Barycenta

Meet Barycenta, the balance point that Earth and the Moon both circle together.

It is tempting to say the Moon orbits Earth, but each pulls the other. Two bodies bound by gravity both orbit their shared centre of mass, the barycentre. It lies on the line between their centres, closer to the heavier body, at distance r₁ = m₂d/(m₁ + m₂) from the centre of body 1. Newton's laws require this, because neither body can be the fixed one.

With Earth's mass 5.972 × 10²⁴ kg, the Moon's 7.342 × 10²² kg and a mean separation of 384,400 km: r₁ = 384,400 × 7.342 × 10²² / (5.972 × 10²⁴ + 7.342 × 10²²) ≈ 4,670 km. Earth's radius is about 6,371 km, so the barycentre sits inside Earth, about three quarters of the way out.

The same wobble lets astronomers find planets around other stars: a planet makes its star circle a barycentre, which shows up as small shifts in the star's light. The Sun–Jupiter barycentre lies just outside the Sun's surface.

The sticker marks the barycentre in code, and the sizes are not to scale.