[CliffordK (OP)]

I was just thinking tonight.
One should be able to replicate the Hafele and Keating Experiment using NASA's STEREO solar satellites.

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I had thought that the satellites were targeted for L4/L5 orbits, but apparently they aren't, with each satellite at a slightly different orbital speed around the sun. 

However, with our sun orbiting around the Milky Way at approximately 782,000 kph, so for a few weeks, or perhaps a month or so each year, the satellites should be traveling more or less in additive, or subtracting speeds around the sun.

So, one would effectively be traveling at:
782,000 kph - 107,000 kph = 675,000 kph
And the other one would effectively be traveling at:
782,000 kph + 107,000 kph = 889,00 kph

Do we need to calculate in the Milky Way's apparent motion in the visible universe?

Six months later, the two would have completed a half orbit around the sun, and reversed their respective directions, and one could repeat the experiment.  Actually, one could run the experiment continuously, and one should see an oscillation in clock speeds with respect to Earth, or the L1 SOHO satellite.

So...
One would expect that during the two experimental periods.
The satellite going "backwards" from the solar orbit around the Milky Way would be traveling slower, and would have a faster clock, and the one going "forwards" with respect to the solar orbit around the Milky Way would be traveling faster, and have a slower clock.  Then the two would flip six months later.

(or do I have my clock speeds backwards)?  []

Radio transmission delay would be a problem, especially since neither satellite is in a perfect 365 day orbit.  But, the speed with respect to the Earth for each individual satellite would be the same for the two experimental periods, so it should be able to be compensated for.

Do the satellites have the atomic clocks necessary for the experiment?

Perhaps if NASA, or another space agency chooses to launch L4/L5 satellites in the future, the experimental capabilities could be added.

[Soul Surfer]

In order to look at what could happen you have to allow for the fact that the plane of the solar system is strongly angled with respect to the plane of the galaxy so the orbital velocity changes around the galaxy are in effect much smaller.

Most spacecraft have very precise GPS like ranging techniques built into their communications systems so precise positions and timings can be quite accurate but I doubt that the stability of the on board clocks is good enough.

[CliffordK (OP)]

Ahhh,
Thanks,
Somehow I thought that the solar system was aligned with the Galactic Plane, but apparently that theory has been updated a few years ago.

Here is an illustration that I found online.
http://www.abovetopsecret.com/forum/thread791425/pg1


So, twice every 240 million years or so (orbital period around Milky Way), the direction of motion of the solar system would be aligned along the galactic plane.  But, this apparently isn't one of those periods.  With vector math, one could still compute the forward and reverse components along the galactic plane, but it wouldn't be nearly as significant.

However, the other important measurement seems to be with respect to Cosmic Microwave Background Radiation (CMB).  And, apparently the solar plane does align more or less with the CMB plane.  With the Milky Way moving with a speed of 552 km/s, or 1,987,200 kph.  Perhaps all is not lost.

http://www-personal.umich.edu/~huterer/PRESS/CMB_Huterer.pdf
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