Originally Posted by
Tourist
I would suggest that anything that can make squillions of tons of water and earth move up and down meters is relevant....
And I would suggest that you are making some rather broad and incorrect assumptions here.
As Awblain said, the amount the effective gravity changes at the earth's surface due to lunar and solar effects is about one ten-millionth of total gravity. Yes, it is sufficient to cause tides. No, it ain't gonna make much difference in how fast an object falls. For an object of say 10 kg, that means it's weight will vary between 98 newtons and 98.000001 newtons. For a falling object, the effects are the difference between and acelelration of 9.8 m/sec/sec and 9.80000001 m/sec/sec.
The difference is very small, and orders of magnitude below the noise level for something like predicting falling debris.