Tides: Two Bulges, Two High Tides & the Spring-Neap Rhythm

Why the ocean has two bulges

Gravity weakens with distance. The ocean on the side of Earth facing the Moon is about 6,400 kilometers closer to the Moon than Earth’s center is, and the ocean on the far side is about 6,400 kilometers farther. Small as those differences are next to the Moon’s 384,400-kilometer distance, they matter: the near-side water feels a pull roughly 7 percent stronger than the far-side water does.

Here is the key move. Earth as a whole is falling freely around the Earth-Moon system’s common center of mass, so the average pull is already accounted for; nobody feels it, just as astronauts do not feel the gravity that holds their station in orbit. What the ocean responds to is only the difference from that average, which physicists call the tidal force or differential gravity. Subtract the average pull everywhere and a clear pattern is left over: the near side is tugged toward the Moon, the far side is left behind and effectively pushed away, and the sides are squeezed gently inward.

That is why there are two bulges, not one. Water heaps up under the Moon because it is pulled hardest, and it also heaps up on the opposite side of the planet because the solid Earth is pulled out from under it, leaving the far-side water behind. If the far-side bulge feels wrong, hold on to this picture: the Moon pulls Earth’s body away from the far-side ocean slightly faster than it pulls the far-side ocean itself.

One more consequence hides in the subtraction. Because the tidal force is a difference between nearly equal pulls, it falls off with the cube of distance rather than the square. That single fact decides who rules the tides. The Sun’s raw gravitational pull on Earth is about 180 times stronger than the Moon’s, but a pull that strong and that uniform barely varies across Earth’s width, which is a tiny fraction of 150 million kilometers. Run the numbers and the Sun’s tidal force comes out at only 46 percent of the Moon’s; equivalently, the Moon’s tide is about 2.2 times the Sun’s. The nearby Moon wins because tides reward closeness far more than mass.

Two high tides every lunar day

The bulges stay lined up with the Moon while Earth rotates underneath them. In one turn of the planet, your stretch of coast sweeps through a bulge (high tide), a trough (low tide), the second bulge (high tide again), and the second trough. Two highs and two lows, which is exactly the rhythm most of the world’s coasts keep.

But the cycle is not 24 hours, because the Moon does not stand still. While Earth spins once, the Moon travels about 13 degrees farther along its orbit, and Earth needs roughly 50 extra minutes of rotation to bring the Moon back over the same spot. That interval, 24 hours 50 minutes, is the lunar day (also called the tidal day), and it is the same reason the Moon rises about 50 minutes later each night on the moon calendar.

With two high tides per lunar day, successive highs come about 12 hours 25 minutes apart, and the whole schedule slides about 50 minutes later from one day to the next. Anyone who fishes, surfs, or walks mudflats knows this drift by heart; now you know it is simply the Moon’s orbital motion written into the sea. Both rhythms, the tidal day and the fortnightly spring-neap alternation below, have their own entries in the cycles by length catalog.

Spring and neap tides

The Sun raises its own pair of bulges, at that 46 percent strength. What the ocean actually does is add the two patterns together, and the sum depends on the angle between the Sun and the Moon, which is exactly what the phase of the Moon tracks.

At new moon the Moon sits between Earth and the Sun, so both tide-raisers pull along the same line and their bulges stack: high tides run higher, low tides run lower. These are spring tides. At full moon the Moon is on the opposite side of Earth from the Sun, and here is the part that surprises people: the tides spring just as high. It works because each body raises two bulges on opposite sides of the planet. The bulge pattern is a symmetric stretch along a line, not a heap on one side, so it makes no difference whether the Sun and Moon share a side or face each other across the Earth. Alignment is alignment.

At the quarter moons the Sun and Moon pull at right angles. The Sun’s high water lands on the Moon’s low water and partly fills it in, so the range shrinks to its smallest: neap tides. The Moon still wins (its tide is 2.2 times as strong), so the tides never cancel, they just flatten. Drag the slider through a month above and watch the dashed solar bulge swing from reinforcing the lunar bulge to fighting it.

The names are Old English, not seasonal: spring tides spring up, and “neap” probably comes from a word meaning lacking or without power. Since the alignment repeats at every new and full moon, the spring-neap cycle takes 14.77 days, half of the 29.5-day synodic month.

One refinement worth knowing: the Moon’s orbit is an ellipse, so its distance varies through the month. At perigee, its closest point, the Moon is about 6 percent closer than average, and because tidal force grows with the cube of closeness, its tide runs nearly 20 percent stronger. When a perigee happens to coincide with a new or full moon, the result is a perigean spring tide, the “king tides” that make coastal news. The same geometry makes a full moon at perigee look larger, the popular supermoon, and the slow turning of the perigee point itself is the subject of the apsidal precession lesson.

The tides are reshaping the Earth-Moon system

Tides do more than move water; they carry momentum between the Earth and the Moon. Earth spins much faster than the Moon orbits, and friction with the ocean floor drags the tidal bulge slightly ahead of the Moon’s position. That off-axis heap of water has gravity of its own, and it pulls the Moon gently forward along its orbit, feeding it energy. The Moon responds by spiraling slowly outward: lunar laser ranging, bouncing light off reflectors the Apollo crews left on the surface, measures the Moon receding at about 3.8 centimeters per year.

Earth pays for it with spin. Tidal friction lengthens the day by roughly 2 milliseconds per century, which sounds like nothing until geology adds it up. Fossil corals laid down daily growth bands, and counting bands per yearly layer shows that around 400 million years ago the year held about 400 days, each about 22 hours long. The sea has been braking the planet for eons.

The Moon itself already finished this story. Earth raises far larger tides on the Moon than the Moon raises here, and long ago that friction slowed the Moon’s spin until it matched its orbit, a state called tidal locking. That is why the Moon always shows us the same face: the same physics you are watching above, run to completion.

What the real ocean does

Honesty requires a caveat: the two neat bulges above are the equilibrium tide, the shape the ocean would take if water could respond instantly and no continents stood in the way. The real ocean cannot do that. Continents block the bulges from simply gliding around the globe, so each ocean basin sloshes in its own way, and the tide actually travels as long, slow waves that rotate around points of nearly zero tide called amphidromic points. The idealized picture explains the rhythms beautifully, the 12 h 25 m beat and the spring-neap cycle, but each coastline sets its own volume and timing.

The local differences are dramatic. High tide at most ports does not arrive when the Moon is overhead but hours later, by a lag that is a fixed personality trait of each harbor (its lunitidal interval, which old sailing directions called the establishment of the port). The spring-neap rhythm lags too: at many coasts the biggest tides of the month arrive a day or two after the new or full moon, a delay called the age of the tide, because the ocean needs time to respond. Funnel-shaped bays can resonate with the tidal push the way a bathtub sloshes in time with your hand: the Bay of Fundy in Canada amplifies its tides to as much as 16 meters, while the nearly enclosed Mediterranean manages only a few tens of centimeters. The two daily highs are often unequal as well: when the Moon stands far north or south of Earth’s equator, a given shore passes closer to the heart of one bulge than the other, so one high tide runs higher than the next (the diurnal inequality). Some coasts, including parts of the Gulf of Mexico, go further and get just one high tide a day, because the basin’s geometry nearly mutes the twice-daily component and lets a once-daily one dominate. This is why real tide tables are built from each port’s measured record rather than from raw astronomy, and why the gauge chart above is labeled an idealized shore: in this simple model the neap range drops to about a third of the spring range, while at typical coasts the swing is gentler, roughly 20 percent either side of average.

And a promise kept about honesty: only the Moon and the Sun matter. Because tidal force falls with the cube of distance, Venus at its very closest raises a tide roughly 15,000 times weaker than the Moon’s, and mighty Jupiter’s is more than 100,000 times weaker. Planetary alignments do not flood coasts, trigger earthquakes, or influence people through tides; the arithmetic simply is not there, the same standard we apply to claims about planets and the sunspot cycle. Meanwhile the genuinely measurable tides hide in plain sight: the solid rock beneath you flexes by roughly 30 centimeters twice a day (the body tide), and the atmosphere breathes with tides of its own, driven mostly by the Sun’s heat rather than gravity.