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Relativistic effects are measurable with accurate enough clocks in earth satellites (or even just taking a clock to a mountain) and correction is necessary in systems with finicky time requirements like GPS.

Incidentally, the relative speed you can napkin math estimate - an object in orbit flying that close to the planet is going to have escape-velocity-ish speed. It's around 60km/sec for Jupiter.

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> taking a clock to a mountain

http://www.leapsecond.com/great2005/tour/

They also did the First Atomic Clock Wristwatch...

http://leapsecond.com/pages/atomic-bill/

Fantastic! Has this been shared on HN before?

> We would come back about 20 ns older compared to her [the wife who stayed behind].

≥ Or, the other way to look at it (since this is relativity after all), is that she would become 20 ns younger than us upon our return. Note to husbands: this could be a useful gift idea for your wife.

It has, in the HN equivalent of the Archean eon

https://news.ycombinator.com/item?id=598090

By now I think they managed to measure relativistic effects of clocks that are a few milimeters apart in terms of distance from earths gravitational center.

Sufficiently clever experimentalists also pulled this off in about 20 meters in 1959, the clever bit being ditching the clocks entirely:

https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment

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