Start with the puzzle

How can the Moon make a high tide on both sides of Earth?

The bulge facing the Moon is easy to picture. The one facing away only makes sense when Earth is allowed to move too.

First

The Moon pulls the nearest water

For the first pass, pretend Earth is fixed in space. The Moon’s gravity is strongest at the water closest to it, so that water stretches toward the Moon.

As the Moon circles Earth, the bulge follows. The shortcut explains only the near side.

Hold Earth still

The Moon pulling the nearest waterFor this first view, Earth is held still and the far-side response is hidden.
For this first view, Earth is held still and the far-side response is hidden.

Next

Earth wobbles around an off-center point

Earth and the Moon both orbit their barycenter: their shared center of mass. It sits inside Earth, offset from the planet’s center, so Earth’s center travels around a small circle.

This wobble takes a month. It is part of the shared Earth–Moon orbit, not Earth’s daily spin on its axis.

Center and barycenter comparedAround the barycenter, Earth’s center follows the dotted circle and the far-side water line moves outward.Barycenter
Around the barycenter, Earth’s center follows the dotted circle and the far-side water line moves outward.

Finally

Put the pull and the wobble together

Move the slider from the fixed-Earth shortcut to the shared orbit. The second bulge appears as Earth begins to move around the barycenter.

Earth–Moon system

The shared orbit

The Earth and Moon orbiting togetherNear water pulls ahead of Earth. Far water also falls toward the Moon, but Earth falls faster. Relative to Earth, both sides bulge outward.Barycenter

Near water pulls ahead of Earth. Far water also falls toward the Moon, but Earth falls faster. Relative to Earth, both sides bulge outward.

The three arrows show the Moon’s pull: strongest on the near side, weakest on the far side. Sizes, distances, and the water’s shape are exaggerated.

For the nerds

The numbers behind the picture

These are mean values. The drawing compresses the enormous gap so Earth, the barycenter, and the Moon can share one page.

Plate 01 · Mean Earth–Moon geometry

Section through both centers

Distance compressed · bodies enlarged

Dimensions of the Earth–Moon systemA blueprint-style section through Earth and Moon, naming their centers, the barycenter, diameters, and mean distances.EARTH CENTER — MOON CENTER 384,400 kmBARYCENTER — MOON CENTER 379,729 kmEARTH DIAMETER 12,742 kmCENTER — BARYCENTER 4,671 kmEARTHOCEAN SURFACEEARTH CENTERBARYCENTER1,700 km BELOW SURFACEDISTANCE BREAKMOONMOON CENTER3,475 km

Earth’s center

12.4 m/s

44.8 km/h around the barycenter

Moon relative to Earth

1.022 km/s

Mean orbital speed

One shared orbit

27.3217 days

Relative to the distant stars

The barycenter follows from r = d × Mₘ ÷ (Mₑ + Mₘ). At the mean distance, Earth’s center is 4,671 km from it.

Earth’s speed follows v = 2πr ÷ T. Over the elliptical orbit, the Moon’s distance varies from 363,300 to 405,500 km and its speed from 0.970 to 1.082 km/s.