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Physics
Kepler's three laws
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Explore elliptical orbits, swept areas and the relationship between orbital period and orbit size.
One orbit, two foci
Change the shape, then drag A to check the sum of its distances to the foci.
Time0 yr
Stellar mass: 1 M☉ · T = 1 yr
Trail: the last 0.04 yr
A planet follows an elliptical orbit, with the star at one focus.
The distance sum always equals 2a
0.5 + 1.5 ≈ 2 AU
d₁d₂
Distance to the star d₁0.5 AU
Distance to F₂1.5 AU
a is half the long axis of the ellipse, not the instantaneous distance from the star to the planet.
Model notes
- Two-body model: the star stays at a focus and planetary mass is negligible compared with it. Planet–planet interactions and relativistic effects are omitted.
- Only elliptical orbits viewed face-on are represented. The adjustable ranges are teaching choices, not limits found in nature.
- Star and planet icons are enlarged. Framing adjusts to orbit size; A and B always share the same AU scale.
- Normalized units: AU, years, solar masses M☉ and G = 4π². Values are model calculations, not measurements of a specific planet; arc lengths are approximate.
- Dragging the planet selects a time on its orbit. Changing parameters constructs a new orbit and resets time to zero; it does not apply thrust.