Satellite Orbit around the earth, speed?

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SUMMARY

The discussion centers on calculating the speed of a satellite in a circular orbit around Earth, with a mass of 5.98 x 1024 kg and an orbital period of 6.72 x 104 seconds. The speed formula is established as (2πR)/T, where R is the orbital radius. To determine R, participants suggest using Kepler's Third Law, which relates the period of orbit to the radius. The gravitational force acting on the satellite must equal the centripetal force, emphasizing the importance of unit consistency in calculations.

PREREQUISITES
  • Understanding of circular motion and centripetal force
  • Familiarity with Kepler's Third Law of planetary motion
  • Knowledge of gravitational force and its formula (F = GMm/r2)
  • Basic trigonometry and angular velocity concepts (ω = 2π/T)
NEXT STEPS
  • Study Kepler's Third Law and its applications in orbital mechanics
  • Learn about gravitational force calculations using Newton's law of universal gravitation
  • Explore the concept of angular velocity and its significance in circular motion
  • Practice problems involving satellite motion and orbital speed calculations
USEFUL FOR

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

neoncrazy101
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The question is...
A satellite is in a circular orbit about the Earth (M = 5.98 x 1024 kg). The period of the satellite is 6.72 x 104 s. What is the speed at which the satellite travels?

I know the speed is equal to (2piR)/6.72x10^4s But I can't figure out the radius. I know the Earth's radius is 6.38x10^6 but how can I go about figuring out the radius that the satellite travels?
 
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You need to use the fact that the gravitational force of attraction between the Earth and the satellite is equal to the centripetal force experienced by the satellite.

You know T, so you can get ω using ω =2π /T.
 
alright thanks but one question, I am not familiar with the w looking thing nor the 2n. What are they?
 
neoncrazy101 said:
alright thanks but one question, I am not familiar with the w looking thing nor the 2n. What are they?

ω = omega = angular velocity

n = constant pi = 3.1415...
 
neoncrazy101 said:
The question is...
A satellite is in a circular orbit about the Earth (M = 5.98 x 1024 kg). The period of the satellite is 6.72 x 104 s. What is the speed at which the satellite travels?

I know the speed is equal to (2piR)/6.72x10^4s But I can't figure out the radius. I know the Earth's radius is 6.38x10^6 but how can I go about figuring out the radius that the satellite travels?

You could apply Kepler's Third Law to get the radius. The square of the period divided by the cube of the orbital radius equals 2pi divided by GM (i.e., the universal gravitational constant times the mass of the body at the center of the orbit).

Just be careful with units.
 

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