Tidal Force Calculator
Calculate the gravitational force between two celestial bodies separated by a given distance. Useful for understanding tidal interactions, orbital dynamics, and the gravitational pull between moons, planets, and stars.
About this calculator
This calculator computes the gravitational force between two bodies using Newton's Law of Universal Gravitation: F = G × M × m / r², where F is the force in newtons, G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), M and m are the masses of the two bodies in kilograms, and r is the distance between their centres. Note that the distance input is in kilometres and must be interpreted accordingly in the formula. This force is symmetric — body A pulls body B with the same magnitude as body B pulls body A. In the context of tidal forces, what matters is the difference in this force across the diameter of a body, but the raw gravitational force computed here is the foundational quantity. It governs orbital dynamics, tidal locking, and the stability of planetary systems.
How to use
Consider the gravitational force between Earth (M = 5.972 × 10²⁴ kg) and the Moon (m = 7.342 × 10²² kg) at a distance of 384,400 km. Using F = G × M × m / r²: numerator = 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 7.342 × 10²² ≈ 1.982 × 10³⁷ × 6.674 × 10⁻¹¹ ≈ 2.923 × 10³⁷ × 10⁻¹¹. Denominator = (384,400,000)² ≈ 1.478 × 10¹⁷. F ≈ 2.923 × 10²⁶ / 1.478 × 10¹⁷ ≈ 1.98 × 10²⁰ N. Enter both masses in kilograms and the separation distance in kilometres to get the force in newtons.
Frequently asked questions
How does distance affect the gravitational tidal force between two bodies?
Gravitational force follows an inverse-square law: F = GMm/r². Doubling the distance reduces the force by a factor of four; tripling it reduces it by nine. This strong distance dependence means tidal effects fall off rapidly as bodies move apart. For example, the Moon's tidal influence on Earth's oceans would be drastically weaker if the Moon were twice as far away. In close binary star systems or planets near massive gas giants, tidal forces can be extreme enough to deform the shape of the smaller body or generate significant internal heating through tidal flexing.
What is the difference between gravitational force and tidal force?
Gravitational force is the total attractive force between two bodies as given by F = GMm/r². Tidal force, strictly speaking, is the differential gravitational force — the difference in gravitational pull felt across the diameter of the secondary body. The near side of the Moon is pulled more strongly than the far side, creating a stretching effect. Tidal force scales as 2GMmΔr/r³, where Δr is the body's radius. This calculator computes the total gravitational force, which is the basis from which tidal differentials are derived. Both quantities are essential in understanding oceanic tides, tidal locking, and the Roche limit.
Why are tidal forces important in planetary and stellar science?
Tidal forces shape planetary systems in profound ways. They are responsible for tidal locking — the reason one side of the Moon always faces Earth. They drive volcanic activity on Jupiter's moon Io by flexing its interior. They govern the Roche limit, inside which a satellite is torn apart rather than held together by its own gravity. In stellar binaries, extreme tidal forces can transfer mass between stars. Even Earth's ocean tides, driven by the Moon and Sun's gravity, have gradually slowed Earth's rotation over billions of years. Understanding tidal forces is therefore central to planetary geology, orbital evolution, and habitability studies.