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EXPERIMENT 002 · GRAVITY

Three bodies. No simple orbits.

Give Earth a second moon and watch their mutual gravity transform the entire system.

Three-body problem
RUNNING0.00 days
Motion of Earth and two moons
● Earth　● Moon　● Moon II＋ center of mass
Earth–CM 5,373 kmEarth displacement 0 kmEnergy error 0.0e+0
Explore the orbitsenergy · orbit shape · distance⌄

Energy ε indicates whether a moon is bound to Earth: ε < 0 means bound, ε = 0 is the escape threshold, and ε > 0 means it can escape from an isolated pair.

Eccentricity e describes the calculated orbit’s shape: e = 0 is a circle, 0 < e < 1 is an ellipse, e = 1 is the escape threshold, and e > 1 is a hyperbola.

These are instantaneous estimates relative to the moving Earth. The third body’s gravity keeps changing them.

MoonEnergy: ε = -0.525 MJ/kgEccentricity: e = 0.0549Ellipse
Moon IIEnergy: ε = -0.404 MJ/kgEccentricity: e = 0.0000Ellipse

1 / 30,000 points · current sampling interval: 7,200.0 s.

Specific orbital energy

MJ/kg · zero is the escape threshold

Chart of the moons’ specific orbital energy

Eccentricity

Instantaneous orbit shape · one is the escape threshold

Chart of the moons’ orbital eccentricity

Distance from Earth’s center

thousand km

Chart of the moons’ distances from Earth
02 /

Why is the motion so hard to predict?

Each body attracts the other two, so their orbits keep changing. Choose a preset or set your own initial conditions and compare the results.

Numerical model
Mutual gravity · realistic scales
No Sun or tidal effects

WHAT THE MODEL CALCULATES

Physics and model accuracy

The orbits are not drawn in advance. At each short time step, the model calculates the mutual Newtonian gravity of Earth and both moons. Earth moves freely. The pink cross marks the system’s current center of mass.

Masses, radii, and distances use SI units. The second moon has the same density as the Moon, so its radius scales with the cube root of its mass.

The model uses velocity Verlet integration. The maximum time step is 120 seconds and decreases during close encounters. The simulation stops when surfaces touch.

Trails and charts store up to 30,000 points. Sampling becomes more frequent during close encounters. Long trails are simplified for drawing without changing the simulation itself.

The model is two-dimensional and isolated. It does not account for the Sun, tides, spin, deformation, or fragmentation.

Experiment video

Two moons

Watch the short video, then try changing the model’s parameters yourself.

Video in Russian

Watch on YouTube