Astronomy & Celestial Mechanics
the sky, computed
Concept

Kirkwood gaps — where it appears

The depleted regions in the asteroid belt at semi-major axes commensurable with Jupiter's period. They are cleared by resonance overlap driving the eccentricity to planet-crossing values within a few million years, rather than by any single resonance acting alone.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Period against size for the planets, around the Sun. Orbital period against semi-major axis on logarithmic axes. The line has slope exactly three-halves — the harmonic law — and the measured bodies sit on it.

The law that links period to size, and weighs everything

Kepler found that the square of the period goes as the cube of the orbit. Newton found the constant of proportionality, and that constant is a mass — which is how every mass in astronomy has been obtained since.

orbits · Harmonic law The Kirkwood gaps. Asteroid numbers against semi-major axis, with the resonant radii marked. Each gap sits where the orbital period is a simple fraction of Jupiter's, and each of those radii is computed from the harmonic law rather than placed by eye.

Resonance clears a gap in one place and locks a moon in another

When two orbital periods are in a simple ratio, small tugs stop averaging away and start accumulating. Sometimes that empties a region entirely. Sometimes it holds three moons together for the age of the solar system.

gravitation · Resonance

Named alongside it

The objects these essays reach for when they reach for this one.

EccentricityAstronomical unit (AU)Black holeDynamical massGravitational massKepler's third lawLaplace resonanceLibrationMean motion resonanceOrbital periodPeriapsisResonant angle

All concepts