Tidal force

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 which 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 the earth is on the order of $\scriptstyle 2.2\times 10^{-}6{\frac {m}{s^{2}}}$. (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 the earth on the moon is much greater: about $\scriptstyle 4.9\times 10^{-}5{\frac {m}{s^{2}}}$.

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 the 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 the 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 the earth, and irregularities in the composition of the earth and the hydrosphere). The solid mass of the earth is similarly elongated, but by a smaller amount, approximately 0.7 metres elongation and narrowing, due to the rigidity of the earth as compared to the hydrosphere.

Due to the rotation of the earth relative to the moon, the points on the earth which 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 the 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. This is significantly complicated by the shape of the ocean shoreline, and by the Sun, which exerts a tidal force on the earth about $\scriptstyle 1.0\times 10^{-}6{\frac {m}{s^{2}}}$, about 45% that of the moon, but usually acting in a different direction.