Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Students · Kepler Orbits

Kepler Orbits for a spinning top

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a spinning top live below — adjust the inputs and watch it respond, right in your browser.

Kepler Orbit StudioLive

two-body gravity · conic-section orbits

Controls

Speed1×

Set the eccentricity to trace Kepler's orbits — a circle, ellipse, or (past e=1) an escape hyperbola. The star sits at the focus. Drag the planet on the canvas to reposition its starting point and reshape the orbit.

Presets

Eccentricity e

Semi-major axis

▶ Run in Python

Data Inspector

Eccentricity0.60

Orbitelliptical

LawKepler / 1-r²

Governing equation

r = \frac{a ( 1 - e ^{2} )}{1 + e cos θ} = \frac{140 ( 1 - 0.6 0 ^{2} )}{1 + 0.60 cos θ}

Reading this result: At e=0.60 the orbit is an ellipse with the star at one focus. The planet sweeps equal areas in equal times, so it runs fastest at perihelion and slowest at aphelion. A higher e means a more elongated ellipse. The period grows as a^(3/2) (Kepler's third law), so a=140 sets the year length.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Kepler Orbits

Kepler Orbits for a projectile from a cannon Kepler Orbits for a bouncing ball Kepler Orbits for a pendulum clock Kepler Orbits for a car braking Kepler Orbits for a roller-coaster loop Kepler Orbits for a satellite orbit Kepler Orbits for a mass on a spring Kepler Orbits for a skydiver's free fall

Frequently asked questions

Is this good for students?: Yes — this version of "Kepler Orbits for a spinning top" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.