Tidal force

The tidal force on a celestial body is the gravitational force that emanates from another celestial body, delegated power. It is the difference between the force acting at any point of the celestial body, and expanded at its center of gravity of the acting force of gravity. Although it everywhere ( including inside the body ) occurs, with tidal power mostly acting on the surface meant. It is at those surface points facing or facing away from the other heavenly bodies, the largest and shows there away from the heavenly bodies. Mostly, the two bodies orbit each other, they form a two-body system.

The tidal force takes its name from the "maritime tides " discernible effects on the earth. Here the earth together with the moon and the sun with a three-body system. The greater proportion of this tidal effect of the moon.

The tidal force occurs between all celestial bodies, but only in large bodies or in gravitational fields with high spatial rate of change noticeable impact. An interaction between the planet and its host star, it is immediately apparent, under double stars or between interacting galaxies they can be specified theoretically, with larger periods must be taken into account here.

Formation and size of tidal power

Reference system outside of the observed celestial body

Instead of tidal power tidal acceleration is given quantitatively in the following, which caused a mass M located at a distance r celestial body with the diameter 2R. This is about:

The gravitational acceleration a of an object in an external gravitational field of the mass is given by M

With the gravitational constant G and the distance r of the center of mass to M.

A mass member on the body surface ( a distance R from the center of gravity), for simplicity lying on the connecting line between center of gravity and the mass, which produces the gravitational field acts to accelerate

Here r R is part of the point on the side facing away from the crowd, rR facing to the on her.

Since the movement of said mass member, however, is to refer to the movement of the body center of gravity, it undergoes the following relative acceleration ( acceleration tides ):

The approximation follows from the series expansion for R / r = 0 ( R << r) and abort after the linear term of

Tides acceleration facing away on both sides from the center of gravity. But it is on both sides not quite the same size, which is easy to recognize when terminating the derivation of the formula before the approximation used above.

The vivid effect of both sides facing away from the body center of gravity acceleration is the tide of the body forming an ellipsoid.

The tidal power scales with the cube of the distance from the center of gravity and falls off faster than the gravitational force, which scales quadratically. This results, for example, to the fact that the tidal forces of the moon much closer to the earth are larger than that of the sun, although this carries about 175 times the force of gravity on the ground. Compared to the moon the sun and some planets cause the following tidal effects on the Earth:

The tabulated deflection is the rise of the water level on the open sea.

On the other hand, the tidal power in proportion to the expansion of the body to which it is applied to. This is important, for example in the assessment of tidal effect on the outermost atmosphere of a planet, which may extend far into the room. In some considerations and rigid models of extended systems are formed. Example: If we take the two-body Earth-Moon system as a rigid rotating structure under the influence of the sun, then the tidal force caused by the sun acts on a system with a radius of 380,000 km.

A steep gravitational potential, as near small, very massive objects ( black hole, neutron star ) occurs, also causes strong tidal forces.

Considered celestial bodies as the reference system

The gravitational force on the celestial body is the radial force (generally on a curved path ) its motion on a circular path causes. On the orbiting celestial body, the centrifugal force is appropriately introduced, which makes the balance ( action equals reaction ) with the impressed force of gravity. In the circles of the celestial body (pictured left) is formed around the joint with the second celestial body center of gravity ( center of mass ) in each of its points a centrifugal force of the same magnitude (Figure right: circulation without rotation, also called the Revolution). This force is always directed away from the second celestial body.

The quantitative description is the same in this point of view with the above mentioned, since the centrifugal force has the same value as the average gravity there included in the comparison. This type of observation has only a descriptive advantage. It forms at the respective surface sites balances in there localized forces, because the centrifugal force is there also exists. The "naive" understanding that on the opposite him side could be no force in the opposite direction by attraction of the moon, will not overused, because on the moon side facing away from the attraction is smaller, but is surpassed by the force acting in the opposite direction centrifugal.

Roche limit

Main article: Roche limit

If the distance of a moon to its central body is very small, the tidal forces are very strong.

In order to investigate the stability of the body, looking at the tidal forces in comparison to the gravitational forces, which hold the body itself. The stability limit is in this case achieved when the tidal forces become greater than the gravitational forces, wherein the satellites are used to estimate divided into two partial bodies, each having half the satellite mass at a distance corresponding to its radius:

With the distance r from the central mass, C is hereby a constant of the order 1 with the average density ρ and ρt of the central body and of the satellite, as well as the radius R of the central body obtained

A more accurate calculation gives

At a distance of less than 2.44 times the radius of its central body a Trabant with the same density by tidal forces will be torn apart or can not only form itself. This distance is named after Édouard Albert Roche, who has carried out this assessment the first time Roche limit.

These considerations apply to larger bodies, which are held together by their own gravity (see dwarf planet ). For smaller bodies, the stability outweighs by cohesive forces. For artificial satellites of the cohesion by its own gravity plays no role.

Cosmic Examples

Saturn's rings lie largely within the Roche limit of Saturn. This is in addition to the shepherd moons, whose stability is increased by internal cohesive forces, the main reason for the stability of the ring system.

The comet Shoemaker- Levy 9 passed in July 1992, the planet Jupiter, and broke it into 21 fragments between 50 and 1000 m size, strung on a multi-million -kilometer-long chain. Between 16 and 22 July 1994, these fragments then beat on Jupiter.

In close encounters of stars with a distance which is less than the Roche limit, these are greatly changed in a so -called star collision, usually the smaller one is torn.

On Earth, the tides in the oceans to cause tides. However, the tides also act on the mantle itself, so that the continents themselves follow the tide with a delay of two hours, but the effect with vertical movements of 20 to 30 centimeters is significantly less than the several meters high tides in the oceans.

Due to the tides in large seas locally very strong currents can occur due to the tidal range. The leveraging existing kinetic energy can be used by means of a tidal power plant.

Tidal friction

The tidal forces slow down the rotation of the body involved, while the rotational angular momentum due to conservation of angular momentum is transferred to the orbital angular momentum of the moon. The mechanism for this is the following: Due to the tidal forces leads to a deformation of the central body (tidal mountains, ie tidal waves on Earth, but also the deformation of the solid Earth's surface due to the tides ). If the planet rotates faster than the moon orbits, these tides always move mountains "before" the moon. This is a consequence of the inertia of the masses on the central body ( in the general sense, not only of inertia in terms of conservation of momentum ). This leading tidal mountains cause a component in the gravitational force acting on the moon in the forward direction ( "forward" within the meaning of lunar cycle ). The so- supplied energy is immediately converted into potential energy, so that the moon is slowly but surely occupies a higher, slower orbit.

A tidal friction occurs conversely, on the orbiting moon.

This effect ultimately results in rotation of the attached small body as, for example, is the case with Earth's moon. If, during two bodies bound to a rotation, we speak of co-rotation.

As a further effect increases as the orbital angular momentum and having the same rotation direction, the spacing of the two bodies, when the rotation of the larger body is faster than the rotation of the lower body. Are orbital angular momentum and rotation opposite to what may occur, especially with the trapped bodies, or orbits of smaller bodies to larger faster it rotates as the distance is reduced, however.

In a more detailed analysis of energy and angular momentum in this process must be accounted for separately because each is a law of conservation of both quantities in physics. The following explanations go for better intelligibility of an isolated planet - from Moon system. This is not a complete model, as there are other planets, the sun can give (central star) and other external influences that would interfere with this system (see also perturbation theory (classical physics ) ).

Energy Conservation: The planet loses rotational energy through friction in the continuous formation of the tidal peaks ( deformation of the planet due to the tidal force), and by the transfer of energy to the moon due to the gravitational effect of the tides mountains. This energy is found in the rotational energy of the moon, a heating (heat energy) of the earth by friction, the currents in the Earth's interior (kinetic energy, Geodynamo ) and triggered by an MHD process changes in the magnetic field of the earth.

Conservation of angular momentum: The angular momentum loss during the deceleration of the Earth's rotation is transmitted to the earth on the angular momentum of the moon in its orbit around the Earth ( orbital angular momentum ), the angular momentum of flows within the Earth, and the Earth's magnetic field (electromagnetic field ).

Which of these forms of energy or angular momentum for a given planet Moon System of importance depends on the circumstances. Since it is generally processes in the field of magnetohydrodynamics under the influence of gravity, the task is usually not trivial.

For exotic constellations may need to be taken into account, can wear that even elementary energy and angular momentum ( particle ).

Effects summarized,

• The tidal forces on the earth lead to the maritime tides, where their name is derived. The almost rigid earth system remains largely unaffected, whereas the effect on the more mobile water on its surface is clear.
• By tidal forces deform the heavenly bodies, they can easily be pulled in the direction of the other body in the length. Rotates the heavenly bodies, it will be passed " by fulled ", similar to a flat tire on the car. Wherein rotational energy is converted into heat; this slows down the rotation so long to get up to synchronous rotation. The Earth's Moon always shows the earth due to this effect to the same page. When Jupiter 's moon Io are tidal forces that provide the thermal energy for the volcanism.
• In binary systems, tidal forces can cause a flow of matter from one star to another, which in certain cases to a supernova (type 1) may result.
• If the tidal forces stronger than the forces that hold an object, they can also lead to tearing of the object, as happened when the comet Shoemaker -Levy 9 (see Roche limit ).