A few other things

Quarters and Eighths

The year is naturally divided into four parts by the two equinoxes (when the sun rise is exactly opposite the sunset) and the two solstices (when the sun rise or set is the furthest North or South that it will be that year). These four quarters are the basis of what we often now call the four seasons.

It is natural also to note the midpoints of these quarters - that is, half-way between a solstice and the following or preceding equinox. These four 'eighth days', sometimes called the 'cross-quarter' days, are the traditional Celtic festivals of Beltaine, Lugnasagh, Samhain and Imbolc. Quite possibly the festivals would be celebrated on the full moon following this point in the solar year. The date of Easter is still found like this, being based on the first full moon after the Spring equinox.

The modern European or Western calendar - the 'Gregorian' calendar - divides the year into twelve rather than eight, this is perhaps inspired partly by the fact that there are approximately twelve lunar cycles in a year. (There are 12 synodic months plus about ten or eleven days, in a year.)

The Gregorian calendar does not epecially note the solstices or equinoxes, and is based at a rather arbitrary point - January 1st is not exactly Northern mid-winter. (In fact it's close to, but not exactly at, Earth's 'perihelion', the moment when the Earth is closest to the Sun in its annual elliptical orbit, but that has no major effect on the terrestrial seasons.)

Heliacal rising of a star

Because the Earth is spinning, stars appear to rise over the Eastern half of the horizon, move across the sky and set in the Western half. (Although some stars - those whose latitude is greater than the observer's - either never set, or never rise in the first place. This depends on where the observer is on Earth. The ones that never set are called 'circumpolar'.) The Sun of course also rises and sets like this, but takes slightly longer than the stars to do so because the Earth's orbit round the Sun makes the Sun appear to move slowly Eastwards against the background of the stars, during the year. A sidereal (fixed-stars-based) day is about 4 minutes shorter than a solar day.

If you watch the Eastern half of the sky during the early hours of the morning, while it's still dark, you can see stars rising. Eventually dawn comes, and you can no longer see the stars - though they're still there, the sky is too bright to see them. The following night, you'll see the same stars about four minutes earlier (because the sidereal day is shorter than the solar day.) So you may see a star rise, just before the Sun, that you couldn't see rise the previous evening because it was hidden by the Sun. This is called the heliacal rising of that star. For a given star and a given place, it happens once a year. For example, this annual first sighting of Sirius was used as a marker for the passage of the year by the ancient Egyptians.

Over the following months, the star will become more visible, and visible earlier and earlier in the night, until it finally becomes an evening star, and sets just after the Sun - heliacal setting - and then cannot be seen again until it is again a morning star, months later. The word heliacal derives from 'helios', the Greek name for the Sun.

Co-ordinates

Co-ordinates, in this context anyway, means numbers which are used to specify a position. On the celestial sphere, like on the surface of the Earth, we need a pair of numbers. One meaures around an equator or similar; the other number measures up or down (plus or minus) up to 90 degrees from this, to cover the whole sphere.

There are three main spherical coordinate systems used in Earth-based astronomy: Ecliptic Longitude and Latitude (based on the Earth's orbit), the equator-based 'Right Ascension' and 'Declination', and an observer's horizon-based 'Azimuth' and 'Altitude'.

To specify a point on the Earth's surface, we can use 'latitude and longitude', based on the Earth's equator, with a 'zero' point on the Greenwich meridian. Longitude is measured East or West from this meridian, and latitude up to 90 degrees North or South from the equator. We can project this system out to the celestial sphere, but for the zero point we then use 'Aries zero' - the position of the Sun on the Spring equinox. This produces the celestial coordinate system called 'Right Ascension and Declination' - R.A. is like longitude, and declination is the celestial latitude. Right Ascension is conventionally measured Eastwards - the same direction as the Sun appears to travel against the background of the 'fixed stars', during the year. Also, it's often measured using 'hours' as units - 24 hours being equal to 360 degrees in this context. Most star tables give positions using this system; it's fairly easy to figure out where to find a star in the sky at a given time, from this information.

We can instead use the ecliptic - also with a starting point at Aries zero - to provide a basis for our coordinates. In this case, we're measuring around the zodiac, which is how many tables of planetary positions are calculated. Ecliptic longitude, like R.A., is measured from West to East. Converting accurately from ecliptic to equatorial coordinates will require some sort of (spherical) trigonometrical calculations.

Finally, for a specific observer (i.e. place) on Earth, we could base our coordinates on their sky - measuring altitude of a star above their horizon, and its bearing or azimuth measured from North, moving East. This pair of numbers - Azimuth and Altitude - can be called horizon-based, or horizontal, coordinates.