Astronomy & Celestial Mechanics
the sky, computed
Concept

Admittance — where it appears

The ratio, at each wavelength, of a planet's gravity anomaly to its topography. Its dependence on wavelength says how the topography is supported: by the rigidity of the lithosphere at short wavelengths and by buoyancy, as compensation, at long ones.

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

Also named here as lithosphere — the same set of essays touches all of them, so they are one junction rather than several.

A moment of inertia that is a shape plus an assumption. The Darwin–Radau relation: the polar moment of inertia a body would have, given the ratio of its rotation parameter to its flattening, if it were a hydrostatic fluid. The curve passes through exactly 0.4 at q/f = 0.8, which is the uniform sphere and the one point that needs no interior model, and falls as the body becomes more centrally condensed. Four of the five worlds drawn sit on it within a few per cent of their independently measured moments, which is what makes the relation usable at all. The world that does not appear on the plot is the Moon, whose q/f is 0.025 — far outside the window in which the relation has a real solution, because its shape is a fossil frozen in when it was much closer to its primary and has nothing to do with its present rotation. That failure is the useful one. A relation that returns a wrong answer quietly is dangerous; this one returns no answer at all.

The part of a shape the spin cannot explain

A rotating planet bulges by a predictable amount. Subtract that amount from the shape actually observed and something is usually left over — a few parts in a hundred thousand for the Earth, and ninety-seven per cent of the whole bulge for the Moon. The residue is not an error. It is the only remote measurement of what a planet's interior is doing that does not average over the whole body.

gravitation · Moment of inertia Gravity per kilometre of topography, by wavelength. The free-air gravity anomaly per kilometre of topography — the admittance — on Earth, against the wavelength of the topography, for elastic plates 5, 25, 100 km thick, with crust of density 2800 kg/m³ over mantle of 3300 and compensation at 35 km. Short wavelengths are uncompensated and give the full attraction of a slab of crust, 117 mGal per km. Long wavelengths are compensated and give nearly nothing, because the mass of the mountain is cancelled by the root beneath it. Where the curve falls between the two is set by the plate's thickness, so a measured admittance spectrum is a measurement of how strong the lithosphere was when the load was applied.

A mountain's gravity says what holds it up

A mountain can stand because the rock beneath it is strong, or because it floats on a deep root of light crust like an iceberg. The two leave different gravity behind them, and the difference depends on the mountain's size — so the ratio of gravity to topography, measured wavelength by wavelength, is a measurement of how stiff a planet's outer shell was when the mountain was built.

gravitation · Moment of inertia

Named alongside it

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

LithosphereDarwin radauDynamical ellipticityElastic thicknessFlexureFossil bulgeFree air anomalyGravity anomalyHydrostatic equilibriumIsostasyMass anomalyMoho

All concepts