Calculating Orbital Speed and Period of a Weightless Satellite

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SUMMARY

The discussion focuses on calculating the orbital speed and period of a weightless satellite orbiting the Earth at a height H above the surface. The key equations involve gravitational force and centripetal acceleration, leading to the conclusion that a person inside the satellite experiences weightlessness due to the satellite's free-fall state. The radius of the Earth (R) is crucial for determining the orbital parameters, and the concept of gravitational influence extending infinitely is emphasized.

PREREQUISITES
  • Understanding of gravitational force and centripetal acceleration
  • Familiarity with orbital mechanics and satellite motion
  • Knowledge of basic physics equations related to motion
  • Concept of weightlessness in a free-fall environment
NEXT STEPS
  • Study the equations for gravitational force and centripetal acceleration in detail
  • Learn about the derivation of orbital speed and period formulas for satellites
  • Explore the concept of free-fall and its implications for weightlessness
  • Investigate the effects of altitude on gravitational force and satellite dynamics
USEFUL FOR

Students in physics, aerospace engineers, and anyone interested in satellite dynamics and gravitational effects on motion.

missnuss
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1. Homework Statement : An artificial satellite revolves about the Earth at height H above the surface. If the radius of the Earth is R, calculate the orbital speed and the orbital period such that a person in the satellite will be weightless.



Homework Equations





The Attempt at a Solution

Alright, I have I= [tex]\sum[/tex] H ri^2 = [tex]\sum[/tex] HR^2= ([tex]\sum[/tex])R^2 = MR^2
 
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The problem doesn't make sense. A person in a satellite will always seem weightless, because his center of mass coincides almost exactly with the satellite's, so he'll experience almost exactly the same acceleration for all time. A person in a satellite will also never be weightless, since Earth's gravity extends to infinity.
 

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