Tidal force
Tidal force is a secondary effect of the force of gravity and is responsible for the tides. It results from the gravitational gradient that exists across a body's diameter. 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.
The tidal force in the equation of motion arises from subtracting a constant gravitational acceleration (that at the center of the smaller body due to the larger) and hence leads to a bulge on both sides of the smaller planet – see diagram. Consequently, the tidal forces exist independently of the motion of the two planets – in particular, their rotation has no effect on the tidal forces though it does, of course, strongly affect the actual tides.
Tidal forces arising from Newtonian gravity follow an approximate inverse cube law. Differentiating Newton's law of gravity with respect to distance gives:
- <math>
F_t = \frac{2GMmr} {R^3}
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where M is the mass of the primary body, m is that of the orbiting body, R is the orbital radius and r << R is the orbiting body's radius. The tidal forces experienced will be 2Ft outwards along the axis between the two bodies' centres of mass (at the secondary's "front" and "back"), and -Ft (inwards) on the plane perpendicular to this axis (that is, at the secondary object's poles).
Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes, where they are responsible for the "spaghettification" of infalling matter. 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. Tidal force is responsible for tidal locking.
See also
