Tidal force

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Tidal force is a secondary effect of the force of gravity. When a large body is acted on by the gravity of another body, the difference in the gravitational force can vary considerably between the near side and the far side. This tends to distort the shape of the large body without altering its volume; supposing it were initially a sphere, the tidal force will tend to distort it into an ellipsoid, with two bulges, pointing towards and away from the other body.

Tidal forces follow an inverse cube law. The exact tidal force at any point is described by the Weyl tensor. However, an approximation is often useful. Differentiating Newton's law of gravity with respect to distance gives:

  Ft = GMml / r3,  dr << r

where M is the mass of the primary body, m is that of the orbiting body, r is the orbital radius, and l is the distance from the center of mass of the orbiting body. The tidal forces experienced will be 2Ft outwards along the axis between the two bodies' centers of mass, and -Ft (inwards) on the plane perpendicular to this axis.

Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes. Tidal forces are also responsible for the oceanic tides, where the large body is the water in Earth's oceans, and the attracting bodies are the Moon and the Sun.