Calculate Geosynchronous Orbit Dist. to Earth's Center

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Homework Help Overview

The problem involves calculating the distance from a satellite in a geosynchronous orbit to the center of the Earth, using the provided mass of the Earth and a formula related to orbital mechanics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply a formula relating orbital period and radius but encounters difficulties with the calculation. Some participants question the units used in the formula, particularly regarding the period.

Discussion Status

The discussion is ongoing, with participants exploring the implications of unit consistency in the formula. There is no explicit consensus yet, but guidance has been offered regarding the examination of units.

Contextual Notes

Participants are discussing the assumptions related to the units of the variables in the formula, particularly the period T.

Shaunzio
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Homework Statement


A satellite is in a circular, geosynchronous orbit (makes one revolution around Earth in 24 hours). Calculate the distance in meters from the satellite to the Earth's center. Mass of Earth = 5.97 x 1024 kg



Homework Equations


T=((2*Pi)*r^(3/2))/sqrt(GM)


The Attempt at a Solution



I thought T equals the period 2Pi. So the the 2Pi's cancel and then you just plug in the variables. Unfortunately I'm not getting the right answer which is supposed to be: 4.2*10^7.

Any help would be greatly appreciated.
 
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Check to see what units the formula will produce.
 
Would the units for T be radians?
 
Shaunzio said:
Would the units for T be radians?
You're guessing? Why don't you expand the units from the formula and actually see what it is?
 

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