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Mass of Planet Using Radius and Doppler Effect

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Imagine you are observing a spacecraft moving in a circular orbit of radius 128,000 km around a distant planet. You happen to be located in the plane of the spacecraft's orbit. You find that the spacecraft's radio signal varies periodically in wavelength between 2.99964 m and 3.00036 m. Assuming that the radio is broadcasting normally, at a constant wavelength, what is the mass of the planet?


    2. Relevant equations
    [tex] M= \displaystyle{\frac{rv^2}{G}}; \space

    where \space G= 6.67\times10^{-11} \space m^3 kg^{-1} s^{-2},

    \space r \space is \space km, \space and \space v \ is \space
    km/s
    [/tex]



    3. The attempt at a solution

    Well, as we have a change in wavelength 2.99964 m and 3.00036 m respectively, the original signal should equal 3.00000m. With the formula from my textbook ( "Astronomy" 6th edition by Chaisson and McMillan, page 63), [tex] \frac{apparent\space \lambda}{true \space \lambda} -1 = speed \space in \space c[/tex] Then I multiply it by c and convert meters to kilometers and get[tex] \approx 36 km/s. [/tex]

    I input r and G as [tex] G= 6.67\times10^{-11} \space m^3 kg^{-1} s^{-2}, \space r= 128, 000 km. [/tex]


    So: [tex] M= \displaystyle{\frac{(128000km)*(36 km/s)^2}{6.67\times 10^{-11}\space m^3 kg^{-1} s^{-2}}} = 2.48\times10^{18} kg. [/tex]


    When I input this answer into the website in which we do our homework by, it gives me a lousy red X. I'm sure I messed up, because I was expecting a planet approximately in the 10^20-28 kg range.


    Regardless, I've been stuck on this for a bit. Help is much appreciated.


    Sincerely,


    Nikos
     
  2. jcsd
  3. Sep 16, 2012 #2

    phyzguy

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    Check your units, I think you are not converting km to m.
     
  4. Sep 16, 2012 #3

    Simon Bridge

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    possibly you are using different values for your constants, or you have rounded off differently?
    [edit]ah - your value for G has length in meters.
     
  5. Sep 16, 2012 #4
    Hey there,


    Aha! I missed that my constant was in meters.



    Honest mistake. Thanks a lot.
     
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