Earth–Moon Barycenter Wobble
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
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.
More from Gravity & Orbits
Other simulators in this category — or see all 22.
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Three-Body Figure-Eight
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Restricted 3-Body (map)
CRTBP: escape vs collision vs chaos proxy; μ slider.
Multistage Rocket (Tsiolkovsky)
Δv per stage; sum vs single-stage with same total propellant.
Orbital Debris & Kessler (toy)
LEO shell: n = N/V, collision rate ∝ N²; optional fragment cascade.
Gravity-Assist Fly-By
Planet frame |u_out|=|u_in| rotated by δ; star frame v = V + u — Δ|v| from moving planet.