Astronomy & Celestial Mechanics
the sky, computed
Concept

Ascending node — where it appears

The point at which an orbit crosses the reference plane going northward, and the direction to it from the central body. It is undefined for an orbit in the reference plane, which is the second of the two coordinate singularities the classical element set carries.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

An orbit at i = 42°, Ω = 35°, ω = 55°. The three orientation elements. The orbit is generated in its own plane and rotated by the standard sequence, so the inclination, the node line and the argument of periapsis are the angles that produced the drawn curve rather than labels applied to it.

Six numbers that fix an orbit for all time, and the sixth is the awkward one

Five of the orbital elements describe a curve that never changes. The sixth says where on it the body is, and it is the only one that has to keep being measured.

orbits · Orbital elements Three rotations, applied in order. An orbit of eccentricity 0.45 carried into space by the three orientation angles, one panel per rotation: the argument of periapsis ω = 40°, then the inclination i = 42°, then the longitude of the ascending node Ω = 55°. The last panel applies the same three angles in the reverse order and arrives somewhere else, because rotations about different axes do not commute.

Three rotations that put an orbit in space, and they do not commute

An orbit's orientation takes three angles. Give the same three angles in a different order and the orbit ends up somewhere else — which is why the convention is part of the data.

orbits · Orbital elements Three periods that nearly share a multiple. How far the draconic and anomalistic months are from a whole number, after a whole number of synodic months, in hours. At 223 synodic months — 6585.321 days — both are within an hour of closing, which is what makes an eclipse repeat. The draconic residual is 0.87 hours and the anomalistic 5.19 hours.

The eclipse that repeats a third of a world away

Three lunar periods nearly share a multiple after 6,585 days. The word "nearly" is what makes eclipses predictable, and the leftover third of a day is what moves each repeat a third of the way round the Earth.

sky · Phases and eclipses

Named alongside it

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

Orbital inclinationAnomalyArgument of periapsisEccentricityEpochOrbital elementsPeriapsisEquinoxLibrationLunar phaseMean anomalyReference frames

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