Lunar Tides: How the Moon Creates Ocean Tides

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Spring tide at new moon — maximum tidal range ~1.0 m

At new moon, the Sun and Moon are aligned on the same side of Earth, combining their gravitational pull to create spring tides with the largest tidal range. The tidal cycle repeats approximately every 12 hours and 25 minutes.

Formula

Tidal force: F_tidal = 2GMm·r / d³ (differential gravity)
Tidal period: T = 12h 25min 14s (semidiurnal lunar)
Spring range ≈ 1.46 × mean range; Neap range ≈ 0.54 × mean range

The Moon's Gravitational Fingerprint

Twice each day, the ocean rises and falls in a rhythm dictated by the Moon. The mechanism is differential gravity: the Moon pulls harder on the near side of Earth than the far side, stretching the ocean into two bulges. As our planet rotates beneath these bulges, any coastal location experiences two high tides and two low tides roughly every 24 hours and 50 minutes — the lunar tidal day.

Spring Tides and Neap Tides

The Sun also generates tides, about 46% as strong as the Moon's. When Sun and Moon align during new and full moons, their forces add constructively, producing spring tides with the largest tidal range. During quarter moons, the forces act at right angles, partially canceling to create neap tides with the smallest range. This two-week spring-neap cycle dominates tidal patterns worldwide.

Perigee and Apogee

The Moon's orbit is elliptical, varying from 356,500 km at perigee to 406,700 km at apogee. Since tidal force varies as the inverse cube of distance, perigean tides are about 20% stronger than apogean tides. When perigee coincides with a spring tide (perigean spring tide or "king tide"), coastal flooding risk increases significantly — a growing concern as sea levels rise.

Tidal Resonance and Extremes

The Bay of Fundy in Canada experiences the world's largest tides — over 16 meters between high and low water. This extreme range occurs because the bay's natural resonant period nearly matches the 12.42-hour tidal forcing period, amplifying the tide like pushing a swing at just the right moment. Ocean basin geometry, not just celestial mechanics, determines local tidal behavior.

FAQ

Why does the Moon cause tides?

The Moon's gravity pulls on Earth's oceans, but the pull is stronger on the near side than the far side. This differential creates two tidal bulges: one facing the Moon (direct pull) and one on the opposite side (centrifugal effect of the Earth-Moon orbit). As Earth rotates through these bulges, coastal areas experience two high tides and two low tides per day.

What is the difference between spring and neap tides?

Spring tides occur during new and full moons when the Sun, Moon, and Earth are aligned, combining gravitational forces for maximum tidal range. Neap tides occur during quarter moons when the Sun and Moon pull at right angles, partially canceling each other for minimum tidal range. Spring tides are about 20% larger than average.

Why are there two high tides per day?

The tidal force creates two bulges on opposite sides of Earth — one facing the Moon and one facing away. As Earth rotates, a given point passes through both bulges, experiencing two high tides roughly 12 hours and 25 minutes apart. The extra 25 minutes accounts for the Moon's orbital motion.

How strong are tidal forces compared to regular gravity?

Tidal forces are extremely weak compared to Earth's gravity — about 10 million times weaker. A 70 kg person experiences a tidal force of only about 0.001 newtons. But because ocean basins are vast and water is fluid, even these tiny forces produce measurable tidal ranges of 1-15 meters in some locations.

Sources

Embed

<iframe src="https://homo-deus.com/lab/oceanography/tidal-forces-moon/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub