Tidal force

A tidal force is the differential gravitational force experienced by an extended body in the presence of a non-uniform gravitational field. It arises because the gravitational attraction from a distant mass (like the Moon or Sun) is stronger on the side of the body facing the mass and weaker on the opposite side. This difference in force stretches the body along the line connecting the two centers and compresses it in the perpendicular direction.¹

Mathematically, the tidal acceleration at a point is the gradient of the gravitational field. For a body of radius R at a distance r from a mass M, the tidal acceleration is approximately 2GM R / r³. This inverse-cube dependence means that tidal forces diminish rapidly with distance, making them significant only for close encounters or large bodies.

The Moon's tidal force is the primary cause of Earth's ocean tides. The Moon's gravitational pull creates two tidal bulges: one on the side facing the Moon and one on the opposite side, due to the centrifugal force from the Earth–Moon system's rotation. As Earth rotates, these bulges move around the planet, producing high and low tides approximately every 12 hours and 25 minutes.²

The Sun also exerts a tidal force on Earth, about half as strong as the Moon's. When the Sun, Moon, and Earth align (during new and full moons), their tidal forces combine to produce spring tides with higher high tides and lower low tides. When they are at right angles, neap tides occur with smaller tidal ranges.³

Tidal forces deform solid bodies, causing tidal bulges that can lead to tidal heating. On Jupiter's moon Io, tidal flexing generates immense internal heat, driving volcanic activity. On Earth, the solid Earth experiences tidal deformation of about 30 cm, which is measurable with sensitive instruments.

Tidal forces also cause tidal locking, where a body's rotation period matches its orbital period, always showing the same face to its primary. The Moon is tidally locked to Earth, and many exoplanets in close orbits are likely tidally locked to their stars.⁴

In astrophysics, tidal forces play a crucial role in many phenomena. They can disrupt comets and asteroids passing close to planets, as seen with Comet Shoemaker-Levy 9, which was torn apart by Jupiter's tidal forces before impacting the planet in 1994. Tidal forces also drive the spiral structure of galaxies, as galaxies exert tidal forces on each other during close encounters, distorting their shapes and triggering star formation.

Near black holes, tidal forces become extreme, leading to spaghettification, where an object is stretched into a long thin shape before being torn apart. This process is a key source of accretion disk material and is studied in the context of tidal disruption events.

Beyond the familiar ocean tides, tidal forces have subtle and surprising effects. For instance, the Moon's tidal force causes the Earth's crust to flex, generating 'earth tides' that can influence volcanic eruptions and earthquake activity.⁵ Tidal forces also affect the orbits of satellites: the Moon's tidal force gradually increases the Earth–Moon distance by about 3.8 cm per year, while slowing Earth's rotation.

In the solar system, tidal forces are responsible for the rings of Saturn and the ice geysers of Enceladus. The tidal heating of Enceladus powers its subsurface ocean and cryovolcanic plumes.⁶ Tidal forces also influence the internal structure of planets, potentially affecting their magnetic fields and thermal evolution.

One of the most extreme tidal environments is the binary neutron star system, where tidal forces can deform the stars and emit gravitational waves, as detected by LIGO in 2017.⁷

Tidal bulge

A deformation of a body caused by tidal forces, resulting in a slight elongation along the line to the attracting mass.

Tidal locking

A state where a body's rotation period equals its orbital period, causing it to always show the same face to its primary.

Spaghettification

The stretching of an object into a long thin shape due to extreme tidal forces, typically near a black hole.