The Schwarzschild Metric: Part 1, GPS Satellites - Comments

Answers and Replies

  • #2
13,141
9,922
Just a little remark. It is Johannes Kepler, not Keplar.
 
  • #3
PeterDonis
Mentor
Insights Author
2019 Award
29,722
8,978
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).
 
  • #5
RUTA
Science Advisor
Insights Author
1,161
260
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 :-)
 
  • Like
Likes Greg Bernhardt

Related Threads on The Schwarzschild Metric: Part 1, GPS Satellites - Comments

  • Last Post
Replies
3
Views
3K
  • Last Post
4
Replies
99
Views
25K
  • Last Post
Replies
3
Views
843
Replies
21
Views
3K
  • Last Post
Replies
23
Views
1K
  • Last Post
Replies
10
Views
6K
  • Last Post
Replies
1
Views
2K
Top