Create a stable figure-8 orbit with three equal masses. What initial conditions are needed?

Specific symmetric initial conditions; try equal masses at 120° with tangential velocities.

Add Jupiter (large planet) to a solar system with Earth. How does it perturb Earth's orbit?

Jupiter's gravity slightly shifts Earth's orbital elements — this is real! Jupiter acts as a 'vacuum cleaner'.

Why are chaotic 3-body systems practically unpredictable over long timescales?

Lyapunov exponents grow exponentially; initial precision required grows exponentially.

Pro 🔒~25 min

My Solar System

Build and simulate your own multi-body solar system

How it works

My Solar System demonstrates a key principle: The N-body gravitational problem involves calculating the motion of multiple masses under mutual gravitational attraction. The N-body gravitational problem involves calculating the motion of multiple masses under mutual gravitational attraction. For 2 bodies, exact analytical solutions exist (elliptical orbits). For 3+ bodies, the problem is generally chaotic — tiny changes in initial conditions lead to wildly different outcomes over time. Real solar systems are stabilized by large mass ratios (Sun >> planets) and widely spaced orbits.

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Step-by-step

Add bodies by clicking.
Set mass and initial velocity using the control panel.
Run the simulation and watch orbits form.
Add a third body to observe orbital perturbations.
Try creating a stable binary star with two equal masses.

Key formulas

$\vec{F}_{12} = -G\frac{m_1 m_2}{r_{12}^2}\hat{r}_{12}$ Gravitational force between bodies
$\vec{a} = \sum_{j\neq i}\vec{F}_{ij}/m_i$ N-body acceleration

Frequently asked questions

Create a stable figure-8 orbit with three equal masses. What initial conditions are needed?: Specific symmetric initial conditions; try equal masses at 120° with tangential velocities.
Add Jupiter (large planet) to a solar system with Earth. How does it perturb Earth's orbit?: Jupiter's gravity slightly shifts Earth's orbital elements — this is real! Jupiter acts as a 'vacuum cleaner'.
Why are chaotic 3-body systems practically unpredictable over long timescales?: Lyapunov exponents grow exponentially; initial precision required grows exponentially.