Insights The Schwarzschild Metric: Part 1, GPS Satellites - Comments

fresh_42

Mentor
Insights Author
2018 Award
10,702
7,312
Just a little remark. It is Johannes Kepler, not Keplar.
 
25,243
6,382
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

Science Advisor
Insights Author
1,006
172
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 :-)
 

Want to reply to this thread?

"The Schwarzschild Metric: Part 1, GPS Satellites - Comments" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top