Period of an orbiting object?

  • Thread starter choyphin
  • Start date
  • #1
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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!
 

Answers and Replies

  • #2
mgb_phys
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Put the units in - it will help !
 
  • #3
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I did that, but still got an unreasonable answer: 2.6x10^26
 
  • #4
mgb_phys
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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
 
  • #5
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Is the answer 106.6 KM? Thanks so much for the explanations by the way!
 
  • #6
mgb_phys
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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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