Astronomy & Celestial Mechanics
the sky, computed
Concept

Gravitational constant — where it appears

The constant G in Newton's law, known only to about twenty parts per million because gravity between laboratory masses is so weak. In the sky only the product GM is measured, so a change in G over time is indistinguishable from a change in the mass it multiplies.

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

G: 14 determinations in two families. Published determinations of G, each with its quoted one-sigma interval, sorted into two families — torsion balance, in one form or another, against beam balance, pendulum, atom interferometry. The shaded band behind each family is that family's inverse-variance weighted mean: 6.67435 ± 0.00004 across 11 of them, against 6.67343 ± 0.00009 across 3. The difference is 0.00092 ± 0.00010 10⁻¹¹ m³ kg⁻¹ s⁻², which is 9.3 standard deviations, computed here from the quoted errors alone. The arithmetic is the same one the Hubble figure uses and here it should be distrusted, because the scatter inside each family already exceeds what the intervals allow: eleven torsion-balance determinations spread over 500 parts per million with quoted intervals of 12 to 130 cannot all be right, whatever the difference between the families comes to. That is why the recommended value's uncertainty is expanded far beyond any single experiment's rather than being the weighted combination drawn here — the disagreement is between laboratories using the same method, not between methods.

Nothing in the sky is weighed in kilograms

The Sun's gravitational parameter is known to eleven significant figures. The Sun's mass is known to five. The two statements are about the same object and the difference between them is a constant measured in basements, which is the worst-determined fundamental constant in physics.

gravitation · Gravitational constant A band and a strip, and the constant where they cross. The plane of the two quantities a planetary ephemeris cannot separate: the fractional rate of change of the gravitational constant, vertically, and of the Sun's mass, horizontally, both in units of 10⁻¹⁴ per year. The orbits respond only to their sum, the rate of change of GM☉, so a measurement of that sum — drawn here as −9.0 ± 3.0 × 10⁻¹⁴ per year, the precision recent ephemerides reach, not any one published value — is a diagonal band. On its own it allows any Ġ/G at all, provided the Sun's mass is changing to compensate. The vertical strip is the Sun's mass loss computed from its luminosity and its wind, −9.9 to −8.8 × 10⁻¹⁴ per year. Where the two overlap, Ġ/G lies between −3.2 and 3.9 × 10⁻¹⁴ per year. The bound on a change in a fundamental constant is therefore set as much by how well the solar wind is measured as by how well the planets are.

A constant measured through a Sun that is getting lighter

Whether the gravitational constant changes with time is tested by watching the planets, and the planets report only the product of G with the Sun's mass. The Sun is losing mass — four million tonnes a second as light, a million and a half more as wind — at nearly a ten-trillionth of itself a year, and every bound on a changing G is a statement about the solar wind as much as about gravity.

gravitation · Gravitational constant Oceans that a changing G would have boiled. The Earth's surface temperature in a crude climate — equilibrium temperature for a fixed albedo, scaled as the received flux to the quarter power, plus a fixed greenhouse warming of 33 K — against time before the present, if the Sun's luminosity goes as G⁷ and the Earth's orbit as 1/G, so the flux goes as G⁹, on top of the Sun's own brightening. With Dirac's G ∝ 1/t and an age of 13.8 Gyr, the oceans boil 1.9 Gyr ago; with G falling by 10⁻¹¹ of itself a year, the surface is 292 K at 3.8 Gyr. Rocks of that age were laid down in water. Constant G gives the faint young Sun's cooling, 270 K in this climate — a separate problem, which the real atmosphere solved.

A constant bounded by the oceans

In 1937 Dirac proposed that the gravitational constant falls as the universe ages. Eleven years later Teller pointed out what that would have done to the Earth: a star's luminosity depends on G to about the seventh power, the Earth's orbit shrinks as G grows, and the sunlight reaching the Earth goes as the ninth power. Run backwards, Dirac's G boils the oceans less than two billion years ago. The rocks were laid down in water, so G cannot have changed that fast — the first bound on a changing constant came from geology.

gravitation · Gravitational constant

Named alongside it

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

Adiabatic invariantAstronomical unit (AU)Lunar laser rangingVarying constantsDegeneracyDimensional analysisEphemerisFaint young sunGravitational parameterHelioseismologyKepler's third lawThe mass–luminosity relation

All concepts