Two views, one instant
The top pane is the horizon: you are standing at Lesbois, and the arc is the Moon's whole trip from where it rises to where it sets. The bottom pane is the orbit: the same moment seen from outside, with Earth inside its reference planes.
Both run off one ephemeris and one clock, so anything that moves in one is immediately readable in the other. That is the method: everything below is a claim you can check by scrubbing.
Altitude and azimuth
Two numbers fix any point in the sky as seen from one spot. Altitude is the angle up from the horizon: 0° at the skyline, 90° overhead. Azimuth is the compass bearing round to it: 0° north, 90° east, 180° south.
Both belong to you, not to the sky, which is exactly what the two grids show. The alt-azimuth graticule is pinned to your ground: its poles are the zenith and the point under your feet, its equator is the horizon. It never moves, and the sky slides through it. The equatorial one is pinned to the sky, so it turns with everything on it and the horizon cuts across it at an angle. Switch between them and watch which one holds still.
Declination sets the ceiling
Declination (δ) is the sky's own latitude: the angle north or south of the celestial equator. It changes slowly. Your latitude (φ) does not change at all. Between them they fix how high anything can ever get:
peak altitude = 90° − |φ − δ|
From Lesbois at 48.44° N a Moon at δ = −28° tops out near 13.6°, and no hour of the night can lift it higher. Run a month past and watch the Declination and Peak altitude readouts: the peak follows the declination and never argues with it.
Three planes, two tilts
The orbital pane draws three discs at one radius, so the angle where any two rims cross is the true angle between those planes.
The celestial equator is Earth's equatorial plane, cutting the globe exactly on the equator. The ecliptic is the plane of Earth's orbit, tilted 23.4° off it, which is why it crosses the tropics rather than the equator. The lunar orbit is tilted a further 5.1° off the ecliptic.
Those two tilts do not simply add. Depending on where the Moon's orbit currently has its nodes they reinforce or cancel, so the Moon's declination range breathes between about ±18.3° and ±28.6° over 18.6 years. Near the wide end, a major lunar standstill, the Moon swings further south than the Sun ever does, and from northern Europe it crawls along the horizon.
What the colours mean, Earth-centred
- Celestial equator
- Ecliptic
- Earth’s orbit
- Lunar orbit
- Sun
Rotation against orbit
Two motions run at once, at wildly different speeds. Earth turns once in 23 h 56 m: about 15° of sky every hour. The Moon creeps along its own orbit at roughly 13.2° a day: half a degree an hour, about its own width.
So the arc across the sky is very nearly Earth's rotation alone, and the orbit shows up only as a slow eastward drift against the stars. That drift is why moonrise comes about 50 minutes later each day. Hold the throttle at 1 hour/sec and the arc sweeps; hold it at 1 day/sec and the arc itself walks.
Sidereal and synodic month
The Moon returns to the same star after 27.32 days: a sidereal month, one real lap of the orbit. It returns to the same phase after 29.53 days: a synodic month.
The difference is Earth's own travel. While the Moon went round once we moved about 27° along our orbit, so the Sun is no longer where it was and the Moon needs another two days to make the same angle to it. Run at 1 day/sec: the Moon comes back to the same place on its green ring well before it comes back to the same phase.
Why an arc flattens at the top
Altitude near culmination varies as the cosine of the hour angle, and a cosine is flat at its peak. In the hour either side of its highest point a body gives up only a few percent of its climb, while it keeps travelling sideways at the full rate.
On a high arc nobody notices. On a shallow one (a peak of 13° rather than 60°) there is barely any vertical motion to lose, so for two or three hours the Moon holds almost exactly the same height while sliding along the southern horizon. It looks stuck. It is moving as fast as it ever does; it is simply not moving up.
Phase is geometry, not shadow
Half the Moon is lit at all times. Phase is only how much of that lit half happens to face us, and it follows one number: the Sun–Moon–Earth angle. Earth's shadow has nothing to do with it. That is an eclipse, which needs the Moon at a node and is rare.
The line between lit and unlit is the terminator: the Moon's own sunrise and sunset. It is drawn here from the real Sun direction, which is why the phase in the orbital view and the phase in the horizon view are one fact drawn twice, and agree at every instant.
Earth's orbit, with Earth still at the centre
The ecliptic disc is the plane of Earth's orbit. The bright ring drawn on it is the path: a circle centred on the Sun, of exactly the Earth–Sun distance, which therefore passes through the Earth. So the Earth stands on its own orbit without being moved off centre.
Scrub a year past and the ring pivots about the Earth as the Sun swings round. That is our orbit, seen from the one place none of us can step off. The ticks are the first of each month and the four instants that divide the year. Every mark says where Earth is, never where the Sun appears.
The Sun-centred view, and what is exaggerated
Press Sun-centred to step outside the Earth altogether. The Sun goes to the middle, the eight planets take their real places on their real orbits, inclinations and axial tilts included, and the Earth carries its Moon round with it. Nothing changes reference frame: the solar system is simply drawn about the origin instead of about the Earth, which is why the ecliptic sits at the same angle in both views.
Two things are exaggerated, and both have to be. Distances are compressed as a power of the true ones: Neptune is 78 times further out than Mercury, and drawn honestly either the inner planets are a knot or Neptune is off screen. The Earth–Moon pair is enlarged, because at true scale the Moon is a four-hundredth of Earth's distance from the Sun and would be less than a pixel. Directions, tilts, phases and the place of every body in its orbit are untouched.
What the colours mean, Sun-centred
- Sun
- Ecliptic plane
- Earth + Moon, enlarged
- Distances compressed
