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I know theoretically it should decrease with $r^2$ increasing in the denominator of the equation, but has any experiment confirmed that this is approximately the change in gravity with altitude variation?

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    $\begingroup$ Related: physics.stackexchange.com/q/22010/2451 and links therein. $\endgroup$
    – Qmechanic
    Nov 7, 2021 at 18:02
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    $\begingroup$ We've been putting things in high and low orbits around our planet, sending them, to the moon and to other planets and the Sun for quite a while. Pretty sure that proves it. $\endgroup$ Nov 7, 2021 at 18:02

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Every precision measurement of the moon's orbital dynamics uses that relationship. If it were wrong, so would be those measurements.

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  • $\begingroup$ Actually special and general relativity corrections are needed for the gps that depends on the satellites , so there is measurable deviation astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html to the 1/r2 $\endgroup$
    – anna v
    Nov 7, 2021 at 18:17
  • $\begingroup$ @annav The article to which you referred addresses how clocks ticking at different rates due to altitude and orbital speed. Corrections to the orbit itself due to relativity do exist but are very small. $\endgroup$ Nov 7, 2021 at 18:34
  • $\begingroup$ @DavidHammen sure, these are very small also, but measurable, $\endgroup$
    – anna v
    Nov 7, 2021 at 19:55

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