> However, when you look at the actual accelerations involved the moon is much more attracted to the earth (by over 100x) than it is to the sun
Your "over 100x" figure is entirely made up. The correct answer is 0.46.
Depth of the well does not matter, it is the steepness of the well. In other words, what is pulling the hardest on the Moon. The Sun pulls twice as hard as the Earth, so there is a compelling argument that the Sun is the Moon's primary.
The black hole at the center of the Milky Way is (rounding up for your benefit) 4 million solar masses and 27000 ly away. But that inverse square law really hurts and the Sun's gravitational force is 733e15 times stronger than the black hole's.
Let's step it up and include all 10 billion solar masses in the center. The Sun is still ahead by a factor of 290 trillion. The galactic core has almost no effect on the solar system, so it is silly to claim that any planetary body orbits the core.
Regarding tidal lock, the force of tidal lock is (more or less) proportionate to gravitational force * angular velocity. While the Earth's gravitational force on the Moon is half as strong as the Sun's, the relative angular velocity is 12 times faster. So the Earth's tidal forces on the Moon are six times stronger than those of the Sun. Naturally, the Moon is tidal locked to the Earth.
Your "over 100x" figure is entirely made up. The correct answer is 0.46.
Depth of the well does not matter, it is the steepness of the well. In other words, what is pulling the hardest on the Moon. The Sun pulls twice as hard as the Earth, so there is a compelling argument that the Sun is the Moon's primary.
The black hole at the center of the Milky Way is (rounding up for your benefit) 4 million solar masses and 27000 ly away. But that inverse square law really hurts and the Sun's gravitational force is 733e15 times stronger than the black hole's.
Let's step it up and include all 10 billion solar masses in the center. The Sun is still ahead by a factor of 290 trillion. The galactic core has almost no effect on the solar system, so it is silly to claim that any planetary body orbits the core.
Regarding tidal lock, the force of tidal lock is (more or less) proportionate to gravitational force * angular velocity. While the Earth's gravitational force on the Moon is half as strong as the Sun's, the relative angular velocity is 12 times faster. So the Earth's tidal forces on the Moon are six times stronger than those of the Sun. Naturally, the Moon is tidal locked to the Earth.