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The effect of the sun on tides

In addition to the Moon’s tidal forces on Earth’s oceans, the Sun exerts a tidal force as well. The gravitational attraction of the Sun on any object on Earth is nearly 200 times that of the Moon. However, as we show later in an example, the tidal effect of the Sun is less than that of the Moon, but a significant effect nevertheless. Depending upon the positions of the Moon and Sun relative to Earth, the net tidal effect can be amplified or attenuated.

[link] illustrates the relative positions of the Sun and the Moon that create the largest tides, called spring tide     s (or leap tides). During spring tides, Earth, the Moon, and the Sun are aligned and the tidal effects add. (Recall that the tidal forces cause bulges on both sides.) [link] (c) shows the relative positions for the smallest tides, called neap tide     s . The extremes of both high and low tides are affected. Spring tides occur during the new or full moon, and neap tides occur at half-moon.

You can see one or two animations of the tides in motion.

Figure a shows the earth centered within a horizontal shaded ellipse labeled spring tide. The sun is positioned to the right of the earth and the moon is in line, in between the earth and sun, and orbits counterclockwise. Figure b shows the earth centered within a horizontal shaded ellipse labeled spring tide. The sun is positioned to the right of the earth and the moon is in line with the earth and sun but to the left of the earth, and orbits counterclockwise. Figure c shows the earth centered within a vertical shaded ellipse labeled neap tide. The sun is positioned to the right of the earth and the moon is below the earth, and orbits counterclockwise. The ellipse in part c has a noticeably smaller vertical major axis than the horizontal major axes of the ellipses in parts a and b.
(a and b) The spring tides occur when the Sun and the Moon are aligned, whereas (c) the neap tides occur when the Sun and Moon make a right triangle with Earth. (Figure is not drawn to scale.)

The magnitude of the tides

With accurate data for the positions of the Moon and the Sun, the time of maximum and minimum tides at most locations on our planet can be predicted accurately.

Visit this site to generate tide predictions for up to 2 years in the past or future, at more than 3000 locations around the United States.

The magnitude of the tides, however, is far more complicated. The relative angles of Earth and the Moon determine spring and neap tides, but the magnitudes of these tides are affected by the distances from Earth as well. Tidal forces are greater when the distances are smaller. Both the Moon’s orbit about Earth and Earth’s orbit about the Sun are elliptical, so a spring tide is exceptionally large if it occurs when the Moon is at perigee and Earth is at perihelion. Conversely, it is relatively small if it occurs when the Moon is at apogee and Earth is at aphelion.

The greatest causes of tide variation are the topography of the local shoreline and the bathymetry (the profile of the depth) of the ocean floor. The range of tides due to these effects is astounding. Although ocean tides are much smaller than a meter in many places around the globe, the tides at the Bay of Fundy ( [link] ), on the east coast of Canada, can be as much as 16.3 meters.

Two photos of the same marina at the Bay of Fundy and appear to be taken from the same location. The photo on the left was taken when the water is high, the water line is nearby and the boats are all floating in the water. The photo on the right was taken when the water is low. The water line is quite distant and the boats are resting on mud.
Boats in the Bay of Fundy at high and low tides. The twice-daily change in sea level creates a real challenge to the safe mooring of boats. (credit: Dylan Kereluk)

Comparing tidal forces

Compare the Moon’s gravitational force on a 1.0-kg mass located on the near side and another on the far side of Earth. Repeat for the Sun and then compare the results to confirm that the Moon’s tidal forces are about twice that of the Sun.

Strategy

We use Newton’s law of gravitation given by [link] . We need the masses of the Moon and the Sun and their distances from Earth, as well as the radius of Earth. We use the astronomical data from Appendix D .

Questions & Answers

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In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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