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Relativity question.

  1. Aug 25, 2008 #1
    A space shuttle is in orbit travelling with velocity v with respect to the Earth, along the x direction. The crew launch a satellite forward with velocity u in their own rest frame. The speed of the satellite relative to the Earth is w. A beacon on the satellite emits photons of wavelength [tex]\lambda[/tex] in all directions in the satellite rest frame.

    i) Define the z axis as the axis joining the photon to the Earth, i.e perpendicular to its velocity in the rest frame of the satellite. Give an expression in terms of w and [tex]\lambda0[/tex] for
    1. the wavelength [tex]\lambda1[/tex], of a photon emitted along the x axis

    2. the wavelength [tex]\lambda2[/tex], of a photon emitted along the z axis

    as seen by an observer stationary with respect to the Earth.


    ii)A realistic value for w is v=30m/s. comment on the values of [tex]\lambda1[/tex] and [tex]\lambda2[/tex] in this case, and on the implications of your answer for GPS satellites which emit a signal at a particular frequency.

    iii)Write down the equation for time dilation, and comment on the effect on a clock on the satellite which has to stay in time with one on the Earth.

    iv)Wrtie down the four-vector momentum, p, of a photon which is emitted along the x direction, in terms of [tex]\lambda0[/tex]

    Give a matrix equation for the four-vector momentum, p', of this photon in the rest frame of the Earth, in terms of u, v and p.

    Use this equation to show that the velocity, w, of the satellite in the rest frame of the Earth is given by

    [tex]w=\frac{u+v}{1+\frac{uv}{c^2}}[/tex]

    ii) and iii) I can do with ease (they are the easy bits after all)

    I can't even seem to start parts i) or iv)
     
    Last edited: Aug 25, 2008
  2. jcsd
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