Planetary Orbits

Algebra 2 · Axiom Academy

Every planet in the solar system traces an ellipse — and the Sun doesn't sit at the center. It sits at one focus. In 1609, Johannes Kepler broke a 2,000-year-old assumption: planets don't circle the Sun in perfect circles — they trace ellipses , and the Sun sits off-center, at one focus . Set how elongated the orbit is. Every shape you can make still has the Sun at a real, derived focus — never guessed — a distance c = (a² − b²) from the center. Hit Orbit and watch the planet complete one full lap around it. The one thing that never changes Drag the planet anywhere around this orbit. Its distance to the Sun and its distance to the empty focus both change constantly — but add them together and watch what happens. How far off-center is a real planet? Same semi-major axis, four real eccentricities. Step through the planets and watch how far the Sun actually sits from dead-center. Any shape defined by a constant sum of distances to two fixed points is an ellipse — orbits are only the start. A whispering-gallery ceiling carries a whisper from one focus to the other; a lithotripter aims shockwaves from one focus so they converge exactly on a kidney stone sitting at the other.

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