Tidal force

The tidal force or tide-generating force is the difference in gravitational attraction between different points in a gravitational field, causing bodies to be pulled unevenly and as a result are being stretched towards the attraction. It is the differential force of gravity, the net between gravitational forces, the derivative of gravitational potential, the gradient of gravitational fields. Therefore tidal forces are a residual force, a secondary effect of gravity, highlighting its spatial elements, making the closer near-side more attracted than the more distant far-side.

This produces a range of tidal phenomena, such as ocean tides. Earth's tides are mainly produced by the relative close gravitational field of the Moon and to a lesser extent by the stronger, but further away gravitational field of the Sun. The ocean on the side of Earth facing the Moon is being pulled by the gravity of the Moon away from Earth's crust, while on the other side of Earth there the crust is being pulled away from the ocean, resulting in Earth being stretched, bulging on both sides, and having opposite high-tides. Tidal forces viewed from Earth, that is from a rotating reference frame, appear as centripetal and centrifugal forces, but are not caused by the rotation.

Further tidal phenomena include solid-earth tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. Tidal forces have also been shown to be fundamentally related to gravitational waves.

In celestial mechanics, the expression tidal force can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Earth), but is also perturbed by the gravitational effects of a third body (for example, the Moon). The perturbing force is sometimes in such cases called a tidal force (for example, the perturbing force on the Moon): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.

When a body (body 1) is acted on by the gravity of another body (body 2), the field can vary significantly on body 1 between the side of the body facing body 2 and the side facing away from body 2. Figure 2 shows the differential force of gravity on a spherical body (body 1) exerted by another body (body 2).

These tidal forces cause strains on both bodies and may distort them or even, in extreme cases, break one or the other apart. The Roche limit is the distance from a planet at which tidal effects would cause an object to disintegrate because the differential force of gravity from the planet overcomes the attraction of the parts of the object for one another. These strains would not occur if the gravitational field were uniform, because a uniform field only causes the entire body to accelerate together in the same direction and at the same rate.

The relationship of an astronomical body's size, to its distance from another body, strongly influences the magnitude of tidal force. The tidal force acting on an astronomical body, such as the Earth, is directly proportional to the diameter of the Earth and inversely proportional to the cube of the distance from another body producing a gravitational attraction, such as the Moon or the Sun. Tidal action on bath tubs, swimming pools, lakes, and other small bodies of water is negligible.

Figure 3 is a graph showing how gravitational force declines with distance. In this graph, the attractive force decreases in proportion to the square of the distance (Y = 1/X²), while the slope (Y′ = −2/X³) is inversely proportional to the cube of the distance.