# Tidal force

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Tidal force is a pseudoforce within an object resulting from the differential in gravitational force experienced at different distances from a massive object. Tidal forces are experienced as a force that causes elongation of an object in the direction of a massive object.

Theoretically, all objects cause tidal forces in all other objects, but due to the weakness of gravitational forces, tidal forces are normally only considered with planetary or larger masses and objects kilometers across. For example, the tidal force induced by the Moon on Earth is on the order of ${\displaystyle \scriptstyle 2.2\times 10^{-}6{\frac {m}{s^{2}}}}$. (This is technically the difference in acceleration towards the moon of an object on the point on Earth nearest the moon and an object on the point on Earth furthest from the moon.) The tidal force exerted by Earth on the moon is much greater: about ${\displaystyle \scriptstyle 4.9\times 10^{-}5{\frac {m}{s^{2}}}}$.

## Tides on Earth

Tidal forces cause distortion in the shapes of astronomical objects, because no object is truly rigid. The tidal force of the moon causes the hydrosphere of Earth to elongate about 2 metres in the direction of the moon and to narrow about 2 meters at a ring where the hydrosphere is about the same distance from the moon as the center of Earth. (To simplfy, one can say that the hydrosphere is drawn into an ellipsoid with the axis pointing towards the moon being about 4 meters longer than the other two axes, but the hydrosphere would not be truly spherical in the absence of the moon, due to the rotation of Earth, and irregularities in the composition of Earth and the hydrosphere). The solid mass of Earth is similarly elongated, but by a smaller amount, approximately 0.7 metres elongation and narrowing, due to the rigidity of Earth as compared to the hydrosphere.

Due to the rotation of Earth relative to the moon, the points on Earth that are the most elongated move in a cycle about 24 hours and 50 minutes long. In each cycle, the peak elongation occurs twice. As the elongation of the hydrosphere (oceans) is greater than the elongation of the solid body of Earth, what is experienced on Earth is a rise and fall of the level of the ocean, with peaks about 12 hours and 25 minutes apart, which is commonly known as a tide. This is significantly complicated by the shape of the ocean shoreline, and by the Sun, which exerts a tidal force on Earth about ${\displaystyle \scriptstyle 1.0\times 10^{-}6{\frac {m}{s^{2}}}}$, about 45% that of the moon, but often acting in a different direction.

## Tidal locking

If one object is rotating as well as elongated due to tidal forces from a second astronomical object, the rotation causes the elongation to move slightly out-of-line from the second object. When this happens, the gravitational pull from the second object on the elongation causes a retarding torque on the first object, slowing its rotation. Eventually, the first object is rotating just enough to keep the same side always facing the second object as it orbits. This is why the same side of the Moon is always facing Earth.