Ocean Tides: Why the Moon Pulls Harder Than the Sun

Tides are a gradient, not a pull

It is tempting to think the Moon "pulls up" the water directly beneath it, but that gets the mechanism backwards. The Moon pulls on every part of the Earth — the near side, the centre, and the far side — but not equally: the near side is closer and feels a stronger pull, the far side is farther and feels a weaker one. A tide is the result of that difference across the Earth's diameter, not the pull itself. Subtract the pull on the Earth's centre (which is what actually determines the planet's orbital motion) from the pull at any point, and what remains is the tide-raising force at that point.

Because the near side is pulled slightly more than the average and the far side slightly less, the net effect stretches the Earth (and its oceans) along the Earth-Moon axis — raising two bulges roughly opposite each other, not one. As the Earth rotates underneath this fixed axis roughly once a day, any given coastline passes through both bulges, which is why most of the world sees two high tides and two low tides in about 24 hours 50 minutes — a lunar day, slightly longer than a solar day because the Moon itself moves along its orbit while the Earth turns.

Why the exponent is 3, not 2

Newton's law of gravitation falls off as 1/r². The tide-raising force is the derivative of that force with respect to distance across the Earth's diameter — differentiating 1/r² with respect to r brings down a factor of r and drops the power by one, leaving a force that scales as 1/r³:

gravitational force        F  ∝ M / r²
tidal (differential) force F_tide ∝ M · d / r³      (d = Earth's diameter, d << r)

That extra power of r is why distance matters so much more for tides than for ordinary gravity. The Sun is about 27 million times more massive than the Moon, which would make its gravitational pull on the Earth completely dominant — and it is: the Sun's gravity keeps the Earth in orbit, the Moon's does not. But the Sun is also about 389 times farther away, and 389³ is roughly 59 million, which outweighs the 27-million mass advantage. Run the numbers and the Moon's tide-raising force comes out at roughly 2.2 times the Sun's — smaller mass, but close enough that the cube of the distance ratio wins.

Spring tides and neap tides

The Sun raises its own, smaller pair of tidal bulges along the Earth-Sun axis, and the ocean simply responds to the vector sum of both. Twice a lunar month, at new moon and full moon, the Sun, Earth and Moon line up (syzygy) and the two tidal bulges reinforce each other — a spring tide, with an unusually large range between high and low water. This has nothing to do with the season; "spring" here means the tide "springs up."

new moon / full moon  →  Sun + Moon aligned      →  SPRING tide (max range)
first / third quarter →  Sun + Moon at 90°        →  NEAP tide   (min range)

At first and third quarter the Sun-Moon angle is close to 90° as seen from Earth, and the Sun's bulge partly fills in the Moon's low tide and partly flattens its high tide — a neap tide, with an unusually small range. The lunar orbit's eccentricity and the roughly month-long cycle of the Moon's distance add a secondary modulation (perigean versus apogean tides) on top of this, which is why not all spring tides are equally large.

Why real coastlines don't look like the simple model

The two-bulge picture above is the equilibrium tide — what the ocean surface would look like if it could respond instantly to the tide-raising force with no land in the way. Real oceans cannot: water is confined to basins with their own natural sloshing period, and Earth's rotation deflects moving water via the Coriolis effect. The result, formalised as the dynamic theory of tides (Laplace, 1776), is that each ocean basin has its own resonant response, often rotating around a no-tide point called an amphidromic point. This is why the Bay of Fundy sees tidal ranges over 15 metres — its basin happens to resonate close to the tidal forcing period — while nearby open Atlantic coastlines see under a metre for the same lunar and solar forcing.

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