What is the orbital distance for a satellite with a 125 min period around Earth?

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Homework Help Overview

The discussion revolves around determining the orbital distance of a satellite with a specified period of 125 minutes around Earth. The problem involves gravitational constants, mass of the Earth, and the radius of Earth, indicating a focus on orbital mechanics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the formula relating orbital period and radius, with attempts to rearrange and solve for the radius. There are questions regarding unit consistency and the interpretation of results, particularly concerning negative values and unreasonable answers.

Discussion Status

Some participants have provided guidance on unit conversion and formula manipulation. There is an ongoing exploration of the implications of the results, such as the distinction between the orbital radius and altitude above Earth's surface. Multiple interpretations of the calculations are being considered.

Contextual Notes

Participants note the importance of using consistent units and the need to clarify whether the period is expressed in seconds. There is also mention of the requirement to subtract Earth's radius to find the altitude of the satellite.

choyphin
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Homework Statement


At what distance about Earth would a satellite have a period of 125 min?
G=6.673x10^-11
T=125 Min
Mass=5.97x10^24
Radius of Earth=6.38*10^6

Homework Equations


T=2pi*Square root of (R^3/constant*mass)


The Attempt at a Solution


125=2*3.14*Square root of ((6.38x10^6)^3+R^3/6.673x10^-11*5.97x10^24)
I got a negative #... Which i know is wrong!
 
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Put the units in - it will help !
 
I did that, but still got an unreasonable answer: 2.6x10^26
 
T=2pi*sqrt(R^3/GM)
so T/2pi = sqrt(R^3/GM)
Square both sides (T/2pi)^2 = R^3/GM
Finally R = cube root ( GM * (T/2pi)^2 )

Check the units (m^3 kg^01 s^-2 * kg * s^2)^1/3 = (m^3 )^1/3 = m
 
Is the answer 106.6 KM? Thanks so much for the explanations by the way!
 
I think you have a slight mistype there, do you have T in seconds?
Remember that the result is the radius of the orbit from the centre of the Earth - if you want the altitude you need to subtract the radius of the Earth.
 

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