Astronomy & Celestial Mechanics
the sky, computed
Concept

Isolation mass — where it appears

The mass a growing body reaches by sweeping clean the annulus its own gravity reaches. It goes as the solid surface density to the three-halves power, so a step in available solid material is a larger step in the biggest core that can be assembled locally.

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

Three orders of magnitude in astronomical units, and a factor of 9.6 in mutual Hill radii. Every adjacent pair of planets in three systems, plotted by the separation between them measured in their own mutual Hill radius, ((m₁+m₂)/3M⋆)^⅓ · (a₁+a₂)/2. In astronomical units the same 17 separations span a factor of 2554 — from 0.0043 AU between two TRAPPIST-1 planets to 10.9 between Uranus and Neptune — and carry no visible structure at all. In this unit they span 9.6, with a median of 11.8. The solid line at 2√3 = 3.46 is a theorem: two planets on circular coplanar orbits wider apart than that can never have a close encounter, whatever else happens, and every pair here is clear of it. The dashed line at 10 is a fit, to integrations of systems of several planets over billions of years, and it is the one that bites — a system packed tighter than about ten does not survive, which is why the observed distribution has a floor there and not at the theorem. A planetary system's spacing is not measured in kilometres. It is measured in a unit the planets define.

A feeding zone, and the spacing it forces

The radius that decides what a planet may keep also decides what it could reach while it was growing — and measuring the gaps between planets in that unit turns a distribution spanning three orders of magnitude in astronomical units into a band a factor of ten wide, with a floor that is partly a theorem and partly a fit.

gravitation · Hill sphere The ice line at 2.7 AU, and the 3.4-fold jump in solid material across it. Two temperature thresholds turned into radii, against stellar mass, both axes logarithmic. The shaded band is the habitable zone, where water can be liquid on a planet's surface. The heavy line is the snow line of the disc the planets formed in — the distance at which a passively heated disc, whose temperature falls as the inverse square root of radius, reaches 170 K and water freezes. For a solar-luminosity star it sits at 2.71 AU, just outside the asteroid belt, and it is 1.6 times further out than the outer edge of the habitable zone; around a 0.15 solar-mass star both have moved inwards and the ratio is 5.5. What makes the line matter is what happens as it is crossed. Water is by far the most abundant condensable material after hydrogen and helium, so freezing it raises the surface density of solids by roughly 3.4 times in one step. Everything about the architecture of a planetary system follows from that step: a core massive enough to capture gas can be assembled outside the line and not inside it, which is why the solar system has small rocky planets in and giant ones out, and why a giant planet found at 0.05 AU is a statement about migration rather than about formation. The line is drawn where a mature disc puts it; a young, accreting disc is hotter and its line is several times further out, sweeping inwards as the disc drains.

The line beyond which ice counts as rock

A disc of gas around a young star gets colder outwards, and at about a hundred and seventy kelvin water stops being vapour and becomes a building material. Crossing that one line multiplies the solid mass available by roughly three and a half, in a single step, and the architecture of every planetary system is downstream of it.

exoplanets · The snow line

Named alongside it

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

PlanetesimalThe snow lineCondensation sequenceCore accretionDisc evolutionDynamical spacingEquilibrium temperatureFeeding zoneGiant planet formationHill stabilityJacobi constantThe mutual Hill radius

All concepts