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Because the Moon's mass is a considerable fraction of that of the Earth (about 1:81), the two bodies can be regarded as a double planet system, rather than as a planet with a satellite. This is apparent from the fact that the plane of the Moon's orbit around the Earth lies close to the plane of the Earth's orbit around the Sun (the ecliptic), rather than in the plane perpendicular to the axis of rotation of the Earth (the equator) as is usually the case with planetary satellites. Hence the Earth and Moon orbit the Sun together.
The mass of the Moon is sufficiently large and it is sufficiently close to raise tides in the Earth: the matter of the Earth, in particular the water of the oceans, bulges out to the direction of the Moon (and opposite to it). This follows the Moon in its orbit, which takes about a month. The Earth rotates under this tidal bulge in a day. The actual matter of waters rotate with the Earth, but they rise and fall as the Moon comes overhead. However, the rotation drags the position of the tidal bulge about 2° ahead of the position directly under the Moon. As a consequence, there exists a substantial amount of mass that is offset from the line through the centers of the Earth and Moon. This mass exerts a gravitational pull on the Moon, and hence accelerates it in its orbit. Conversely, the gravitational pull from the Moon on this mass exerts a torque that decelerates the rotation of the Earth.
As in all physical processes, angular momentum and energy are conserved. So the orbital angular momentum of the Moon increases, while it moves away from the Earth. As it stays in orbit, it follows from Kepler's 3rd law that its velocity decreases: so the tidal acceleration of the Moon is an apparent deceleration of its motion across the celestial sphere. As its kinetic energy decreases, its potential energy increases.
As a consequence, the rotational angular momentum of the Earth decreases: its rotation slows down, and the length of the day increases. The corresponding rotational energy dissipates through friction of the tidal waters along shallow coasts, and is lost as heat.
This mechanism must have been working for 4.5 billion years, since oceans formed on the Earth. There is geological evidence that the Earth rotated faster and that the month was shorter (so the Moon was closer) in the remote past.
This process will continue until in the remote future the rotational period of the Earth is the same as the orbital period of the Moon. At that time, the Moon will always be overhead the same place on Earth. Note that in the converse situation, the stronger tidal forces of the Earth working on the solid Moon already have locked its rotation to its orbital period: the Moon always turns the same face to the Earth.
The Pluto- Charon system is another example of a double planet system in our solar systemA generic solar system (or planetary system consists of at least one star and various orbiting objects (such as asteroids, comets, moons, and planets). The term originated to describe the planetary system around Sol, the Latin name for our sun. The planet that went through tidal evolution of the orbit and rotation of its components. This system already has completely evolved, and both components always turn the same side to each other. Also see tidal lockingA separate article treats the phenomenon of tidal resonance in oceanography. See the article tidal acceleration for a more quantitative description of the Earth-Moon system. Tidal locking makes one side of an astronomical body always face another, like th.
The tidal acceleration is one of the few examples in the dynamics of the solar systemA generic solar system (or planetary system consists of at least one star and various orbiting objects (such as asteroids, comets, moons, and planets). The term originated to describe the planetary system around Sol, the Latin name for our sun. The planet of a truly secular effect, i.e. a perturbation of an orbit that continuously increases with time and is not periodic. Up to a high order of approximation, mutual gravitationalThis article covers the physics of gravitation. See also gravity (disambiguation). Gravitation is the tendency of masses to move toward each other. The first mathematical formulation of the theory of gravitation was made by Sir Isaac Newton and proved ast perturbations of planetA planet (from the Greek , planetes or "wanderers") is a body of considerable mass that orbits a star and that produces very little or no energy through nuclear fusion. Prior to the 1990s only nine were known (all of them in our own solar system); as of 3s only cause periodic variations in their orbits, i.e. it oscillates between maximum values. The tidal effect gives rise to a quadratic term, which grows forever. In the mathematical theories of the planetary orbits that form the basis of ephemerides, quadratic and higher order secular terms occur: but these are mostly Taylor expansionsIn mathematics, the Taylor series of an infinitely often differentiable real (or complex) function f defined on an open interval a − r a + r is the power series : Here, n is the factorial of n and f n a denotes the n''th derivative of f at the point of very long time periodic terms.
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