Illustrated Physics
physics, drawn
Concept

Post-newtonian parameters — where it appears

A set of numbers, such as γ and β, describing how any metric theory of gravity departs from Newton's in weak fields. General relativity gives both exactly one; γ measures the space curvature produced by unit mass.

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

The month a binding energy would bend. The Moon's orbit seen with the Sun held off to the right, drawn as it would be if the Earth's binding energy fell towards the Sun more weakly than the rest of it. The Earth is bound by 4.5 × 10⁻¹⁰ of its mass-energy and the Moon by 1.9 × 10⁻¹¹, so with the Sun pulling at 5.93 mm/s² the Moon is pushed sunward relative to the Earth by 2.6 × 10⁻¹² m/s² for every unit of η. That push turns once a synodic month relative to the orbit, 29.53 days, and Hill's equations about a circular orbit — integrated from the forced solution and held on it to 4 × 10⁻¹¹ over twelve months — give a radial displacement of 8.0 m times η times the cosine of the lunar phase: outward at new moon, inward at full. The complete lunar theory, with the Sun's tide on the orbit included, gives 13.1 m. The displacement is drawn about 7 × 10⁶ times larger than it would be at η = 1.

The binding energy that has to fall too

Every laboratory test of the equivalence principle compares bodies whose own gravity is a part in 10²⁵ of their mass, so none of them can ask whether gravitational binding energy falls like everything else. The Earth is bound by five parts in ten billion and the Moon by twenty times less, and if that difference fell differently the Moon's orbit would lean towards the Sun once a month — by a distance lasers have been measuring since 1969.

astrophysics · Equivalence principle The slice through a mass that a ruler has to climb. A plane through the centre of a uniform body whose compactness 2GM/Rc² is 0.34 — about a neutron star's — drawn as a curved surface on which distances along the surface are the distances rulers measure. The body's edge is a circle whose circumference is 2πR; a ruler laid from the centre to that edge along the surface measures 1.068 R, 6.8 per cent more. Outside the body the surface is Flamm's paraboloid; inside it is a cap of a sphere. The flat line beneath is what Euclid would give. The height of the surface means nothing; only lengths along it are measured. For the Earth the same excess is 1.5 mm in 6,371 km and the surface would be indistinguishable from the flat line.

The radius a mass adds that no circumference shows

Walk round the Earth's equator and divide by 2π, and the number is the Earth's radius. Dig to the centre and measure the same radius with a tape, and the tape comes out about two millimetres longer. Nothing is wrong with either measurement. A mass does not only slow the clocks near it; it stretches the rulers too, and the stretch is exactly as large as the slowing. Clocks cannot see it. Light can, and half of every bend and every delay that light suffers near the Sun is this.

astrophysics · Gravitational redshift

Named alongside it

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

Binding energyEquivalence principleExcess radiusGeneral relativityGravitational massGravitational redshiftLight deflectionLunar laser rangingNull experimentResonanceSchwarzschild metricSelf-gravity

All concepts