A day --- can also be measured two ways. A SOLAR DAY is the time between
successive meridian crossings of the Sun. A SIDEREAL DAY is the same idea,
using a star instead. The sidereal day is about 4 minutes shorter than a
solar day, reflecting the fact that the Earth is moving on its orbit in the
same sense as it is rotating on its axis. This means that a given star will
rise about 4 minutes EARLY from one night to the next. This works out at
about 2 hours per month (or 24 hours per year, so you are back where you
started). Eventually, any given star moves out of the night sky and into the
daytime sky, and then back to the night sky again.
Tilt of the Earth --- The obliquity of the ecliptic is caused by the fact
that the Earth's axis of rotation is tilted by 23.5 degrees to the plane of
its orbit round the Sun. This is the cause of the seasons, and the variation
of the length of daylight over the course of the year (at most latitudes).
The latitudes of the arctic and antarctic circles and the tropics reflect this
tilt.
The technical way of speaking about where the Sun is north or
south of the equator is to think about the Sun's declination, and we checked
that the Nautical Almanac predicted that this would be about 19
degrees south of the equator for Friday Jan 22. This is as it should be, not
long after the winter solstice, when it would be 23.5 degrees south. we also
checked that the Sun is indeed heading north (decreasing southerly
declination).
Astronomical definition of the tropics --- We also showed that the Sun can be
at zenith at noon only if the Sun's declination is the same as your latitude.
This is true only for latitudes between 23.5 degrees north (tropic of cancer)
and 23.5 degrees south (tropic of carpricorn). These are the tropical
latitudes. We checked with the Nautical Almanac that indeed there will be two
days this year when the declination of the Sun is the same as the latitude of
Hawaii, in May and in July, once when the Sun is heading north to the summer
solstice and once when it is heading back south to the autumn equinox.
Seasons --- caused by the interaction of the tilt of the
Earth's rotation axis with the plane of its orbit round the Sun.
The angle of the Sun from the equator changes
over the year, causing different amounts of solar illumination at different
latitudes, and different amounts of day and night, according to
latitude.
Tropics, Arctic and Antarctic Circles --- Special
latitudes on the Earth that reflect the Sun's apparent north/south motion
over the year. Tropics are the extreme latitudes of the Sun's travel
[23.5 degrees N (Cancer) and S (Capricorn)]. Further N or S the Sun can
never be overhead. Arctic (antarctic) circles are furthest S (N) latitudes
where 24-hour days or nights can happen. e.g. at arctic circle
(66.5 degrees N) Sun is on the horizon (never sets) on the summer solstice,
though will set for some of each day on other days. In winter, latitudes N
of arctic circle experience some 24-hour nights. At North Pole, there is 6
months day and six months night. (Opposite for South Pole at same time of
year.)
How stable is this? We saw that there was something funny about the Earth's
orbit round the Sun. this can be seen by the fact that the two ways of
measuring a "year", which is the period of the Earth's revolution round the
Sun 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; it is 365.242 days. The sidereal year is masured
from the stars, and is a bit longer, 365,256 days. This is in fact because
the position of the vernal equinox on the ecliptic is moving gradually, 0.008
seconds of arc in a day. this is the "precession of the equinoxes".
Precession ---- The position of the
North Celestial Pole, and with it, the star that is the "Pole Star", the
position of the vernal equinox ("first point of Aries") and of the solstices
have all changed in historical time. (This is due to the wobble of the Earth's
rotation axis (precession) caused by forces on the Earth, just like a spinning
top or gyroscope makes a circular motion if it is hit.) We know that one
rotation takes about 25,800 years. Along with this, the equinoxes --- the
places where the equator and ecliptic cross --- have also moved around the
equator in the same time. This shift in the vernal equinox is what makes the
tropical year different from the sidereal year.
Time---is measured from the interaction of the rotation of the Earth and its
revolution round the Sun. We use Mean Solar Time, which is measured in
average solar days. Because the year is not an exact number of days we have
leap years of 366 days every four years (plus additional adjustments from time
to time). So time as measured by your watch is an artefact, that is suggested
by the actual cycles of the sky, but not exactly the same as them. I
mentioned that the fact that the (real) year is not a qhole number of days
suggests that there is no close connection between the EArth's revolution
round the Sun and its rotation on its own axis. By "close connection" I mean
"close physical connection. Note this is not true for the Moon in
its orbit round the Earth (see later).