But they (and their clocks) did acquire a different acceleration history than their earthbound counterpart. Accelerating to flight speed and centripetal acceleration from flying around the Earth (arot = v2 / r) are the difference, not the relativisticaly insignificant velocity difference.

Using speed measurements of the gas at different distances from the Galactic center, the Sun appears to be cruising along at 200 kilometers per second and it takes 240 million years to complete the grand circuit around the Galaxy. This speed is an absolute speed.

Relative to what? The center of the galaxy? Galactic orbital velocity? All motion is relative Vince, pick your reference fame.

Nature and nature's laws lay hid in night, God said, "Let Newton be," and all was light.

--Alexander Pope, "Epigram on Sir Isaac Newton"

It did not last; the devil howling "Ho! Let Einstein be!" restored the status quo.

--J. C. Squire (1884-1958), "Answer to Pope's
Epitaph for Sir Isaac Newton"