[jeffreyH (OP)]

If we send a satellite into orbit with an uncorrected clock, so not like a GPS clock, can we learn something? We csn have the satellite send back the time as it completes each orbit. At a ground station on earth, at the position where the satellite is overhead and sending its update of the time, we can record the earth based time. Then we can use these times along with the distance of the orbit to calculate what velocity local and remote observers will record for the satellite. Has this been done?

[evan_au]

If we send a satellite into orbit with an uncorrected clock, so not like a GPS clock

GPS satellites have a clock which is calibrated with a known frequency "error" before launch, so they will be exactly on-frequency when in orbit.
Since we know precisely what this frequency "error" is, what would an uncorrected clock tell you that you couldn't find out from a pre-corrected clock?

[evan_au]

NIST used two very accurate aluminium-ion clocks which were calibrated together at the same level. So they were not corrected for height.

Then one was jacked up about a foot, and the time compared.
As expected, the higher clock ran faster.

See: https://www.nist.gov/news-events/news/2010/09/nist-pair-aluminum-atomic-clocks-reveal-einsteins-relativity-personal-scale

[jeffreyH (OP)]

If we send a satellite into orbit with an uncorrected clock, so not like a GPS clock

GPS satellites have a clock which is calibrated with a known frequency "error" before launch, so they will be exactly on-frequency when in orbit.
Since we know precisely what this frequency "error" is, what would an uncorrected clock tell you that you couldn't find out from a pre-corrected clock?

The point is to calculate the perceived velocities from both viewpoints. We can of course correct and calculate but this is not direct observational evidence. We may be making assumptions incorrectly.

[jeffreyH (OP)]

Say we have an object in a circular orbit around a dense mass. The clock on the surface of the central mass records the speed based one orbit of the object as s. The clock on the orbiting object records its speed as 1/2s since its clock is running twice as fast. Is this correct??