Pounded into a keyboard by monkeys assisted by: David Morgan-Mar
The author writes:
Okay. With no numbers:
Picture the Moon in orbit around the Earth. The Earth's mass exerts a gravitational force on the Moon. But the force of gravity always decreases with distance. Hence the Earth is pulling a little bit harder on the side of the Moon closest to it than on the side of the Moon that's furthest away. That difference acts like a force that's trying to pull the Moon apart. The Moon's body responds by stretching and flexing slightly, producing measurable bulges that point toward and away from the Earth.
The same thing happens because of the Moon's gravity acting on the Earth, of course. The Earth's rocky body shifts slightly in the course of each day, causing the surface under our feet to rise and fall a couple of inches as we rotate under the Moon. The oceans, being much less rigid, respond much more definitely; the result is the ocean tide that's familiar to anyone who's spent time at the beach.
Hence, all the phenomena related to this differential gravity pull are called "tidal effects."
Okay, now consider the bulge in the Earth's body that results from the lunar tides. There's always a slight delay in the rise and fall of material - not even the oceans respond instantly as they are rotated under and then away from the Moon. Since the Earth is spinning faster than the Moon orbits, the bulge is always slightly ahead of the line between Earth and Moon (not behind, as you might expect). The Moon pulls on this bulge, trying to haul it back into alignment with the Earth-Moon line. This effect tends to slow the Earth's rotation with respect to the Moon. Over time, and if nothing else intervenes, the Earth's rotation will slow to a stop with respect to the Moon.
Of course, the Earth's pull on the Moon is much stronger than the Moon's pull on the Earth - and the tidal effects are correspondingly stronger. Although the Earth still rotates with respect to the Moon, the Moon no longer rotates with respect to the Earth. Hence the Moon always presents (more or less) the same face to us. That's a "tidal lock."
Another effect of the tidal bulge that the Moon produces on the Earth: just as the Moon pulls on the tidal bulge, the bulge pulls on the Moon. This tends to accelerate the Moon slightly in its orbit, which in turn causes the Moon's orbit to get wider. This effect has actually been measured, by instruments used during the Apollo missions; the rate at which the Moon's orbit is growing wider is on the order of a few inches per year. Another tidal effect.
Okay, now the "Roche Limit." The astronomer and mathematician Édouard Roche observed that since the tidal "force" grows stronger as you get closer to a planet, and since the rocky materials that make up a moon don't have infinite tensile strength, it's reasonable to assume that if a moon came too close to its primary planet, the tidal "force" would actually tear it apart. Roche calculated the distance at which this would probably occur, given reasonable assumptions for the mass and composition of both bodies - that distance is the Roche limit.