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Tidial Acceleration by the Moon and the Sun

You may use the keys m, d, h to increase the month, day, or hour,

or shift key and md, h to decrease the month, day, or hour.

Click into the applet area first !

Click the applet area first. Then:
enter decimal degree values for Latitude (southern negative) into the text field of the applet, and press Enter key,
enter decimal degree values for Longitude (western negative) into the text field of the applet, and press Enter key.

Latitude 51.51 (=N), Longitude 13.41 (=E)is Berlin/Germany.
Latitude 40.76, Longitude -73.97 (=W) is New York.

tidal force sun moon
High tides at the sublunar point and its antipodal point at New Moon and Full Moon.
The tidal forces of the Moon is reinforced by the Sun (spring tide):
aMoon + aSun ≈ (1.1 + 0.50)⋅10-6 m/s2 = 1.610-6 m/s2

tidal force moon sun
When the Moon is at first quarter or third quarter (Sun and Moon separated by 90° when viewed from the Earth) the solar tidal force partially cancels the Moon's (neap tide):
a aMoon - aSun (1.1 - 0.50)⋅10-6 m/s2 = 0.6010-6 m/s2

The axial tidal acceleration a by the Moon is approximately:

tidal force formula
Earth's radius r=6371 km, Moon's mass M=7.349 1022 kg, mean distance Earth-Moon R =384401000 m:
aMoon ≈ 1.110-6 m/s2
Sun's mass M=1.989 1030 kg, mean distance Sun-Earth R=1.4961011 m
aSun ≈ 0.5010-6 m/s2
The applet is using the ecliptical geocentric longitudes of the Moon and the Sun (neglecting their declinations), and the geocentric distances of the bodies.

Select "Draw Tides" from the "Details" menu:
tidal force diagram

The applet is also computing the geocentric and topocentric distance of the Moon from the Earth (kilometers), the apparent angular size (arc minutes), the illuminated fraction of the Moon's disc (per cent), and the Moon's phase:
0.00 = new Moon
0.25 = first quarter
0.50 = full Moon
0.75 = last quarter
1.00 = new Moon

The altitude is taking into account the horizontal parallax of the Moon.

Distance / km
Perigee 356,375
Mean 384,401
Apogee 406,720

Select "Write Data" from the "Details" menu:

deata table

F(EM)/F(SM) is the ratio of the gravitation forces between Earth and Moon F(EM) to Sun and Moon F(SM).
The mean value of about 0.45 for the Earth's Moon is unique in the solar system:

Select "Diagram" from the Details menu:

earth moon distance

The change of distance may be up to about 6,300 km per day.

The mean perigee distance of 284 anomalistic months is 362562.4 km.

Please visit my:

GeoAstro Applet Collection

Please visit my Moon Applet Collection

Visit my page: The Moon: orbit and phases

Web Links

Gezeiten Vorhersage (Gezeitenkalender)

Gezeiten deutsche Nordseeküste (BSH)

Tide (Wikipedia)

Tidal acceleration (Wikipedia)

Tidal force (Wikipedia)

Theory of Ocean Tides

About Water Levels, Tides and Currents (NOAA)

George Howard Darwin: Ebbe und Flut sowie verwandte Erscheinungen im Sonnensystem, Teubner, Leipzig und Berlin, 2. Aufl. 1911.

© 2011-2016 J. Giesen

Last modified: 2016 May 02