The original question was: If a machine enclosed in a building could, as I think it could, detect the tidal forces of the sun and moon upon the Earth could the effect be used to extract useful energy from those forces and what would the effect be on the motion of the Earth?
Physicist: “Useable” energy; yes. But probably not too useful. You can calculate the maximum total energy caused by lunar and solar tides on something the size and mass of a building, and you find that it’s really, really tiny.
To generate power from tidal forces directly, in a self contained building, you’d want to lift something very heavy when the gravity is “turned down”, and then lower it and generate power when gravity is “turned up”. That difference is not big. It’s about 1 part in 3 million at best (even less for the Sun). Unfortunately, motors and generators that are more than 99.99996% efficient just aren’t made, so that tiny “1 part in 3 million” may as well be zero since it won’t cover energy lost to inefficiency.
A building the size of the Burj Khalifa could generate an absolute maximum of around 100MJ of energy, twice daily (two tides), using perfectly efficient machines. It would just be a huge block of iron that is lifted and dropped at the right times. So under unrealistically ideal conditions, such a building could daily provide electricity to the United States for not quite half a millisecond.
However, it is both possible and feasible to harvest the tide for power. Basically you find a bay with a single small inlet and you put free flow hydroelectric turbines in the inlet to catch the ocean tide flowing in and out. You don’t have to build a huge weight and a bunch of machines to raise and lower it, you just anchor some turbines on the bottom of a bay. Much easier. There are a bunch of these already in use, and they tend to be far more compact and powerful than wind turbines. Water, being denser, carries a lot more energy and packs a much bigger punch than air.
Ultimately, all of the energy gained from tidal forces has to come from somewhere, and that somewhere is the rotational kinetic energy of the Earth. So, when you generate power from tides you literally slow the Earth down. But that slowing isn’t something to worry about. The oceans, and the crust of the Earth itself, are already doing more than their part.
Right now the “tidal bulge” of the Earth leads the Moon (just because it takes a little time for things to move around), and the effect of this is to slow the rotation of the Earth while speeding up the Moon’s orbit.
Every attempt to harvest energy from the tide comes down to keeping extra mass higher than it “should” be for a little extra time, and this amounts to making the tidal bulge just a tiny bit bigger. But even if we “captured the tide” along every coast in the world, our efforts would be statistical noise compared to the sloshing of the entire ocean.