Verifying Time Effect of Gravity: Accurate to a Few Thousands of a Percent

[FactChecker]

To date, the most accurate verification of the time effect of gravity is where two satellites were accidentally put into elliptical orbits where the altitude varied by 8,500 kilometers ( 5,282 mi). Their atomic clocks ran slower near Earth and faster at higher altitude. The agreement with GR was within a few thousands of a percent. (see https://www.sciencenews.org/article/satellite-oops-reaffirms-einstein-theory-gravity )

 

[Dale]

two satellites were accidentally put into elliptical orbits

Oh, that sounds like a horrendously expensive woopsie

 

[LURCH]

Just curious; what does GR predict about the effects of this elliptical orbit on the clocks? I mean the overall effect when averaged over time. When the satellite is at apogee, it is farther out of the gravity well, and when at perigee, it is deeper inside the gravity well. It sounds like these two effects should cancel out, leaving the overall progress of the clock to be the same as if the satellite were in a circular orbit (or equal area), with the highs and lows having opposite it equal effect. However, for some reason I find myself doubting my own conclusion, there. Would the inverse square law mean that the two extremes of altitude would have opposite but unequal effect (see, that doesn’t sound right either)?

Also, thanks for the link; really interesting stuff. Glad that something useful game of it.

 

[PeterDonis]

When the satellite is at apogee, it is farther out of the gravity well, and when at perigee, it is deeper inside the gravity well.

Remember that there are two effects here: altitude (lower -> clocks run slower) and speed (faster -> clocks run slower). (I am glossing over a number of technical points that are beyond the scope of a B level thread.) A satellite in an elliptical orbit spends more time at higher altitude and lower speed, and less time at lower altitude and higher speed. So off the top of my head, I would expect the overall effect to be more elapsed time per orbit (i.e., clocks running faster) as compared to an "equivalent" circular orbit. But I have not tried to do the math in detail.