Is the wobble drawn to true scale?

No. The amplitude slider multiplies the displacement so the path is visible at screen resolution. The readout gives the correct order of magnitude (~4700 km offset).

Why not show inclined lunar orbit?

The Moon's orbit is inclined ~5° to the ecliptic; projecting to 2D with coplanar motion keeps the barycenter idea clear before adding inclination.

Earth–Moon Barycenter Wobble

Heliocentric path of Earth’s center: barycentric ellipse plus lunar epicycle (exaggerated).

About this model

The Earth and Moon orbit their common center of mass (barycenter) while that barycenter follows an approximately elliptical path around the Sun. Because the Moon carries about 1/81 of Earth's mass, the barycenter lies ~4 700 km from Earth's center—still inside the solid Earth—so Earth's center executes a small monthly epicycle superimposed on the heliocentric orbit. The simulator exaggerates that wobble for visibility and uses scaled angular speeds so both yearly and monthly motion can be appreciated in one view. It is a planar cartoon, not a JPL ephemeris.

Who it's for: Astronomy and mechanics courses linking center-of-mass ideas to heliocentric motion; complements binary-star and tides pages.

Key terms

Barycenter
Center of mass
Epicycle
Earth–Moon system
Heliocentric orbit
Orbital motion

How it works

The Earth–Moon system orbits the Sun about their common barycenter. Because the Moon’s mass is not negligible, the Earth’s center follows a slightly wavy path: roughly the smooth barycentric ellipse plus a small epicycle at the monthly period (here greatly exaggerated in amplitude for clarity). The offset |r_E − r_bary| ≈ a_EM · M_M/(M_E+M_M) ≈ 4700 km—inside the solid Earth, so both bodies “wobble” around an interior point. This is a 2D cartoon with scaled periods for animation, not a numerical ephemeris.

Key equations

r_E ≈ r_bary − (M_M/(M_E+M_M)) a_EM e^{iω_m t} (vector sketch)

Frequently asked questions

Is the wobble drawn to true scale?: No. The amplitude slider multiplies the displacement so the path is visible at screen resolution. The readout gives the correct order of magnitude (~4700 km offset).
Why not show inclined lunar orbit?: The Moon's orbit is inclined ~5° to the ecliptic; projecting to 2D with coplanar motion keeps the barycenter idea clear before adding inclination.

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Earth–Moon Barycenter Wobble

About this model

How it works

Key equations

Frequently asked questions

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About this model

How it works

Key equations

Frequently asked questions