Chronology Current Month Current Thread Current Date [Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] relativity trivium

bc finds the nature of the comments interesting -- one practical** and tother theory analysis.***

** physics teacher sos list

*** PHYS-L is a list dedicated to physics and the teaching of physics with about 700 members from over 35 countries, the majority of whom are physics educators.

[Both have physics doctorates.]

On 2010, Oct 30, , at 15:24, Paul Doherty wrote:

38,000 nanoseconds = 38,000 feet = 7 miles error per day if the GPS was not corrected for special and general relativity.

Paul D

On 2010, Oct 30, , at 15:20, John Mallinckrodt wrote:

This agrees with a simple analysis based on nothing more than the orbital radius of GPS satellites:

Because the orbital radius is r = 26,600 km (≅ 4.17 R_e), the orbital speed is v = sqrt(GM_e/r) = 3.87 km/s.

The special relativistic effect causes GPS clocks to run SLOW by gamma – 1 ≅ (1/2)v^2/c^2 = (1/2)GM_e/rc^2 = 7.2 microsec/day.

The general relativistic effect causes GPS clocks to run FAST by delta phi/c^2 = GM_e/rc^2(r/R_e – 1) = 45.6 microsec/day.

Thus, the overall effect is that GPS clocks run fast by about 38 microsec/day. It's interesting to note that the general relativistic effect is by far the largest contributor and it's also interesting to note that the orbital radius at which the two effects cancel each other is r = 3/2 R_e.

John Mallinckrodt
Cal Poly Pomona

On Oct 30, 2010, at 1:53 PM, Bernard Cleyet wrote:

38 microseconds – discrepancy in GPS satellite time per day (compensated by clock speed) due to relativity

Microsecond - Wikipedia, the free encyclopedia

bc finds the darndest things while googling.
__________________________________