Do gyroscopes prove that the earth is moving?

You cannot prove too much with a gyroscope; all you can prove is that there are forces external to the gyroscope that control its angular momentum. That is why gyroscopes work in airplanes: as the gyroscope rotates it connects with an external force that keeps the plane on course. The question is, what is that force? To the heliocentric system it is mysterious; to the geocentric system it is not, because we know these external forces are real, the inertial forces. In order for the gyroscope to move against something, it has to be connected to it, and when it rotates it connects with the centrifugal, Coriolis, and Euler forces, which together give the inertial frame of reference. Now the Coriolis force is 2 omega cross V, so it needs a velocity, unlike the centrifugal force, and that velocity cannot come from a merely rotating universe; it requires an inertial separation from a non-moving substance. We explain this by a Planck medium that is the non-moving inertial background against which the universe of stars, galaxies, and gases rotates. The universe has more mass on one side than the other, so when it rotates it precesses, wobbling horizontally and vertically like a free-floating gyroscope, and that double precession, spiraling the sun through 47 degrees, is what makes our seasons.