Astronomy & Celestial Mechanics
the sky, computed
Concept

Triaxiality — where it appears

The fractional difference between a body's two equatorial moments of inertia, divided by its polar one. It sets the restoring torque on a locked body and therefore the period of its free libration, which is the orbital period divided by the root of three times it.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

Where the fuel goes, and it is not where a satellite points. Left, the orbit pole of a geostationary satellite, in degrees from the Earth's. The Sun and the Moon between them carry it round a circle of radius 7.4° in 53 years, and a satellite launched into the equatorial plane starts on the rim of that circle rather than at its centre — so its inclination climbs from zero at 0.88° a year, reaches 14.8° after 27 years, and comes back. Right, what holding it costs. A plane change of 0.88° at 3.07 km/s is 47.1 m/s a year; holding the longitude against the equatorial bulge, computed from the same resonant term that makes the longitude a pendulum, is 1.8 m/s a year. North–south is 96% of the budget, and a satellite that gives up on it does not fail — it starts tracing a figure of eight on the sky 1.8° tall in the first year, which a fixed dish cannot follow and a steerable one can. Retiring at the end of the propellant is therefore a choice about which service ends first.

The orbit that has to be paid for every year

A geostationary satellite is not in equilibrium in any direction. The Sun and Moon tilt its plane by 0.85 degrees a year, the Earth's equatorial ellipticity makes two longitudes stable and two unstable, and the end of a satellite's life is the end of its propellant.

spaceflight · Station-keeping A free libration does not last. How long a free libration survives before tidal dissipation removes it, against the tidal quality factor, for four locked bodies — with the age of the solar system marked. A lightly damped oscillator loses its amplitude in about Q of its own periods, and a free libration's period is years, so the decay time is thousands to hundreds of thousands of years for any plausible Q. Against 4.5 billion years that is instantaneous. A free libration that is observed today was excited within the last geological instant, and one that is not observed bounds how much has happened. The Moon's is detected, at a few arcseconds, and requires something recent — an impact, a core–mantle interaction, or a resonance passage. Mercury's has been searched for and not found, and the upper limit is the constraint.

A rocking nobody started

A locked body is a pendulum, and a pendulum has a period of its own. That free libration is damped by tides in thousands of years, so any body still oscillating at its own frequency was disturbed in the last geological instant — and the Moon is, while Mercury is not.

sky · Libration An excess the hole cannot afford for long. The mass a 10⁶-solar-mass hole gains from disrupted stars, in units of its own mass, against how long an excess in the disruption rate lasts, for excesses of 30, 100, 300 over the relaxed nucleus's 7.4·10⁻⁵ a year, with half of each Sun-like star accreted. An excess of 100 doubles the hole in 2.7·10⁸ years, an excess of 300 in 9·10⁷. The post-starburst phase that selects the hosts lasts about a billion years, so an excess of a hundred sustained through it would have grown every such hole several times over, and the galaxies that were post-starbursts a few billion years ago would carry holes several times heavier than their stars' motions predict. A binary's spike of 0.1 a year for 3·10⁵ years feeds it only 1.5%.

A flare rate a hole cannot afford for long

Tidal disruption flares are found in galaxies that stopped forming stars within the last billion years far more often than those galaxies' numbers allow — by factors estimated between thirty and two hundred. Each proposed cause can be priced. A dense cluster from the burst would need ten times the hole's mass of new stars inside a parsec; a triaxial nucleus would give twenty times too much; and any excess of a hundred, kept for the length of the phase, would feed a million-solar-mass hole several times its own mass.

galaxies · Tidal disruption

Named alongside it

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

Black hole growthCore mantle boundaryEnd of lifeExcitationForced librationFree librationGeostationary orbitGraveyard orbitInclination driftLibrationLoss coneLunar laser ranging

All concepts