The Wheel Overhead

Earth spins around an axis — the line through the north and south poles — once a day, turning toward the east. You ride along, so the whole sky appears to turn the opposite way, toward the west. Stars rise over the eastern horizon, arc across the sky, and set in the west, exactly as the Sun does. One point never moves: the spot straight above Earth's north pole. Polaris happens to sit there.

Stars near that still point never reach the horizon at all. They ride small circles around Polaris all night, every night of the year. The Big Dipper is one of them for most of North America and Europe — always up, somewhere.

The sky appears to rotate about two fixed points, the celestial poles — the spots directly above Earth's own poles. From mid-northern latitudes the north celestial pole stands partway up the northern sky, at Polaris, at your latitude's altitude. Stars close to it trace complete circles above the horizon and never set: they are circumpolar. Stars farther from the pole spend part of each turn below the horizon — they rise and set. The dividing rule is clean: any star within your-latitude degrees of the pole is circumpolar for you.

The turn is steady: 360 degrees in 23 hours 56 minutes — near enough 15 degrees per hour. Ninety minutes of spin moves every star in the sky by about one fist.

The sky's rotation period, 23 h 56 m 4 s, is the sidereal day — one true rotation of Earth measured against the stars. The familiar 24-hour solar day runs longer because Earth advances about one degree along its orbit each day and must spin that extra degree before it faces the Sun again; one degree costs four minutes. Rates worth owning: 15° per hour, and one full-Moon width — half a degree — every two minutes.

Geometry sets each star's arc. A star rising due east climbs a path tilted toward the south, meeting the horizon at an angle of 90° minus your latitude, and peaks as it crosses the meridian — the north-to-south line passing overhead. The never-setting condition: the star's distance from the pole must be less than your latitude. At the equator, every star rises and sets; at the pole, none do either.

Stand in your room and spin slowly. The walls seem to glide past you. But the walls are still — you are the one turning. The sky works the same way. Earth turns, so the stars seem to slide.

Earth turns toward the east. So the stars seem to move the other way, toward the west. The Sun does it too: up in the east, down in the west. Polaris sits over the spin point, so it stays.

A star's diurnal circle is its parallel of declination δ, traversed at constant angular rate — 2π per sidereal day. Its altitude at hour angle H obeys sin a = sin φ sin δ + cos φ cos δ cos H: maximum altitude 90° − |φ − δ| at upper transit, circumpolar when δ > 90° − φ, never visible when δ < −(90° − φ). Setting a = 0 yields the semi-diurnal arc, cos H₀ = −tan φ tan δ, which is why high-declination stars spend well over half of each turn above a northern horizon.

The Polaris rule is a two-line proof: the pole's altitude equals the angle between the horizon plane and Earth's rotation axis, and the horizon tilts away from that axis by exactly the observer's colatitude. Hence pole altitude = latitude, everywhere and always.

Earth's rotation is the clock behind local sidereal time: LST is the hour angle of the vernal equinox, and a star transits when LST equals its right ascension — the operating principle of every transit circle, and the bridge to folio 3's coordinates. The rotation rate itself is monitored by VLBI against extragalactic sources; UT1 drifts against atomic time, with tidal braking lengthening the day by roughly 2 ms per century and the atmosphere trading angular momentum with the crust seasonally.

Strictly, the 23 h 56 m 04.09 s sidereal day is referred to the slowly moving equinox; one rotation against inertial space — the stellar day — runs about 8 ms longer, the difference being precession's daily displacement of the reference point.