What does softening ε do?

Close encounters make 1/r² forces blow up and can crash the integrator. Softening replaces the denominator with (|r|² + ε²)^{3/2}, so gravity stays finite at small separations. Larger ε is more stable but less Newtonian up close; smaller ε is sharper but riskier numerically.

Do merges conserve energy?

Overlapping bodies combine with mass-weighted position and velocity, so mass and momentum are conserved, but the merger is inelastic: orbital kinetic energy is lost. Softening also changes the potential, and finite timesteps add small drift — treat energy as qualitative, not an ephemeris-grade invariant.

Can I use this as a solar-system ephemeris or mission planner?

No. This is a 2D qualitative sandbox for intuition about mutual gravity, chaos, and flybys. Real mission design needs high-fidelity ephemerides, many perturbing bodies, relativity and non-gravitational forces, and carefully controlled integrators — none of which this toy provides.

Gravity Sandbox

Place masses and watch N-body gravitational interactions unfold.

About this model

N-body gravity: place masses and watch mutual attraction evolve. Good for intuition about Lagrange-like balance, slingshots, and instability in multi-body systems.

Who it's for: Astrophysics curious learners; conceptual N-body play (not a mission planner).

Key terms

N-body
gravity
superposition
orbital mechanics

How it works

A playful N-body sandbox: every mass attracts every other mass with Newton’s law, softened slightly (ε) so close encounters stay numerically stable. Drag a body to pin it; release to let gravity take over again. When two bodies overlap, they merge — mass and momentum combine. Start with the built-in binary or clear and place your own stars. This is a qualitative toy, not a solar-system ephemeris.

Key equations

aᵢ = Σⱼ G mⱼ (rⱼ − rᵢ) / (|rⱼ − rᵢ|² + ε²)^{3/2}

Velocity Verlet integration (symplectic-ish)

Frequently asked questions

What does softening ε do?: Close encounters make 1/r² forces blow up and can crash the integrator. Softening replaces the denominator with (|r|² + ε²)^{3/2}, so gravity stays finite at small separations. Larger ε is more stable but less Newtonian up close; smaller ε is sharper but riskier numerically.
Do merges conserve energy?: Overlapping bodies combine with mass-weighted position and velocity, so mass and momentum are conserved, but the merger is inelastic: orbital kinetic energy is lost. Softening also changes the potential, and finite timesteps add small drift — treat energy as qualitative, not an ephemeris-grade invariant.
Can I use this as a solar-system ephemeris or mission planner?: No. This is a 2D qualitative sandbox for intuition about mutual gravity, chaos, and flybys. Real mission design needs high-fidelity ephemerides, many perturbing bodies, relativity and non-gravitational forces, and carefully controlled integrators — none of which this toy provides.

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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