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).
Sidereal cycle of the Moon --- can be observed by noting that the Moon appears
to move quite fast in the sky relative to the background stars, about one
whole Moon diameter (0.5 degrees) per hour. The exact amount is 13.2 degrees
per day (24 hours). The Moon moves backwards (in terms of the
diurnal motion of the sky), that is, eastwards. Knowing it moves 13.2 degrees
in a day means we can calculate it moves a full cycle of 360 degrees in
(360/13.2) days, or 27.3 days. This is the sidereal period of the
Moon, a sidereal month.
Retardation --- Because the Moon moves to the east in our sky, it rises
later from night to night, the "retardation" of the Moon, by an
amount that is the time for the EArth to swing through an extra 13.2 degrees
in its rotation. Since the Earth takes 24 hours, or (24x60) minutes to rotate
360 degrees, it takes (13.2/360) times (24x60) minutes to rotate 13.2 degrees.
This is about 50 minutes.
Path of the Moon on the sky---- is nearly the ecliptic, never more than 5
degrees away from it. A line in the sky from the Sun (maybe just below the
horizon) at sunset to the Moon (if it's in the night sky) will tell you
approximately the location of the ecliptic. (Right now, it's nearly overhead
in Hawaii.)
Real motion of the Moon --- is round the Earth. Unlike the Sun, which only
appears to orbit the Earth, the Moon really does do this. It
performs the same sidereal cycle month after month, i.e., no matter where the
Earth is in its orbit round the Sun. It also keeps the same face to the Earth
(see later) which suggests very strongly that it is associated with the Earth
and not just another body out there orbiting the Sun (but this isn't a
foolproof argument).
Phases of the Moon --- are the names for the changing appearance of the Moon
in the course of a "month" (actually, a "Synodic month" -- see later). It's
easy to see with the naked eye that the we always see the same face of the
Moon, more or less illuminated -- by sunlight -- depending on the phase (new,
crescent, quarter moon, gibbous, full). (Remember `first quarter' and `third
quarter' refer to the position in the cycle, not to the appearance.) The
phases are the effect of differing relative positions of Earth, Sun and Moon
over the month. A technical term for this is in terms of another angle:
The Elongation of an object --- is the angle between the direction to the Sun
and the direction to the object, measured by an observer on Earth. So the
phases are caused by the varying elongation of the Moon.
The Synodic Month --- is the time between consecutive new phases of the Moon.
It is therefore tied to the Sun, not the background stars. The reason this is
different from the sidereal month is the same reason the solar day is
different from the sidereal day, namely that the Earth is moving round the Sun
all the time so the angle to the Sun is changing. The Solar Month (though the
term Solar is not used; we talk of the Synodic Month) is longer than the
sidereal month since it takes a bit longer for the Earth, Moon and Sun to be
in a straight line again (for new moon, say). The Earth takes 365.25 days to
move 360 degrees round the Sun, so in 27.3 days it will move through an angle
of (27.3/365.25) x 360 degrees, which is about 27 degrees. So, in order to
line up with the Sun, the Moon has to move that extra 27 degrees along
it's orbit round the Earth. We saw that it moves 13.2 degrees in a
day, so the extra 27 degrees takes about an extra 2 days. In fact, the
Synodic Month is 29.5 days.
The Moon shows its close
connection to the Earth by always keeping one face to us, showing, not that it
isn't rotating, but that it is in synchronous rotation with its orbit
round the Earth (rotates once in an orbit, taking a month to do so).
This
connection is established by gravitational tidal forces, and was not
always so. It is also causing evolution of the Earth-Moon system. (More
later, when we discuss gravity).