Explore Kepler's three laws with an elliptical orbit in 3D - drag eccentricity, watch equal-area sweep wedges, and read T-squared versus a-cubed for Mercury, Earth, and Halley's comet.
Preset buttons load Mercury, Earth, or Halley's comet with published eccentricity and semi-major axis figures; the eccentricity slider morphs the ellipse from near-circular to highly elongated.
Teal area wedges from the Sun to successive planet positions illustrate Kepler's second law - equal areas in equal times - as the body moves faster near perihelion. On-screen orbit size is scaled for readability; AU and year numbers in the panel are real.
Kepler Orbits 3D Explorer
Explore Kepler's three laws with an elliptical orbit in 3D - drag eccentricity, watch equal-area sweep wedges, and read T-squared versus a-cubed for Mercury, Earth, and Halley's comet.
Drag to orbit the view, scroll or pinch to zoom, and press Mercury, Earth, or Halley to load published orbital figures. An eccentricity slider from 0 to 0.97 morphs the ellipse; play/pause controls the motion and a sweep toggle shows or hides the equal-area wedges.
The facts panel lists semi-major axis a, eccentricity e, orbital period T, T squared, and a cubed so you can see Kepler's third law T^2 proportional to a^3 in AU and years - the same units astronomers use for solar-system orbits.
- Sun at one focus of an ellipse; planet mesh animated via Kepler's equation (mean anomaly to eccentric anomaly)
- Equal-area sweep wedges (teal) illustrate Kepler's second law - equal areas in equal times
- Preset buttons: Mercury (e=0.206, a=0.387 AU), Earth (e=0.017, a=1 AU), Halley's comet (e=0.967, a=17.8 AU)
- Eccentricity slider 0-0.97 (default 0.017) to morph the ellipse without leaving the page
- Play/pause orbit animation; toggle to show or hide area wedges
- Runs fully in the browser with the vendored three.js engine - no account, no upload
Teachers use it to connect textbook ellipses to real eccentricities, students compare T^2 and a^3 across presets, and curious readers drag e toward 0.97 to see how Halley's elongated path differs from Earth's near-circle.
| Body | Eccentricity e | Semi-major axis a | Period T | T^2 = a^3 check |
|---|---|---|---|---|
| Mercury | 0.206 | 0.387 AU | 0.241 yr | 0.058 = 0.058 (NASA fact sheet) |
| Earth | 0.017 | 1.0 AU | 1.0 yr | 1.0 = 1.0 (definition of AU-year units) |
| Halley's comet | 0.967 | 17.8 AU | 75.3 yr | 5671 = 5640 (IAU/NASA comet catalogues) |
Everything renders on your device with WebGL. The 3D engine loads once (about 0.7 MB) and is cached; no scene data is sent to a server.
The scene is an educational visualization using Kepler's equation - it does not run a full N-body gravity integrator or model perturbations, inclination, or multiple bodies. On-screen orbit size is scaled for readability; AU and year figures in the table are real.
For a step-by-step walkthrough, read the Kepler Orbits 3D Explorer step-by-step guide. The Space 3D collection also includes a Solar System 3D Explorer with animated planet orbits and a Saturn Rings 3D Explorer with NASA ring radii.
Frequently Asked Questions
What does the Kepler Orbits 3D Explorer show?
The Sun at one focus of an elliptical orbit with a planet mesh moving along the path using Kepler's equation. Teal area wedges from the Sun to successive positions illustrate equal areas in equal times, and the facts panel lists a, e, T, T^2, and a^3 for each preset.
What are the Mercury, Earth, and Halley presets?
Mercury loads e=0.206 and a=0.387 AU (NASA planetary fact sheets). Earth loads e=0.017 and a=1.0 AU. Halley's comet loads e=0.967 and a=17.8 AU (IAU/NASA comet catalogues). Each preset updates the panel with the same published figures.
What does the eccentricity slider do?
The slider runs from 0 to 0.97 (default 0.017 for Earth) and morphs the ellipse shape in real time. At e=0 the path is a circle; at e=0.97 it is highly elongated like Halley's comet. The panel switches to a custom orbit label when you drag away from a preset.
What do the teal area wedges mean?
They illustrate Kepler's second law: a line from the Sun to the planet sweeps equal areas in equal times. The planet moves faster near perihelion (closest to the Sun) and slower near aphelion. Press Hide area wedges to toggle them off.
How does Kepler's third law appear in the panel?
The panel lists orbital period T in years, T squared, and a cubed in AU^3. For solar-system units, T^2 = a^3 - Earth's row shows 1.0 = 1.0, and Mercury's row shows 0.058 = 0.058 from NASA figures.
Is this a physics simulation?
The scene is an educational visualization using Kepler's equation - it does not run a full N-body gravity integrator or model perturbations, inclination, or multiple bodies. On-screen orbit size is scaled for readability; AU and year figures in the panel are real.