Astronomy & Celestial Mechanics
the sky, computed
Concept

TRAPPIST-1 — where it appears

A small red dwarf forty light-years away with seven rocky planets, three or four of them in its temperate zone. Its planets are the best-studied test of whether rocky worlds around the commonest stars keep their atmospheres.

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

Libration and circulation of a resonant angle. The critical angle of a resonance over time, integrated from the pendulum equation it obeys. Below the separatrix the angle oscillates about a fixed value — the body is locked; above it, the angle runs without bound and the body is not.

A chain that could not have been assembled in place

Seven planets whose successive period ratios are all close to small whole numbers. Capture into a resonance requires the orbits to converge slowly, and converging slowly is something planets can only do in a disc.

exoplanets · Resonance The same worlds, placed by the light that strips. The bodies of the shoreline plane, each moved from its present instellation to the cumulative X-ray and extreme-ultraviolet energy it has received over its star's life, both relative to the Earth's (arrows). The Sun's planets do not move, by construction. A planet of a small red dwarf moves up by a factor of 7 to 16: its star stayed at its saturated activity level — a thousandth of its light in X-rays and extreme ultraviolet — for 2.3 billion years for TRAPPIST-1 against 0.1 for the Sun, and its planets have absorbed that for longer. TRAPPIST-1 e, which receives 0.65 of the Earth's sunlight, has received 10 times the Earth's lifetime XUV and moves from well inside the line to above it. Every planet measured as bare, TRAPPIST-1 b, TRAPPIST-1 c, LHS 3844 b, now lies above the line. The saturation times are a scaling with stellar mass rather than a fit to any one star.

A shoreline measured in light already spent

In the solar system one line of slope four, in the plane of escape velocity against sunlight, separates every world with air from every world without. Drawn against the light a planet receives today it puts the temperate planets of a small red dwarf safely on the side with air. Drawn against the stripping light their star has already spent, it moves them an order of magnitude toward the airless side — and leaves most of them inside a band that the line's unknown height cannot resolve.

exoplanets · Exoplanet atmospheres

Named alongside it

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

Adiabatic invariantConvergent migrationCosmic shorelineDynamical stabilityEnergy-limited escapeEscape velocityLaplace resonanceLibrationMigrationRed dwarfsResonance captureResonant chain

All concepts