Calculating Orbital Speed and Period of a Weightless Satellite

AI Thread Summary
To calculate the orbital speed and period of a weightless satellite, one must consider the satellite's height above Earth's surface and the radius of the Earth. The concept of weightlessness in a satellite is explained by the fact that both the satellite and its occupant experience the same gravitational acceleration, creating a sensation of weightlessness. However, gravity does not disappear; it merely acts uniformly on the satellite and its contents. The calculations involve understanding the relationship between gravitational force, orbital speed, and the radius of the orbit. Ultimately, the discussion highlights the nuances of weightlessness in orbital mechanics.
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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= \sum H ri^2 = \sum HR^2= (\sum)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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