What is a tidal force?

A tidal force is the difference in gravitational pull across the diameter of a body. Because gravity weakens with distance, the side of a body closer to the source body experiences a stronger pull than the far side, creating a net stretching or compressing force.

What is the tidal force formula?

The standard approximation is F = 2GMmr/d³, where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), M is the mass of the source, m is the mass of the target body, r is the target radius, and d is the separation distance. It assumes r ≪ d.

Why does the formula use d³ instead of d²?

Regular gravity falls off as 1/d². The tidal force is the gradient (rate of change) of gravity across the body, which introduces an extra 1/d factor, giving the 1/d³ dependence. This makes tidal forces diminish much faster with distance than gravity itself.

What is the difference between tidal force and tidal acceleration?

Tidal force (F) is the total differential gravitational force on the target body, measured in Newtons. Tidal acceleration (a) is that force divided by the target mass (a = F/m = 2GMr/d³), measured in m/s². Tidal acceleration is useful when comparing distortions regardless of the target mass.

Why is Io so volcanically active?

Jupiter's enormous mass and Io's relatively close orbit produce extreme tidal forces. The competing tugs of Jupiter and other Galilean moons flex Io's interior, converting mechanical energy into heat — making Io the most volcanically active body in the solar system.

Does the formula break down at very close distances?

Yes. The formula F = 2GMmr/d³ is a first-order approximation valid when r ≪ d. For very close encounters (near the Roche limit), higher-order terms become significant and the approximation loses accuracy.

Tidal Force Calculator

Name: Tidal Force Calculator
Availability: InStock
Author: Nham Vu

Calculate the differential tidal force exerted by one astronomical body on another using F_tidal = 2GMmr/d³.

Source Body (M)

Quick Preset

Source Mass (M) (kg)

Target Body (m, r)

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Target Mass (m) (kg)

Target Radius (r) (km)

Separation Distance (d)

Center-to-center Distance (km)

Select source and target bodies,
enter separation distance, then click Calculate.

Summary