Problem: 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.m=200kg, L= 5000 m, v=120 m/s m=800kg, L= 10,000 m, v=40m/sm=400kg, L= 2500 m, v=80m/sm=100kg, L=2500 m, V=160m/sm=300kg, L=10,000m, V=80 m/sm=200kg, L=5000 m, V=160 m/s Part A. Rank each satellite from largest to smallest based on its period. Part B. Rank each satellite from largest to smallest based on its acceleration.

FREE Expert Solution

Part A

Velocity, v:

$\overline{){\mathbf{v}}{\mathbf{=}}\frac{\mathbf{2}\mathbf{\pi L}}{\mathbf{T}}}$

Period, T = 2πL/v

T1 = 2π(5000)/120 = 261.8 s

Problem Details

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.

1. m=200kg, L= 5000 m, v=120 m/s
2. m=800kg, L= 10,000 m, v=40m/s
3. m=400kg, L= 2500 m, v=80m/s
4. m=100kg, L=2500 m, V=160m/s
5. m=300kg, L=10,000m, V=80 m/s
6. m=200kg, L=5000 m, V=160 m/s

Part A. Rank each satellite from largest to smallest based on its period.

Part B. Rank each satellite from largest to smallest based on its acceleration.