Astronomy & Celestial Mechanics
the sky, computed
Field

The observed sky

Coordinates, seasons, phases and shadows — geometry seen from inside it.
celestial poleobserverzenithnorthsouthcelestial equatorthe daily circle of a star at δ = 20°the pole sits 52° up, because the observer is at latitude 52°faint arcs are below the horizon

The sphere that is not there, and why it is still the right model

The stars are at wildly different distances and the celestial sphere is a fiction. It is also the most useful fiction in observational astronomy, because for pointing at things, distance is exactly the information to throw away.

 05101520-40-200204060hour (local solar time)June solstice — 61° at noon, 16.5 h of dayequinox — 38° at noon, 12.0 h of dayDecember solstice — 15° at noon, 7.5 h of daybelow the horizon

The Sun's path, and the tilt that makes the seasons

Summer is not when the Earth is closest to the Sun — that happens in January. It is when the Sun climbs higher and stays up longer, and both come from a 23.4° tilt.

 sunlightnewwaxing crescentfirst quarterwaxing gibbousfullwaning gibbouslast quarterwaning crescentas seen from the centrehalf lit, always

Phases are not shadows, and eclipses are

Half the Moon is lit at every instant of every month. The phase is which part of the lit half faces the Earth — and confusing that with a shadow is the commonest error in astronomy.

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