Tidal Force Calculator

Compute the tidal acceleration the Moon and Sun exert on Earth via a=2GMr/d3, with the Moon to Sun tidal ratio and spring and neap combinations.

Input

From the masses and distances of the Moon and Sun and the Earth radius, find the tidal acceleration a = 2GMr / d^3 at the Earth surface. The default values can be changed.

Earth radius r

Mean radius of the Earth. Default is 6.371e6 m.

Moon (perturbing body)

Moon mass M

Mass of the Moon. Default is 7.342e22 kg.

Distance to the Moon d

Mean distance from Earth center to the Moon. Default is 3.844e8 m.

Sun (perturbing body)

Sun mass M

Mass of the Sun. Default is 1.989e30 kg.

Distance to the Sun d

Mean distance from Earth center to the Sun. Default is 1.496e11 m.

Result

Tidal acceleration of the Moon

1.0992×10^-6m/s²

Tidal acceleration of the Sun

5.052×10^-7 m/s²

Tidal ratio (Moon / Sun)

2.175826 times

Solar tide (Moon = 1)

0.459595

Spring tide (alignment)

1.6044×10^-6 m/s²

Neap tide (quadrature)

5.9403×10^-7 m/s²

Spring / neap ratio

2.700931 times

The tidal acceleration is approximated by a = 2GMr / d^3 with G = 6.674e-11, and excludes ocean and terrain effects.

How it works

The tidal acceleration is approximated by a = 2GMr / d^3, using the perturbing body mass M, the distance d from Earth center, and Earth radius r.
Gravitational constant G = 6.674e-11 N m^2 / kg^2 is used.
Default: mean Earth radius r = 6.371e6 m.
Default: Moon mass = 7.342e22 kg, mean Moon distance = 3.844e8 m.
Default: Sun mass = 1.989e30 kg, mean Sun distance = 1.496e11 m.
Spring tide (alignment) is when the Moon and Sun reinforce each other, combined as a_moon + a_sun.
Neap tide (quadrature) is when the solar contribution partly cancels, combined as the absolute difference of a_moon and a_sun.
This formula is the leading term of the gravity difference between Earth center and the sub body point, and excludes ocean, terrain, and friction effects.

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