[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.