Conic sections & orbits

CONIC SECTION SIMULATION

▸ Building the double cone (shared apex, point-to-point)…

▸ Placing the cutting plane at an angle

▸ Taking the section: circle · ellipse · parabola · hyperbola

▸ Computing foci, directrix & eccentricity e = c/a

▸ Attaching a Kepler orbit around the focus…

▸ Ready — Online. ✅

Eccentricity & parameters

🥧 Circle

e = c / a · conic type

Conic type—

Eccentricity e—

Semi-major axis a—

Semi-minor axis b—

Focal distance c—

Cut angle—

Tip

A plane cuts through a double cone: cut horizontally → a circle, tilt moderately → an ellipse, parallel to a generator → a parabola, steeply through both nappes → a hyperbola. The number eccentricity e = c/a decides both the shape and the orbit type.

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Drag the Eccentricity e bar to morph the conic · change the Scenario (circle · ellipse · parabola · hyperbola · Kepler orbit · sweep e) · click a structure to open its card

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eccentricity e · flatness b/a · cut angle over time eb/acut angle