Tidal Forces

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This Demonstration shows tidal forces due to the Moon and the Sun, separately or in combination. It also shows the influence of the tidal forces at distances between the Earth and Moon and the Earth and Sun.

Contributed by: Tomas Franc (April 2013)
Open content licensed under CC BY-NC-SA



Suppose that the Moon orbits the Earth above the equator with the Earth's axial tilt taken as 0°. We take into account the eccentricities of the Earth's orbit around the Sun and the Moon's orbit around the Earth. This Demonstration shows tidal forces with respect to the relative position of the Moon, the Earth, and the Sun; you can vary the position of the Moon.

The views in 2D graphics are from the Earth's North or South Poles. The black dashed arrow shows the direction to the Moon. The green dashed arrow (along the positive axis) shows the direction to the Sun.

Tidal forces are given as differences between gravitational forces at a particular point on the surface of the Earth or inside the Earth compared to the gravitational force at the center of the Earth. Tidal forces are expressed as forces per unit mass, which has the dimensions of acceleration.

For more information about the calculation of tidal forces, taking into account the eccentricity of the orbits of the Earth and Moon, see [1].


[1] T. Franc, "Tides in the Earth–Moon System," in Week of Doctoral Students 2012—Proceedings of Contributed Papers: Part III—Physics (WDS12), Prague (J. Safrankova & J. Pavlu, eds.), Prague: MatfyzPress Publishing House, 2012 pp. 98–104. www.mff.cuni.cz/veda/konference/wds/proc/pdf12/WDS12_318_f12 _Franc.pdf.

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