

So, for artificial satellite e

e. m=800 kg and L= 5000m

F =  mv²/L

F =  800 kgv²/5000 m

F =  0.16v² N

So, for artificial satellite f

f. m=300 kg and L= 7500m

F =  mv²/L

F =  300 kgv²/7500 m

F =  0.04v² N

So, the net force are in the order b = e > a = c = f > d