14.1: The Tide-Causing Forces

If tides may be considered Mother Nature’s clock, then the Moon is the tides’ clockkeeper, with a little help from the Sun. The gravitational forces of the Moon and the Sun, primarily, and other planetary bodies, to a lesser extent, cause the tides. Textbooks and the internet abound with explanations of the tide-causing forces, many of which are confusing or conceptually incorrect. Here we follow the reasoning provided by Dutch physical oceanographer Theo Gerkema, who has written a highly readable text on ocean tides (Gerkema 2019). (See also Donald Simanek’s website and Steve Hurley’s Explaining Science website for good treatments.)

We start with an Earth completely covered by ocean without friction and where the ocean responds immediately to gravitational forces. We’ll also ignore the Sun for the moment and only consider the Moon. The Earth will remain motionless in this model, other than its rotation on its axis. This simplified model of ocean tides is known as the equilibrium model of tides, and it gives us an intuitive understanding of the tide-causing forces without resorting to mathematics. We will not consider the more realistic dynamic model of tides here (but see Gerkema 2019).

From Newton’s law of gravity, we know that the gravitational force between two objects varies with their mass and distance. This is why the Earth and the Moon orbit the Sun, which is 333,000 times more massive than Earth (and 27 million times more massive than the Moon). However, because the Moon is closer to the Earth than the Sun (238,855 miles versus approximately 93 million miles; e.g., NASA 2023a), the Moon exerts a greater influence on Earth’s tides, nearly twice as much as the Sun. Let’s be clear: Earth and the Moon orbit the Sun. It’s massive and exerts the strongest gravitational force of any object in our solar system. But the Moon’s close proximity to Earth gives it an edge when it comes to the tide-causing forces.

Now, the important part of this discussion comes down to this: the Moon’s gravitational attraction varies for different points on Earth’s surface. Because gravitational attraction depends on distance between two bodies, points nearer the Moon experience a stronger attraction while points farther away experience less of an attraction. These variations give rise to a non-uniform force (a force that varies) across Earth’s surface. Oceanographers refer to these variations in the Moon’s gravity across Earth’s surface as the the tidal forces (Gerkema 2019; Simanek 2022).

The tidal forces cause movements of water. Tidal forces have a radial component—acting vertically—and tractive component—acting horizontally. Radial forces pull upward or downward. Tractive forces pull back and forth. Because Earth’s gravity acts downward (vertically) with a force about 10 million times greater than the upward gravitational force of the Moon, the Moon’s vertical forces are dwarfed by Earth’s gravity. Thus—and this is important—only the tractive (horizontal) forces cause tides. Earth’s tides result from water moving toward or away from different locations depending on the magnitude of the tractive forces. The vertical component of the tidal forces has about as much effect on the ocean as does a seagull landing on or taking off from a cruise ship.

I want to emphasize that the ocean is not lifted by the gravitational attraction of the Moon (or Sun). The tidal forces are horizontal forces. They act tangential to the Earth’s surface (i.e., horizontally), not perpendicular (i.e., vertically). The “bulges” featured in many textbook illustrations of tides represent points toward which the ocean flows. They are not real bulges and they certainly don’t result from water being “pulled up” (on the near-Moon side) or “flung” off (on the opposite-Moon side) of the Earth.

The horizontal movements of water caused by tidal forces are called tidal currents. These tidal currents—water flowing toward or away from different points on Earth—cause the periodic rise and fall of sea level that we experience as tides. The ocean flows toward certain points and away from others at regular intervals. Along a shoreline, we observe sea level rising—the tide coming in—or falling—the tide going out.