Planetary Science
Ocean Tides: How the Moon Pulls the Sea Into Two Bulges at Once
Twice a day, roughly every 12 hours and 25 minutes, the Atlantic surges into Canada's Bay of Fundy and rises more than 16 meters — taller than a five-story building — then drains away again. The engine behind that flood is 384,400 km overhead and exerts a pull on your body 300,000 times weaker than Earth's own gravity. So how does something that faint move entire oceans? The secret isn't the Moon's pull itself but the tiny difference in that pull across the width of the planet — and that difference conjures not one bulge of water but two, on opposite sides of the globe simultaneously.
- Tidal period~12 h 25 min between high tides (semidiurnal)
- Moon vs Sun pullMoon's tidal effect ≈ 2.2× the Sun's
- Theoretical bulge height~0.54 m (Moon) + ~0.25 m (Sun)
- Tidal acceleration~1.1×10⁻⁶ m/s² ≈ 1.1×10⁻⁷ of Earth's g
- Largest tidal range~16 m, Bay of Fundy (Burntcoat Head, up to 16.3 m)
- Mean Earth–Moon distance384,400 km (perigee 356,500, apogee 406,700)
- Spring/neap cycle~14.8 days (twice per lunar month)
- Effect on day lengthtidal friction lengthens the day ~2.3 ms/century
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What you'd actually see: two highs and two lows every day
Stand on a beach with a tide table and you'll notice a rhythm that doesn't match the clock. High tide arrives, then about 6 hours and 12 minutes later the water is at its lowest, then high again — and the whole pattern slides roughly 50 minutes later each day. Over a lunar month the timing drifts all the way around the clock and back. That daily slippage is the fingerprint of the Moon, not the Sun: the Moon returns to the same spot in your sky every 24 hours and 50 minutes (a "lunar day") because while Earth spins, the Moon has moved along in its orbit and Earth must turn a little extra to catch up.
Most coastlines see this semidiurnal pattern — two nearly equal highs and two lows each lunar day. But not everywhere. Some places (parts of the Gulf of Mexico, the South China Sea) get just one high and one low per day (diurnal tides), and many coastlines show a mixed tide, with two unequal highs. The difference comes from the shape of ocean basins, not the Moon itself: each basin has its own natural sloshing frequency, and the tide-generating force excites whichever mode fits best.
The key thing to hold onto is the number two. In a single lunar day the tide-raising force sweeps a point on Earth past two bulges of water — one roughly under the Moon, one roughly opposite it. Understanding why there are two, rather than a single bulge on the Moon-facing side, is the whole puzzle.
The mechanism: it's the difference in gravity, not gravity itself
Here's the crucial idea that trips up almost everyone: tides are not caused by the Moon's gravity, but by how much that gravity changes across the Earth. Gravity weakens with the square of distance. The side of Earth facing the Moon is about 12,742 km (one Earth diameter) closer than the far side, so it feels a slightly stronger lunar pull; the center of Earth feels an intermediate pull; the far side feels the weakest.
Now subtract the pull felt by Earth's center — because that's the acceleration the whole planet shares as it falls around the Earth–Moon barycenter, and it doesn't stretch anything. What's left over is the tidal force, the residual:
- On the near side, the leftover force points toward the Moon (extra pull), lifting water into a bulge.
- On the far side, the Moon pulls that water less than it pulls the Earth's center, so relative to Earth the water is "left behind" and bulges away from the Moon.
- Along the sides (the 90° ring), the residual force squeezes water gently inward and downward, feeding the two bulges.
That's why you get two bulges on opposite sides. The near-side bulge is an "extra tug"; the far-side bulge is a "deficit of tug." Mathematically the tidal force scales as 1/d³ (inverse cube of distance), not the familiar 1/d² of gravity — because it's the gradient of a 1/d² field. That single exponent is the reason the Moon beats the Sun despite being 27 million times less massive, as we'll see next.
The numbers: how a whisper of a force moves an ocean
Let's quantify just how feeble the tidal force is. At Earth's surface the Moon's differential (tidal) acceleration is about 1.1×10⁻⁶ m/s². Compared with Earth's surface gravity of 9.81 m/s², that's roughly one part in nine million (≈1.1×10⁻⁷ g). If tides were about brute strength, the ocean wouldn't budge.
What saves us is geometry and time. The tidal force isn't pulling water straight up against gravity; the sideways component, acting over thousands of kilometers of open ocean and repeating with clocklike regularity, herds water toward the sub-lunar and anti-lunar points. The theoretical equilibrium tide — the bulge you'd get on a smooth all-ocean planet — is only about 0.54 m for the Moon and 0.25 m for the Sun. Real open-ocean tides are close to this, often under a meter mid-Pacific.
So why 16-meter tides in the Bay of Fundy? Resonance and funneling. The Fundy basin has a natural oscillation period of about 13 hours — remarkably close to the 12.4-hour tidal driving period — so the water sloshes in step with the forcing and the amplitude builds, exactly like pushing a swing at its natural rhythm. Add a narrowing, shallowing channel that concentrates the same volume of water into a smaller cross-section, and the range explodes to the world-record ~16 m (up to 16.3 m at Burntcoat Head, Nova Scotia). The Moon sets the beat; the coastline decides the volume.
Spring and neap: why the Sun still gets a vote
The Sun is 27 million times more massive than the Moon, yet it sits 390 times farther away. Because tidal force falls off as 1/d³, that distance is cubed against the Sun: (390)³ ≈ 59 million, which nearly cancels the Sun's mass advantage. Run the arithmetic and the Moon's tidal effect comes out about 2.2 times stronger than the Sun's. The Sun is not negligible — it's the junior partner that modulates every tide.
When the Sun, Earth, and Moon line up — at New Moon and Full Moon (a configuration called syzygy) — the solar and lunar bulges stack on top of each other. You get the biggest tidal range: spring tides, so named from the sense of water "springing up," nothing to do with the season. When the Moon is at first or last quarter, the Sun pulls at right angles to the Moon and partly fills in the lunar troughs, muting the range into gentle neap tides. The full spring-neap cycle repeats about every 14.8 days, twice per lunar month.
Two more knobs fine-tune the height. The Moon's orbit is elliptical, so when it's at perigee (~356,500 km) its tidal force is noticeably stronger than at apogee (~406,700 km) — a perigean spring tide (a "king tide," sometimes marketed as a supermoon tide) can add tens of centimeters. And because the Moon's orbit is tilted about 5° to the ecliptic, the bulges track north and south of the equator through the month, which is part of why two daily highs are often unequal (the diurnal inequality).
The bulge isn't where you'd expect: friction, drag, and a slowing Earth
In the idealized picture the near-side bulge sits directly under the Moon. In reality it doesn't. Earth rotates once every 24 hours, far faster than the Moon orbits (once every 27.3 days), and the planet drags the tidal bulge ahead of the Earth–Moon line by a few degrees. Water has inertia and friction; continents get in the way; the bulge can't keep up perfectly or lag behind — on a fast-spinning Earth it's carried forward.
This offset has profound consequences. The leading bulge's gravity tugs the Moon slightly forward along its orbit, adding energy and nudging the Moon into a wider orbit: the Moon is receding from Earth at about 3.8 cm per year, a distance measured to millimeter precision by bouncing lasers off retroreflectors left by the Apollo astronauts. By Newton's third law, the Moon tugs the bulge — and thus the whole spinning Earth — backward, so tidal friction is braking Earth's rotation. The day is lengthening by roughly 2.3 milliseconds per century from tidal friction alone; post-glacial rebound (the crust still rebounding since the last ice age) partly offsets this, so the net observed long-term rate is closer to ~1.8 ms/century. Fossil coral growth-bands and ancient tidal-sediment records (rhythmites) confirm that ~400 million years ago a day was only about 22 hours and a year held ~400 days.
It's worth naming the misconception this dispels: the far-side bulge is not "centrifugal force flinging water outward." You can derive both bulges purely from differential gravity in a freely falling reference frame — no rotation of Earth required. Earth's spin governs the timing and the lead angle of the bulges, not their existence.
A short history: from Newton's insight to satellites that weigh the tide
Ancient sailors knew tides tracked the Moon — the Greek explorer Pytheas of Massalia linked them around 325 BC, and the Muslim scholar Al-Bīrūnī discussed lunar tidal timing around AD 1000. But nobody could explain why until Isaac Newton published his theory of gravitation in the Principia (1687). Newton's "equilibrium theory" correctly identified differential gravity and predicted the two bulges — a triumph, even though it couldn't capture the real ocean's sloshing.
The next leap was Pierre-Simon Laplace, who in the 1770s replaced the static bulges with a dynamic theory: tides as vast waves obeying fluid equations, deflected by the Coriolis effect and constrained by basin geometry. Laplace's tidal equations explain why the bulges don't sit under the Moon and why some coasts are semidiurnal and others diurnal. In the 19th century William Thomson (Lord Kelvin) built brass "tide-predicting machines" that summed the harmonic constituents mechanically — the analog computers that produced tide tables for a century.
Today the tide is measured from orbit. Satellite altimeters — TOPEX/Poseidon (launched 1992) and the Jason and Sentinel-6 series that followed — bounce radar off the sea surface and map the open-ocean tide to a few centimeters, finally confirming the dynamic bulges directly. And GRACE and GRACE-FO, gravity-mapping satellite pairs, detect how tides and shifting water redistribute Earth's mass. Newton would recognize the physics; he'd be astonished we now watch the bulges from space.
| Feature | Spring tide | Neap tide |
|---|---|---|
| Moon phase | New Moon and Full Moon | First and Last (half) Quarter |
| Sun–Moon geometry | Aligned (syzygy) — pulls add | At right angles — pulls partly cancel |
| Tidal range | Largest (~20% above mean) | Smallest (~20% below mean) |
| How often | About every 14.8 days | About every 14.8 days, offset by ~7 days |
| Name origin | "Springing up" — not the season | Old English "nēp" — scanty, lacking |
Frequently asked questions
Why are there two high tides a day instead of one?
Because the tide-raising force produces two bulges at once — one under the Moon (extra pull) and one on the opposite side (a deficit of pull, where water is 'left behind'). As Earth rotates, any coastline passes through both bulges each lunar day, giving two highs roughly 12 hours and 25 minutes apart.
If the Sun is so much more massive, why does the Moon dominate the tides?
Tidal force depends on the gradient of gravity, which falls off as 1/distance³, not 1/distance². The Sun is about 390 times farther than the Moon, and cubing that distance nearly cancels the Sun's enormous mass. The net result: the Moon's tidal effect is about 2.2 times the Sun's.
Isn't the far-side bulge just centrifugal force throwing water outward?
No — that's a common myth. Both bulges follow directly from differential gravity: the far side feels a weaker lunar pull than Earth's center, so relative to Earth its water bulges away from the Moon. You don't need Earth's rotation to produce two bulges; rotation only sets their timing and lead angle.
How big is the actual tidal bulge in the open ocean?
The theoretical equilibrium tide is only about 0.54 m from the Moon plus about 0.25 m from the Sun, and real mid-ocean tides are often under a meter. The dramatic tides you hear about — like the ~16 m range in the Bay of Fundy — come from resonance and funneling in specific coastal basins, not from a taller bulge.
Do tides really slow down Earth's rotation?
Yes. Friction drags the tidal bulge slightly ahead of the Earth–Moon line, and the resulting torque brakes Earth's spin, lengthening the day by about 2.3 milliseconds per century. The same interaction hands angular momentum to the Moon, which recedes about 3.8 cm per year — measured by laser-ranging off Apollo-era reflectors.
If Earth had no Moon, would there still be tides — and could a lake have tides too?
Yes to both, but faintly. The Sun alone would still raise tides about 46% as strong as the Moon's tide, with no spring–neap variation. As for lakes: the tidal force acts on all water, but a small basin is too short for a meaningful bulge to build, so lake tides are tiny — Lake Superior's is only a couple of centimeters, swamped by wind and pressure effects. Genuine tidal range needs a large, resonant basin.