Azimuth --- is the angle measured from north round the horizon, so a
change from the direction east, say, to the direction northeast would be a
change in azimuth.
Visibility of the sky --- depends on your latitude on earth. From everywhere,
some of the sky will be below the horizon at any time and from everywhere
except the equator, some of the sky will always be below the horizon.
Similarly, some stars are circumpolar, that is, they
don't set. In the northern
hemisphere, Polaris (nearly at the NCP), and the constellations of
Ursa Major, Ursa Minor and Cassiopeia are circumpolar at some
latitudes, and this obviouly varies with latitude.
Navigation --- Stars with different declinations rise and set at
different azimuths (angle round the equator --- N, SW, NE etc). One can
therefore use the rising or setting points of stars as compass points. Also
the altitude of any star will change with the observer's latitude (as well as
the time of night). In particular, the altitude of Polaris (NCP) = latitude
of observer. Remember that the altitude of Polaris is 0 degrees if you are
observing from the equator (0 degrees latitude) and 90 degrees if you are
observing from the north pole (latitude 90 degrees), and it is also true for
intermediate latitudes. So, knowing the altitude of Polaris lets you know
your latitude on Earth. (This also works for any other star, or the Sun, but
then you need to know the time of night as well. (Why?) Can you also work out
the relation between the latitude of observation and the declination range of
circumpolar stars?
Circumference of the Earth --- Because the altitude of Polaris tells
you your latitude, it follows that if you travel north or south
your latitude will change, and so the altitude of Polaris will change. You
can use this to measure the size (circumference) of the Earth (or any other
planet you find yourself on). Suppose you travel M miles north and the
altitude of Polaris changes by P degrees, then
M miles / circumference of Earth =
P degrees / 360 degrees
because you will
have travelled a fraction of the Earth's circumference that is equal to the
ratio of P degrees to a whole circle (360 degrees). Notice that this
gives you the circumference of the Earth. If you want to translate
that into a radius or a diameter (= twice the radius) , then
remember that circumference = 2 x (pi) x radius, where (pi) (Greek letter pi,
that I can't write in HTML) is 3.14159...
Eratosthenes --- in about
200BC used essentially the same reasoning to measure the size of the Earth,
only he used the altitude of the Sun, not Polaris. The story goes that on a
given day in Syene (now Asswan) the Sun was directly overhead (at "Zenith") at
noon, because there were no shadows and the sunlight reached right down to the
bottom of deep wells. But on the same day in Alexandria, some 5000 "Stadia"
to the North (whatever a Stadium was) the Sun was measured to be 7 degrees
away from the vertical. So, with the same reasoning as before,
If we knew how
big the Greeks thought a stadium was in terms of our units (miles, kilometers)
we would know how accurate his estimate was. Actually, this method involves a
bit of inaccuracy because the daily motion of the Sun isn't as simple as the
daily motion of the stars. See later.
Summary so far --- From the daily
("diurnal") motion of the stars (on the celestial sphere, if you like) we can
infer that the Earth rotates on an axis through the poles in the
direction west - east, completing one rotation in a day. This is the
rotation period of the earth. Of course, we need to see what me really
mean by "a day". See later. We can also measure the size of the Earth.
"Motion" of the Sun --- We then started to talk
about the changes that happen from night to night or day to day. We started
with the Sun which shows two (related) effects over the year, namely that its
maximum altitude changes and the azimuth of sunrise or sunset also changes,
swinging more northerly or southerly over the year.
These two together imply
that the declination of the Sun changes over the year --- it moves north-south.
This is also true of its right ascension --- it moves east-west (of course, measured
at the same time of day). We see this from the fact that different stars are
in the sky at different times of the year. This "path" of the Sun in the sky over the course
of a year is called the Ecliptic. The most northerly and southerly points on
the Ecliptic are called the Solstices and the places where the Sun crosses the
Celestial Equator are called Equinoxes.
Ecliptic---constellations in the night sky change over the year as
the Earth moves around the Sun. The Sun appears to move along the Ecliptic
through the Zodiac (the constellations that happen to lie near the ecliptic).
The Ecliptic is not the same as the celestial equator. It is tilted at 23.5
degrees to the equator, the tilt, or "OBLIQUITY" of the Ecliptic, the angle
that the Earth's axis is tilted to the plane of its orbit around the Sun.
R.A. and Dec. are measured with respect to the equator, NOT the
Ecliptic. R.A. is measured in hours, minutes (of time) and seconds (of time),
increasing eastward along the celestial equator, with the zero point at the
vernal equinox (which is one of the places where the equator and the Ecliptic
cross).
Solstices (= 'standing Sun') --- Times of furthest north (summer solstice) and
south (winter solstice) of the Sun's path. At noon on the Summer (winter)
solstice, (June or Dec. 21) the Sun crosses the meridian at declination 23.5 degrees N (S)
latitude.
Equinoxes (= 'equal night') --- Times when the Sun crosses the equator
--(declination 0 degrees) on its
way north (Vernal or Spring Equinox, Mar. 21) and south (Autumn Equinox,
Sep. 21).
Heliacal rising --- of a star is when the star rises just before sunrise.
Similarly heliacal setting is when a star sets just after sunset. The time
between two successive heliacal risings or settings is a (sidereal) year.
A year can be measured two ways, from the Sun or from the stars. The
solar (or "tropical") year is the time between successive vernal equinoxes,
and so is tied to the Sun. The sidereal year is between successive heliacal
risings of a given star (when the star just rises at sunset), and is a bit
longer. (We'll see why later.)