What if the Moon and Sun lined up?

At the beach, the sea comes up and goes back down. These are the tides.

The Moon pulls on the sea. So does the Sun. What if they pulled together, in a line?

Twice a day on most coasts, the sea creeps up the beach and slides back again. These tides are made mostly by the Moon, with help from the Sun.

But the Moon and Sun are not always in the same part of our sky. Sometimes they pull from the same line, and sometimes at right angles. In this lab, the Moon starts at first quarter, at right angles to the Sun. What happens to the tides when the Moon and Sun line up?

Tides arise because the Moon's and Sun's gravitational pulls vary across Earth's diameter, stretching the oceans along the line toward each body. Each produces its own pair of bulges.

The relative orientation of the two tidal patterns changes through the lunar month. This lab sets the Moon-Sun angle (elongation) to 90°, first quarter, and then to 0°, new moon, and asks how the combined tide strength changes.

At a half moon, the Moon and the Sun pull from different sides.

Their pulls partly cancel out. The tides are small.

In the model, the Moon's tide counts as 1 and the Sun's as about 0.46, a bit less than half. At first quarter, when you see half the Moon lit, the two pull at right angles. The Sun's stretch fills in part of the Moon's low places, so the tides are smaller than usual.

The tide meter reads about 0.54. On an imaginary ocean covering the whole planet, the sea would rise and fall by only about 0.29 meters. These small tides are called neap tides.

Tidal acceleration scales as M/d³. With today's Moon as the unit, the model's solar term is S ≈ 0.46. The combined amplitude is √(L² + S² + 2LS cos 2θ), so at θ = 90°, cos 180° = −1 and the total is L − S = 0.54.

The model's equilibrium range for this case is 0.29 m. That figure applies to a frictionless global ocean that instantly takes up the shape of the tidal forces, not to any real coast.

Now the Moon moves into line with the Sun. They pull together!

The tides get much bigger. The sea goes higher and lower.

Choose 'new moon'. The Moon and Sun now pull along the same line, so their stretches add up. The tide meter jumps from 0.54 to about 1.46, about 2.7 times as strong. The ideal ocean's rise and fall grows to about 0.78 meters.

Now try 'full moon'. The Moon is on the opposite side of Earth from the Sun, but the tide is just as big, 1.46. Press play and watch the meter swing between small and big tides twice in each month.

At θ = 0° (or 180°), cos 2θ = 1 and the total is L + S = 1.46, with an equilibrium range of 0.78 m: 2.70 times the neap value. The pattern repeats every half synodic month, about 14.7 days, so there are two spring and two neap periods in each 29.5-day cycle.

Turn the Sun's tides off and the meter reads 1.00 at every phase: without a second body there is nothing to add to or cancel. At 45°, the model gives 1.10.

The Moon and the Sun each stretch the sea a little, like pulling a rubber band.

In a line, the stretches add up. Sideways, they get in each other's way.

Each body stretches Earth's oceans into an oval along the line pointing at it: high water toward it and on the far side, low water in between. When the Moon and Sun are lined up, their ovals point the same way and add together into one bigger stretch.

At right angles, the Sun's high water lands where the Moon's low water is, so they partly cancel. The Moon wins, because its stretch is about twice the Sun's, but the tides are smaller. Our model treats Earth as covered by one deep ocean and leaves out coastlines.

Each tidal field is a quadrupole: it stretches along one axis and squeezes along the perpendicular ones. Two quadrupoles at angle θ combine with a 2θ dependence, so alignment (0° or 180°) gives L + S and quadrature (90° or 270°) gives |L − S|.

The Sun's term is smaller despite its far greater mass because tidal stretching falls with the cube of distance. The model's limits: equilibrium tides, circular orbits in Earth's equatorial plane, and no basin resonances, friction or lag. OpenStax notes that land masses, friction, Earth's rotation, wind and varying ocean depth complicate real tides, so some places have very small tides and others huge ones.

Every month, there are big tides at new moon and full moon.

They are called spring tides. They happen all year, not just in spring!

NOAA, the U.S. ocean and weather agency, explains that when the Sun, Moon and Earth line up, at new and full moon, high tides are a little higher and low tides a little lower: spring tides. The name comes from the tide 'springing forth', not from the season. About seven days later, at the quarter moons, come the moderate neap tides.

When a new or full moon falls close to the Moon's nearest approach to Earth, NOAA says high tides can be more than a foot higher than other spring tides. In Anchorage, Alaska, the difference can be 3 feet or more.

NOAA's tides tutorial describes the solar tide adding to the lunar tide at syzygy (new and full moon) to give spring tides, and partly canceling it at quadrature a week later to give neap tides; each lunar month has two of each. NOAA also notes that 'King Tide' is a popular, non-scientific term for exceptionally high tides.

Perigean spring tides, when syzygy coincides with lunar perigee, often bring high tides more than a foot higher than apogean spring tides; in Anchorage, with a range over 30 feet, the difference can reach 3 feet or more. NOAA adds that seasonal effects on water level can sometimes produce higher tides than perigean ones.