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Re: [Phys-l] relativity trivium

The built in relativity correction has an interesting history. A physicist read an article on the proposed system and wrote and ask them if they were correcting for it. This motivated the designers to build it in but they weren't sure it was necessary so in the first satellites it could be turned off and on. Making it a nice test of General Relativity.
Gary

At 05:20 PM 10/30/2010, you 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) = 45.66 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 perr day (compensated by clock speed) due to relativity > > Microsecond - Wikipedia, the free encyclopedia > > bc finds the darndest things while googling. > _______________________________________________ > Forum for Physics Educators > Phys-l@carnot.physics.buffalo.edu > https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l _______________________________________________ Forum for Physics Educators Phys-l@carnot.physics.buffalo.edu https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l