Re: puzzle: satellite clock crossover

[Leigh Palmer <palmer@SFU.CA>]

At 4:25 PM -0500 1/29/01, John Denker wrote:
> I wrote:
> > > Note that for GPS satellites in orbit, the relativistic contributions
> > > are very significant, necessary corrections.
>
> Then at 11:33 PM 1/27/01 -0800, Leigh Palmer wrote:
> > ...and guess which effect is dominant, the special relativistic time
> > dilation due to the satellite's speed relative to clocks on Earth's
> > surface, or the general relativistic time contraction which may be
> > viewed as a gravitational red shift due to the gravitational
> > potential difference between the positions of the satellite and the
> > Earthbound clock.
>
> Even though I like to think I'm a good guesser, and even though I know the
> right answer to Leigh's question, I claim it would be rather hard to guess
> this one.  I particular, if you leave out the reference to specific "GPS"
> satellites, then no amount of guessing will give a reliable answer, for the
> following reason:

I'm sorry, I thought we were speaking specifically about the GPS
satellites. John is correct; you must know the parameters of the
orbit to answer this question.

Of course I would not have asked the question if the answer was
that the SR effect is dominant; your guess could be based solely
on familiarity with my perverse nature, and you would have got
it right. Each GPS satellite has four atomic clocks on board, so
measuring these chronometric anomalies is very easy, except that
they cannot be separated, of course. The orbiting clocks in the
GPS run faster than similar clocks on Earth's surface. Hand held
civil GPS units are the smallest consumer products I know that
depend for their function on general relativity. (This means I
exclude from that category anything that depends upon gravity
*per se*, like that VW that got stuck in the tree yesterday.)

Leigh