Space Sciences
Orbital Mechanics
1619
IntermediateKepler's Third Law
Orbital period squared is proportional to semi-major axis cubed.
By Johannes Kepler
Space Sciences
Kepler's Third Law
1619 · Johannes Kepler
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Story PortalWho discovered this?Discover how Johannes Kepler and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — satellite orbits.Math PortalWhat does it derive from?Trace the mathematical lineage from universal gravitation.Future PortalWhere is it going?Interstellar trajectory design
Why it matters: Enabled Newton to discover universal gravitation; foundation of spaceflight.
Discoverers: Johannes Kepler (1619)
What does it mean?
Orbital period squared is proportional to semi-major axis cubed.
Why should I care?
Enabled Newton to discover universal gravitation; foundation of spaceflight.
Equation Compass
North — Prerequisites
West — History
East — Applications
South — Derivations
Variables & Units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Period | s | Orbital period | |
| Semi-major axis | m | Orbit size | |
| Central mass | kg | Mass being orbited |
Worked Example
Earth year from a = 1 AU and M = solar mass.
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Equation Universe
Kepler's Third Law
Real-world impact
Satellite constellations
Elliptical orbits place Starlink, GPS, and Webb at precise altitudes.
Photo: Unsplash — satellite orbit
Orbital period squared is proportional to semi-major axis cubed.
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