Algo Art

Orbital Position

θ(t) = θ₀ + 2πt / T

Places each planet on its orbit at every animation frame. Because outer planets have a larger period T, they advance through a smaller angle per second — which is why Neptune crawls while Mercury sprints.

θ₀ = starting angle  ·  T = orbital period (years)

Kepler's Equation

M = E − e · sin(E)

Converts uniform simulated time into a true position on an ellipse. It is solved iteratively each frame for the rocket's transfer arc, reproducing the real effect where spacecraft speed up at periapsis and slow near apoapsis.

M = mean anomaly  ·  E = eccentric anomaly  ·  e = eccentricity

Hohmann Transfer

a = (r₁ + r₂) / 2
e = (r₂ − r₁) / (r₂ + r₁)

Defines the most fuel-efficient path from Earth to the Moon. The rocket coasts along a single elliptical arc — no mid-course burns — reaching the Moon exactly at apoapsis after half an orbit.

a = semi-major axis  ·  r₁ = Earth radius  ·  r₂ = Moon orbit radius