Binary Star System (2D) | mysimulator.uk

Star Masses

Mass A (orange) 1.6 M☉

Mass B (red) 0.7 M☉

Orbit Shape

Separation (semi-major axis) 6.0 AU

Eccentricity 0.30

Simulation speed 1.0×

Orbit Readout

Mass ratio A:B

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Period

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A's orbit radius (a₁)

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B's orbit radius (a₂)

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Current separation

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Energy drift

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How it works

This is a real two-body gravity integration, not a canned ellipse: every frame both stars' accelerations are computed from Newton's law of gravitation and advanced with velocity-Verlet, so the orbit's shape emerges from the physics instead of being drawn from a formula.

a₁ = G·m₂·(r₂−r₁) / |r₂−r₁|³
a₂ = G·m₁·(r₁−r₂) / |r₁−r₂|³
G = 4π²  (AU, solar mass, year units)

Both stars orbit the common barycenter — the heavier star sweeps a tighter path, the lighter one a wider path, in fixed proportion m₂:m₁ so the two orbits always stay similar ellipses. The system is initialised at periapsis with the exact vis-viva velocity for the chosen semi-major axis a and eccentricity e, then left to evolve under gravity alone — the "Energy drift" readout shows how well the integrator is conserving total orbital energy, which stays under ~0.1% even for eccentric orbits.

Kepler's third law falls out of the same integration: period T = √(a³ / (m₁+m₂)) years, matched here to the measured time between periapsis passages.

Star A Star B Barycenter