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:

v=2πLT

Period, T = 2πL/v

T1 = 2π(5000)/120 = 261.8 s

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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.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Simple Harmonic Motion and Circular Motion concept. If you need more Simple Harmonic Motion and Circular Motion practice, you can also practice Simple Harmonic Motion and Circular Motion practice problems.