What a Reference Plane Is
A great circle to measure along and a pole to measure away from — the two-part machine that turns a direction in the sky into a pair of numbers.
The Two Planes
The celestial equator and the ecliptic set side by side — one built on the Earth's rotation, one on its orbit, and both already met.
The Obliquity of the Ecliptic
The 23.4° tilt between the two reference planes, which is the tilt of the Earth's axis, and what follows from it: the Sun's changing declination, the seasons, the tropics and the polar circles.
Ecliptic Coordinates
Celestial longitude and latitude, measured from the ecliptic — the frame astrology is written in, and why one number is usually enough.
Equatorial Coordinates
Right ascension and declination, measured from the celestial equator — the astronomer's frame, and the one the sky's daily turn makes natural.
Right Ascension: Hours or Degrees
Right ascension is one angle written two ways: star catalogues quote hours because the sky turns once a day, and astrological software quotes degrees, at fifteen degrees to the hour.
Projecting Between the Planes
A fence with palings a degree apart, a planet hovering above it, and what happens to the reading when you tilt the fence and leave the planet alone.
Why the Same Degree Arrives at Two Different Times
Search for the same crossing in both planes and the dates differ — by seconds for the Sun, by hours for the Moon, and by three years for Pluto.
Why Signs Don't Apply to Right Ascension
Signs are divisions of the ecliptic. Right ascension is measured around a different circle, so a sign name attached to it would name a region the body is not in, which is why sign names are withheld.
Declination, Parallels and Contraparallels
The relationship two bodies can have across the plane rather than along it — and why the frame you select decides which measurement it is matched in.
Ecliptic and Equatorial Compared
What differs between the two frames — the columns, the vocabulary, the available relationships, and the dates.