[theophrastus]

I always thought it would be an interesting physics exam question to ask: "If a clock were landed on Halley's comet, and retrieved on its next orbit, what would be the expected difference in time relative to an earth bound clock?" It's tricky because all orbiting bodies experience a range of velocities as they orbit their star. But I gather Halley's comet has a particularly eccentric orbit (0.9) with a rapid perihelion of around 70km/sec, an aphelion of about 1km/sec, and about 75 years for a single orbit (ΔT' = ΔT / sqrt(1 - (v²/c²)))

[contravariant]

That would be one hell of an exam question.

Best method I can think of is to measure the proper time of both the trajectory of the earth and the trajectory of Halley's comet, and compare, but with the combined effects of gravity and a changing speed that could be quite challenging.

It's even worse if you insist on using geodesics instead of elliptical orbits, or if you decide to include the rotation of the earth in your calculations.