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.(adsbygoogle = window.adsbygoogle || []).push({});

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)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Relativity question.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**