Tidal force

The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force exerted by one body on another is not constant across it: the nearest side is attracted more strongly than the farthest side. Thus, the tidal force is differential. Consider the gravitational attraction of the Moon on the oceans nearest to the Moon, the solid Earth and the oceans farthest from the Moon. There is a mutual attraction between the Moon and the solid Earth, which can be considered to act on its centre of mass. However, the near oceans are more strongly attracted and, especially since they are fluid, they approach the Moon slightly, causing a high tide. The far oceans are attracted less. The attraction on the far-side oceans could be expected to cause a low tide, but since the solid Earth is attracted (accelerated) more strongly towards the moon, there is a relative acceleration of those waters in the outwards direction. Viewing the Earth as a whole, we see that all its mass experiences a mutual attraction with that of the Moon, but the near oceans more so than the far oceans, leading to a separation of the two.

In a more general usage 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 so-called 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.

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