The Schwarzschild Metric: Part 1, GPS Satellites - Comments

[RUTA]

Greg Bernhardt submitted a new PF Insights post

The Schwarzschild Metric: Part 1, GPS Satellites

Continue reading the Original PF Insights Post.

 

[fresh_42]

Just a little remark. It is Johannes Kepler, not Keplar.

 

[PeterDonis]

Nice Insight? I have one comment, though: it might be worth mentioning that in the calculation of $\Delta \tau_R$ (for the Earth observer), you are assuming the Earth is non-rotating. That turns out to be OK for the particular calculation you are doing because the time dilation correction due to this is roughly two orders of magnitude smaller than the effects you compute; but rotation also introduces other complications, such as correctly defining clock synchronization, which can't be ignored (the excellent Ashby paper you refer to goes into all this).

 

[RUTA]

Just a little remark. It is Johannes Kepler, not Keplar.

Haha, thnx, I fixed that!

 

[RUTA]

Nice Insight? I have one comment, though: it might be worth mentioning that in the calculation of $\Delta \tau_R$ (for the Earth observer), you are assuming the Earth is non-rotating. That turns out to be OK for the particular calculation you are doing because the time dilation correction due to this is roughly two orders of magnitude smaller than the effects you compute; but rotation also introduces other complications, such as correctly defining clock synchronization, which can't be ignored (the excellent Ashby paper you refer to goes into all this).

As an additional problem for my GR students, I have them add the $-\frac{v^2}{c^2}$ term to Eq(4) for the rotation of Earth and show that it’s of order $10^{-12}$ while the $\frac{2M}{R}$ term is of order $10^{-9}$. I considered adding that equation to this Insight, since it’s just one more equation. Given your comment, I think I’ll do that :-)