Astronomy & Celestial Mechanics
the sky, computed
Concept

Anomalistic month — where it appears

The time the Moon takes from one perigee to the next, 27.55 days. It differs from the sidereal and synodic months because the point of closest approach advances round the orbit, and it sets the cycle on which the Moon's speed across the sky varies.

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

The sub-Earth point over 400 days. Where on the Moon the Earth stands overhead, in selenographic longitude and latitude, sampled over 400 days. The excursion in longitude is the equation of centre — the Moon's rotation is uniform and its orbital motion is not, so the face runs alternately ahead and behind by up to 6.3° — and the excursion in latitude is the tilt of its equator, up to 6.7°. The two run on months of different length, so the track never repeats.

The face that is not quite fixed

The Moon keeps one face turned toward the Earth, and the sentence is exactly true only of a fictitious Moon on a circular orbit. The real one rocks by a few degrees each month, in two directions and for two unrelated reasons, and the rocking has shown 59 per cent of its surface to people who never left the ground.

sky · Libration A right angle short by 0.147°, and a ratio of 389 hanging on it. The ratio of the Sun's distance to the Moon's implied by the angle between them at the moment the Moon is exactly half lit, on a logarithmic scale, for angles from 80° to 89.95°. At that moment the angle at the Moon between the directions to the Sun and the Earth is a right angle, so the ratio is the secant of the observed angle — a construction with no distance in it, the same right triangle that gives an inferior planet's orbit from its greatest elongation. Aristarchus measured 87°, which gives 19.1. The mean distances give 389, which corresponds to 89.853°. The curve's steepness is the whole story: across a tenth of a degree centred on each marked angle the ratio changes by 3.4 per cent at 87°, 10.5 per cent at 89° and 103 per cent at the true angle. The method was exact and it asked for a right angle measured to a hundredth of a degree, at an instant the eye can judge only to within hours, on a terminator that is never quite straight.

A right angle short by a seventh of a degree

When the Moon is exactly half lit, the angle at the Moon between the Sun and the Earth is a right angle, so the angle seen from the Earth gives the Sun's distance in units of the Moon's. Aristarchus measured 87° and concluded the Sun was nineteen times further away. The construction was exact; the angle he needed was 89.85°, and at that angle a tenth of a degree is the whole answer.

sky · Apparent motion

Named alongside it

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

Astronomical unit (AU)Cassinis lawsDichotomyDraconic monthElongationEquation of centreError propagationGreatest elongationKepler's second lawLibrationLunar eccentricityLunar laser ranging

All concepts