Calculating Satellite Speed Based on Orbit Period

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SUMMARY

The discussion focuses on calculating the speed of a satellite in a circular orbit around Earth, given its mass (5.98 x 1024 kg) and orbital period (7.12 x 104 s). The user attempted to solve the problem using gravitational equations but received feedback indicating an incorrect answer of 1.26 x 107 m/s. The error likely occurred during the numerical substitution process in the equations used for calculating orbital speed.

PREREQUISITES
  • Understanding of circular motion and gravitational force
  • Familiarity with the formula for orbital speed: v = √(GM/r)
  • Basic algebra for rearranging equations
  • Knowledge of units and conversions in physics
NEXT STEPS
  • Review the derivation of the orbital speed formula v = √(GM/r)
  • Practice problems involving satellite motion and gravitational calculations
  • Explore the impact of varying orbital periods on satellite speed
  • Learn about the significance of the gravitational constant (G) in orbital mechanics
USEFUL FOR

Students studying physics, particularly those focusing on orbital mechanics, as well as educators looking for examples of satellite speed calculations.

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Homework Statement


A satellite is in a circular orbit about the Earth (M = 5.98 x 1024 kg). The period of the satellite is 7.12 x 104 s. What is the speed at which the satellite travels?

2. The attempt at a solution
I used the equation:

http://img171.imageshack.us/img171/7176/math062gg0.gif

Re-arranged it to isolate r:

http://img74.imageshack.us/img74/9274/math065rr5.gif

After I got radii, i solved for velocity:

http://img171.imageshack.us/img171/3975/math053pd6.gif

My answer: 1.26x10^7 m/s
Teacher: Incorrect

Note: The numbers in the equations are not the actual ones i used.
 
Last edited by a moderator:
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The equations seem right to me. Seems like something went wrong when plugging in the numbers. What are the actual numbers you used?
 

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