Kepler Orbit Visualiser

Kepler found his three laws by studying Tycho Brahe's naked-eye-precision data for years — decades before anyone knew why planets should behave that way. The 'equal areas in equal time' law you can toggle on here isn't really about geometry: it's a direct consequence of angular momentum conservation, since gravity always pulls straight along the line between planet and star and can never twist the orbit sideways. That's also why a planet swings fastest through perihelion and crawls through aphelion — conserving L = r×v forces speed up as r shrinks. Newton's gravity, unknown to Kepler, is what finally explained why the pattern he'd already found geometrically had to be true.

Eccentricity is the single number this slider controls - it measures how stretched an orbit is. At e = 0 you get a perfect circle; push it toward 1 and the ellipse elongates into a comet's path, with the star sitting off-center at one focus, never the middle. The surprise for most people: Earth's orbit has e = 0.017, so it is nearly a circle. Seasons come from Earth's axial tilt, not from a changing distance to the Sun.

Watch the planet retrace exactly the same ellipse forever - it never drifts into a slowly rotating rosette. That is not automatic. Bertrand's theorem proves only two force laws let bound orbits close after a single loop: inverse-square gravity (1/r²) and the harmonic spring force (∝ r). Any other power law leaves orbits that never quite repeat. The clean, closed ellipse you see is a fingerprint of gravity's exact 1/r² form.