Changes

My goodness!  Andy and RonLar are ''still'' debating the GPS issue?  You two clearly enjoy debating each other, and I enjoy reading what you have to say.

My goodness!  Andy and RonLar are ''still'' debating the GPS issue?  You two clearly enjoy debating each other, and I enjoy reading what you have to say.

As far as the questions above "who did the Relativity calculations?" and "who did the Newtonian calculations?" for GPS, I don't think it's important for the person doing the relativity calculations to have published his work or otherwise made himself known.  The fundamental formulas for the GR time dilation effect under discussion are known to nearly all physics graduate students.  This isn't to say that GR isn't very complicated, but the number of people who understand it is now ''way'' more than 3.  The equation for the relative incremental time dilation/contraction is <math>g/c^2</math> where <math>g</math> is the strength of the gravitational field.  Now the rest of the derivation is straightforward.  I'll take you through it.  In the vicinity of the Earth, we have

As far as the questions above "who did the Relativity calculations?" and "who did the Newtonian calculations?" for GPS, I don't think it's important for the person doing the relativity calculations to have published his work or otherwise made himself known.  The fundamental formulas for the GR time dilation effect under discussion are known to nearly all physics graduate students.  This isn't to say that GR isn't very complicated, but the number of people who understand it is now ''way'' more than 3.  The equation for the relative incremental time dilation/contraction is <math>g/c^2</math> per meter of distance "uphill" or "downhill" in the gravitational field, where <math>g</math> is the strength of the field. (Since the field is conservative, this distance uphill or downhill is independent of the path; it's just a property of the locations of the two observers.) Now the rest of the derivation is straightforward.  I'll take you through it.  In the vicinity of the Earth, we have

::<math>g = \frac{GM}{r^2}</math>

::<math>g = \frac{GM}{r^2}</math>

so the dilation is

so the dilation is