Observatory · the tide
The tide
The Moon does not lift the sea. It pulls the whole Earth, the near side a little harder than the centre and the centre a little harder than the far side, and that small difference stretches everything along the line between them: the oceans, the rock under your feet, and, near a black hole, you. Everything on this page is worked out in your browser from the real Moon and Sun of the moment, the same ones as on the solar system.
Why two bulges
Fig. I. The Earth drawn out by the Moon, much exaggerated.
The three yellow arrows are the Moon's pull on the near side, the centre and the far side. The whole Earth falls towards the Moon with the centre's pull, all the time, which is what being in orbit means; so take that away, and what is left is the tide: the near side pulled a little ahead, the far side left a little behind, and everything at the sides squeezed inwards. That is why there are two bulges and not one, and why most coasts get two high waters a day. The ball is the solid Earth: it really does stretch, by up to about 30 centimetres, twice a day, under your feet. The drawing makes that millions of times bigger.
The pull, now
Fig. II. The Earth from above the north pole, with its two bulges and the Moon.
- Moon's tide
- Sun's tide
- Sun ÷ Moon
- Moon
- Today
Seen from above the north pole: the Earth turns once a day under two bulges of water that stay lined up with the Moon, so every place passes through both. The brass line is Greenwich. Run the clock at a day a second and watch the bulges swell and shrink over two weeks: when the Sun and the Moon are in line, at new and full moon, their tides add up, a spring tide; at the quarters they pull at right angles and partly cancel, a neap tide. Move the Moon to half its distance and its tide becomes eight times stronger, twice as far and an eighth: that is the d³. The heights are the equilibrium tide, the shape water would take if it could keep up; real oceans cannot, as the next panel says.
The tide at a place
Fig. III. The tide at the chosen place over three days.
The solid line is the Moon and the Sun together, the dashed one the Moon alone; the brass line is the clock above, and it moves. Because the Moon swings up to about 28° north and south of the equator in a month, a place away from the equator passes through one bulge high and the other low, and its two daily high waters differ, the diurnal inequality; near a pole one of them all but disappears. Eindhoven is far from the sea, but that does not matter here: this is the pull, and the ground in Eindhoven rises and falls with it.
What the sea actually does is another matter. Water cannot run round the world at the speed the bulges move, so each ocean basin answers the pull in its own way, sloshing at its own rhythm around points where the tide hardly moves at all. The North Sea has three such points; the Bay of Fundy resonates and gets more than fifteen metres; the Mediterranean, nearly closed, gets a few tens of centimetres at most. The pull is the same everywhere. The answer is the coast.
The same stretch, near a black hole
Gravity's difference falls off as 1/d³, so it is gentle almost everywhere. Not near a black hole: there the same stretch that lifts the oceans pulls a falling body into a thread, and pulls whole stars into streams. That has its own room, spaghettification, next to the event horizon it is all about.
Who worked it out
Where it already matters
The face of the Moon. The Earth raises tides in the Moon too, and over billions of years their drag slowed its turning until it matched its orbit. That is why it always shows us the same face. Most of the big moons of the solar system are locked the same way.
A longer day, a farther Moon. The Earth turns faster than the Moon goes round, so the bulges are carried slightly ahead of it; the Moon pulls them back and they pull the Moon forward. The Earth's day lengthens by roughly two milliseconds a century, and the Moon moves away by about 3.8 centimetres a year, measured by bouncing lasers off the reflectors the Apollo astronauts left there.
Io. Jupiter's tides flex Io, the innermost of the four moons you can watch through the eyepiece, every time it goes round. The heat makes it the most volcanic world we know.
A comet in pieces. In 1992 comet Shoemaker–Levy 9 passed too close to Jupiter and was pulled into a string of fragments, which hit the planet in July 1994. Closer than a certain distance, the Roche limit, a moon cannot hold together; Saturn's rings lie inside it.
Stars torn apart. When a star wanders too close to a supermassive black hole, the same stretch pulls it into a stream, and telescopes see the flare as its gas falls in: a tidal disruption event, now seen many times a year.