Saramsha

No. 009  ·  25 September 2026

Pulled Both Ways

The Moon lifts a bulge of ocean on the side facing it — and an equal one on the far side. That second bulge is why one harbour gets two high tides a day. Drag the Moon round its orbit, or drag across the globe to run the clock.

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Water at the harbourtwo days

Range, over a monthspring and neap

About this piece

The bulge on the far side

Ask why the tide comes in and most people reach for the Moon's gravity: the water on the Moon's side is pulled up into a heap, and the Earth turns under it. That explains one high tide a day. Harbours get two, about twelve hours and twenty-five minutes apart. So there must be a second heap of water on the side away from the Moon — the side where the Moon's pull is weakest. That is the part worth understanding.

The answer is that gravity only does something interesting when it is uneven. The whole Earth, oceans included, is falling freely towards the Moon; a uniform pull would move everything together and raise nothing. What is left once you subtract the average — switch the arrows to The Moon's pull and then to What's left over to watch the subtraction — is a small residual field, and it is symmetric. At the near point the Moon pulls 3.4% harder than average, so the water is left behind by the Earth beneath it. At the far point it pulls 3.2% less than average, so the Earth is pulled out from under the water. Either way the water ends up further from the centre. The two bulges are the same size because the residue is.

The vertical part of that residue is hopeless as a lifting force — about a ten-millionth of ordinary gravity, nothing that could raise the sea by half a metre. The work is done by the sideways component, which you can see in the arrows near the sides of the globe: a gentle, relentless sweeping of water along the sea floor towards the two ends of the Moon line. Given a few hours, that piles the ocean up.

Because the pull depends on the difference across the Earth's diameter, it falls off as distance cubed, not squared. That is why the Moon wins. The Sun is 27 million times more massive but 390 times further away; 27,000,000 / 390³ is about 0.46, so the Sun raises a tide a little under half the Moon's. Turn the Sun on and its bulges slide past the Moon's at their own rate. When the two line up — new Moon and full Moon — the ranges add: spring tides, nothing to do with the season, from an older sense of "spring" meaning to leap up. At the quarters they partly cancel: neap tides. The strip along the bottom is that beat, and its period is 14.8 days.

Every number on the page falls out of the geometry rather than being typed in. The Earth turns once in 23 h 56 m, but the Moon has moved on in the meantime, so the harbour must turn a little further to face it again: a lunar day of 24 h 50 m, two high waters per lunar day, hence 12 h 25 m between them and high water arriving about fifty minutes later each day. Two bulges from the Moon give a 12 h 25 m rhythm, two from the Sun give exactly 12 h 00 m — tide tables call them M2 and S2 — and two waves that close in period beat against each other with a period of half of 29.5 days.

What you see here is the equilibrium tide: the shape a frictionless global ocean would settle into if it had all the time in the world. Newton worked it out in the Principia in 1687, and it is out by a factor of ten or more at most coasts, for a wonderful reason — the ocean cannot keep up. To stay beneath the Moon, the bulge would have to travel at about 1,600 km/h at the equator, and in water four kilometres deep a long wave manages 700. The real tide is therefore not a bulge following the Moon but a forced wave sloshing in ocean basins, spinning around amphidromic points where the range is nearly zero, amplified where a bay happens to resonate. Hence 16 metres in the Bay of Fundy, 20 centimetres in the Mediterranean, and Southampton's odd double high water. Laplace wrote the equations for that in 1775; Kelvin and George Darwin turned them into the harmonic constants that brass tide-predicting machines, and now tide tables, are built on.

Two simplifications here, both worth naming. The view is straight down onto the orbital plane, so the Moon is drawn permanently half lit — the phase you would actually see from the harbour is the little disc in the panel. And the Moon has been put in the equatorial plane, which makes both of a day's high tides equal. In reality it wanders 28° north and south, so most coasts see a big tide and a small one each day, and a few places — the Gulf of Mexico, parts of the South China Sea — get just one.

Everything is computed in your browser; nothing is uploaded. Drag the Moon to move it round its orbit, drag anywhere else to scrub the clock, or Tab to the globe and use the arrow keys. The clock is not a real date: it starts at new Moon, at midnight, with the Moon overhead the far side of the world.