Keplerian Orbits

Multi-body planetary orbital mechanics following Kepler's laws with eccentric anomaly transcendental equation solvers.

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60 FPS • Canvas 2D

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Live Parameters

Orbital Time Scale 0.8

Planetary revolution rate

Mathematical Formulation

77 chars medium

Analytical Equation

r(\nu) = \frac{a(1 - e^2)}{1 + e \cos\nu}, \quad M = E - e \sin E, \quad T^2 = \frac{4\pi^2}{G(M_1 + M_2)} a^3

Compact Formula

E_{k+1} = E_k - (E_k - e*sin(E_k) - M) / (1 - e*cos(E_k)), x = a*cos(E) - ae

Renderer Logic

let E = meanAnomaly;
for (let iter = 0; iter < 4; iter++) {
  E = E - (E - ecc * Math.sin(E) - meanAnomaly) / (1 - ecc * Math.cos(E));
}
const planetX = semiA * Math.cos(E) - focusOffset;
const planetY = semiB * Math.sin(E);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#kepler #orbital-mechanics #astronomy #celestial #ellipse #space

Author: Math Art Core Target: 60 FPS

Keplerian Orbits

Live Parameters

Mathematical Formulation

Mathematical Tags

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