Illustrated Physics
physics, drawn
Concept

Lunar laser ranging — where it appears

Measuring the distance to the Moon by timing laser pulses returned from corner-cube reflectors left on its surface by Apollo and Lunokhod missions. It tracks the Moon to millimetres, measures its recession of 3.8 cm a year and tests whether the Earth and Moon fall alike toward the Sun.

Named by 3 essays across 2 fields — 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 Six ways into a corner, each leaving from the opposite side. A corner cube seen along its axis: its hexagonal face, divided into six sectors by the three edges where its mirror faces meet and by their extensions. A ray entering along the axis meets the three faces in an order fixed by the sector it enters: y → x → z, y → z → x, z → y → x, z → x → y, x → z → y, x → y → z. Traced reflection by reflection, every ray leaves travelling exactly back along its arrival direction, to rounding error, and it leaves from the point diametrically opposite where it entered — in the sector whose order is the reverse of its own.

The corner that sends light home

Three mirrors at right angles send light straight back the way it came, from any direction they can see, because each one reverses one component of its direction. Made from solid glass, a corner reflects by total internal reflection and needs no silver — which is why the reflectors left on the Moon are bare glass — but each of its six sectors then returns a different polarisation, and the returned spot loses three-quarters of its peak.

optics · Total internal reflection Two pulls that should be equal and opposite. Two bodies of equal passive mass, one of an ordinary material and one of a material whose active mass is 30 per cent larger than its passive mass (the difference exaggerated to be seen). Each pulls the other with its active mass and is pulled on its passive mass. The pull the unusual body exerts is therefore larger than the pull it receives, the two arrows are not equal and opposite, and the pair, with nothing outside it, accelerates towards the ordinary body. Newton's third law and the conservation of momentum both require the ratio of active to passive mass to be the same for every material, and that is a separate claim from the one torsion balances test, that passive and inertial mass agree.

The pull that has to equal the pull back

Every test of the equivalence principle drops two things and asks whether gravity pulls them equally. None of them asks whether they pull equally. A body's mass enters gravity twice — once as what is pulled and once as what does the pulling — and if the two ratios differed from one material to another, Newton's third law would fail and a lopsided body could push itself through space. The first test of this used a plastic cylinder floating in a liquid. The best uses the Moon, whose light crust is thicker on the side that never faces the Earth.

astrophysics · Equivalence principle

Named alongside it

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

Equivalence principleGravitational massNull experimentActive gravitational massBinding energyCritical angleDiffractionFar fieldFresnel equationsInertial massMomentum conservationNewtons third law

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