Earth and Moon

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[edit] Tidal effects

The tides on Earth are mostly generated by the Moon's gravitation, with a less significant contribution by the Sun. These gravitational effects are specifically manifested as tidal forces. The combination of the two is responsible for spring and neap tides. Two tidal bulges, one in the direction of the Moon, and one in the opposite direction (figure 1) form as a result of the tidal forces. The buildup of these bulges and their movement around the earth causes an energy loss due to friction. The energy loss decreases the rotational energy of the Earth.

Since the Earth spins faster than the Moon moves around it, the tidal bulges are dragged along with the Earth's surface faster than the Moon moves, and move "in front of the Moon" (figure 2). Because of this, the Earth's gravitational pull on the Moon has a component in the Moon's "forward" direction with respect to its orbit. This component of the gravitational forces between the two bodies acts like a torque on the Earth's rotation, and transfers angular momentum and rotational energy from the Earth's spin to the Moon's orbital movement.

Because the Moon is accelerated in the forward direction, it moves to a higher orbit. As a result, the distance between the Earth and Moon increases, and the Earth's spin slows down (figure 3). Measurements reveal that, at present, the Moon's distance to the Earth increases by 38 mm per year (as determined by lunar ranging experiments with laser reflectors left during the Apollo missions. Atomic clocks also show that the Earth's day lengthens by about 15 microseconds (µs) every year. The formation of tidal bulges on Earth (and the resulting frictional energy loss) is irregular because continents on Earth hamper the buildup of tidal bulges (figure 4).

This tidal drag will continue until the spin of the Earth has slowed to match the orbital period of the Moon, at which time the tidal effect of the Sun will dominate, further slowing the Earth and thereafter causing the orbit of the Moon to steadily shrink. However, long before this could happen, the sun will have become a red giant and either engulfed the earth and moon or blown them into the outer solar system.

The lunar surface is also subjected to tides from earth, and rises and falls by around 10 cm over 27 days. Because the Moon keeps the same face turned to the Earth but not to the Sun, the lunar tides are comprised of a selenographically changing component (due to the Sun), and a fixed one (due to Earth). The vertical motion of the Earth-induced component arises from the Moon's orbital eccentricity; if the Moon's orbit were perfectly circular, there would be solar tides only.

The magnitude of the Moon's tides corresponds to a Love number of 0.0266, and supports the idea of a partially melted zone around its core. Moonquake waves lose energy below 1,000 kilometres in depth, and this may also show that the deep material is at least partially melted. The Earth’s Love number is 0.3, corresponding to a movement of 0.5 metres per day; for Venus the Love number is also 0.3.^[1]

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