Tidal Forces2
of the Moon and the Sun

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First created: Sun Jun 3 2001
Last update: Sun Jul 15 2001

Gravitation And Tidal Forces

The gravitational origin of tides follows from Newton's theory of gravitation, whereby gravitational acceleration is proportional to mass and inversely proportional to distance squared. If g is the acceleration from Earth's gravity at the surface of the Earth, then the maximum acceleration from the Moon's tidal action is 1.1*10-7g. The maximum acceleration from both the Moon's and the Sun's tidal action is 1.6*10-7g.


The altitude and azimuth of the Moon and the Sun can be accurately calculated from Newton's theory. For the Sun the calculation is simple. The Moon's orbit is more challenging. The calculator includes the leading 3-body corrections to the Moon's orbit, namely Ptolemy's Evection, Copernicus' Equation of Center, Tycho Brahe's Variation, Keppler's Annual Equation, and other smaller corrections.

The projections of the tidal vector can be calculated from the altitude and azimuth of the Moon and Sun. The tidal vector is the time dependent tidal force experienced by the Earth. For the East-West projection, East is negative, West positive. For the North-South projection, North is positive, South negative. For the vertical component, z can be positive (up) or negative (down).

Earth and Moon


magnetic gravimeter:

The SciAm Magnetic Gravimeter
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coupled pendulums:

A Double Pendulum Gravimeter
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Sir William Thomson (Lord Kelvin) (1824-1907): Tides, 1882, a great lecture by a great man of science.