Satellite. calculate radius of orbit

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SUMMARY

The discussion focuses on calculating the radius of a satellite's orbit around the Earth, given a period of 25.4 hours. The relevant equations used are the orbital velocity equation, v = 2πr/T, and the gravitational velocity equation, v = √(GM/r). By equating these two expressions for velocity and solving for the radius (r), participants derive the necessary formula to find the orbital radius using the mass of the Earth, 5.98 x 1024 kg.

PREREQUISITES
  • Understanding of circular motion and orbital mechanics
  • Familiarity with gravitational force equations
  • Basic algebra for solving equations
  • Knowledge of constants such as the mass of the Earth
NEXT STEPS
  • Study the derivation of Kepler's laws of planetary motion
  • Learn about gravitational potential energy in orbital mechanics
  • Explore the implications of varying orbital periods on radius calculations
  • Investigate the effects of altitude on satellite speed and orbit stability
USEFUL FOR

Students in physics or engineering, educators teaching orbital mechanics, and anyone interested in satellite dynamics and calculations.

evan b
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Homework Statement





satellite is in a circular orbit around the earth. The period of the satellite is 25.4 hr. Calculate the radius of the orbit of the satellite. Data: Mass of the Earth = 5.98 x 1024 kg
 
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We have two equations we should use:

v = \frac{2\pi r}{T}

and

v = \sqrt{\frac{GM}{r}}

let them equal each other, then solve for r.
 

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