Using Momentum & Energy Principles to Analyze a Satellite Orbit

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SUMMARY

This discussion focuses on applying the momentum and energy principles to analyze a satellite's orbit around Earth. The satellite, with a mass of 4000 kg, orbits at a radius of 9.5x10^6 m, resulting in a gravitational force of 17817.17452 N acting on it. The speed of the satellite, calculated using the momentum principle, is 6505.058761 m/s. The energy principle is utilized to determine the work required to move the satellite to a location far from Earth, which involves subtracting kinetic energy from the gravitational potential energy.

PREREQUISITES
  • Understanding of Newton's law of gravitation
  • Familiarity with the momentum principle in physics
  • Knowledge of the energy principle and work-energy theorem
  • Basic mathematical skills for calculations involving gravitational forces and energy
NEXT STEPS
  • Study gravitational force calculations using Newton's law of gravitation
  • Learn about the momentum principle in-depth with practical examples
  • Explore the work-energy theorem and its applications in orbital mechanics
  • Investigate energy conservation in satellite motion and escape velocity calculations
USEFUL FOR

Physics students, aerospace engineers, and anyone interested in orbital mechanics and satellite dynamics will benefit from this discussion.

ohheytai
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In certain cases, using both the momentum principle and energy principle to analyze a system is useful, as they each can reveal different information. You will use the both momentum principle and the energy principle in this problem.

A satellite of mass 4000 kg orbits the Earth in a circular orbit of radius of 9.5x10^6 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0x10^24 kg.

a)What is the magnitude of the gravitational force on the satellite due to the earth?
F= 17817.17452 N

b)Using the momentum principle, find the speed of the satellite in orbit.
v=6505.058761

c)Using the energy principle, find the minimum amount of work needed to move the satellite from this orbit to a location very far away from the Earth. (You can think of this energy as being supplied by work due to something outside of the system of the Earth and the satellite.)

i can't get C i tried GMm1/r and got 1.69e11 J and its wrong can someone help me out here?
 
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nevermind i figured it out i forgot to subtract KE
 

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