# Problem: 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. To rank items as equivalent, overlap them.A) m=200 kg and L= 5000mB) m=400 kg and L=2500mC) m=100kg and L=2500mD) m=100kg and L=10000mE) m=800kg and L=5000mF) m=300kg and L=7500m

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###### FREE Expert Solution

The force acting on the satellites is given as:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{k}}{\mathbf{m}}{\mathbf{L}}}$

This comes from the velocity of the satellite, given as:

v = 2πL/T

Fc = mv2/L = m(2πL/t)2/L = (4π2/T2)(mL)

k in the force equation is: k = 4π2/T2

###### Problem Details

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. To rank items as equivalent, overlap them.

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