Reading this tutorial answer on models of Earth's gravity field I was realized that I'd never thought of it as time dependent. According to it, the biggest short term changes in the shape of Earth's gravity field in LEO space is the movement of the tides.

It got me wondering, if that question were relaxed and it asked about the total gravity field of the Earth-Moon system, what gravitational force would tend to perturb LEO satellites more, the modulation of Earth's gravity field due to the movement of the tides, or the gravity field of the Moon (which is also causing those tides)?

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    $\begingroup$ The tides are not only caused by the Moon, there is an influence of the Sun too. But on the oceans far away from the coasts, the tides are small, about 0.8 m. 10 to 15 m difference are possible only in small areas at the coast. $\endgroup$ – Uwe Jun 10 '17 at 21:52
  • $\begingroup$ @Uwe Force goes as $1/r^2$ also and tidal bulge is 500 times closer than the moon, but alas, it's not enough to make up for the smaller mass. $\endgroup$ – uhoh Jun 11 '17 at 1:41

The Moon's gravitational field itself, by far. The perturbations on a satellite due to the reshaping of the Earth due to the Moon and Sun's gravity fields are small effects.

The primary impact of this secondary tidal effects is a slight change in $J_2$ ($C_{2,0}$). A description of how the Earth tides affect the gravitational field is in section 6.2 of IERS Technical Note 36. The next section (6.3) covers the impacts of ocean tides. These are smaller yet.

  • $\begingroup$ That looks like a particularly interesting document, will enjoy it over coffee tomorrow. Thanks! $\endgroup$ – uhoh Jun 10 '17 at 20:31

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