The Moon always keeps the same face turned towards
the Earth.
How much we see of that face depends on the
direction of the Sun:
we only see the part which is illuminated by
sunlight,
as shown in the diagrams below.
The
interval between one New Moon and the next is the synodic
month;
it averages 29.53 days.
However, because the
Earth is orbiting the Sun,
the Moon will return to the same place
relative to the stars
in a shorter interval – the
sidereal month;
this
averages 27.32 days.
The diagram shows the Moon at Full, and lined
up with a certain star, at time t0 .
It is lined up
with that star again at time t1 , after one sidereal
month,
but it doesn't reach Full again until time t2 ,
after one synodic month.
The Moon's actual motion is extremely complicated:
it
orbits the Earth in an elliptical orbit,
tipped at an angle to the
Earth's own orbital plane (the ecliptic);
and its orbit is
constantly being perturbed
by the gravitational influence of the
Sun.
This is not the place for the full theory of the
Moon's motion.
However, there are some simple approximations
which
help to determine when the Moon will or will not be visible.
1. When will the Moon
transit the meridian?
At New Moon, the Moon lies in the same direction as
the Sun.
(Owing to the tilt of the Moon's orbit,
it does
not generally pass directly in front of the Sun.)
The
Moon then moves eastwards, relative to the Sun.
It moves 360°
in 29.53 days,
at which time it is lined up with the Sun again
for the next New Moon.
Thus it moves about 12.2° each day,
relative to the Sun;
which corresponds to lagging behind the Sun,
as it crosses the sky,
by about 48.8 minutes of time each day.
So, if you know the "age"
of the Moon
(that is, how many days since the last New Moon),
you
can calculate how much later the Moon will cross the sky, compared to
the Sun.
The Sun crosses the
meridian at noon
(you can be more precise than this,
if you
know your longitude and the Equation of Time).
So you can
calculate the time at which the Moon will cross the meridian.
The result will not be very accurate,
since the
Moon's motion is not uniform,
but should be correct to within an
hour.
Exercise:
The Moon was New on December
25th, 2000.
At St.Andrews, on January 1st 2001,
the Sun crossed
the meridian at 12:15.
At what time did the Moon cross the
meridian?
Click here for the answer.
2. When will the Moon rise and set?
If the Moon were always
on the celestial equator,
it would always rise 6 hours before
transit,
and set 6 hours after transit.
We know that the Sun
does not keep to the celestial equator.
It lies on the equator
at the equinoxes, in March and September,
but its declination
varies between 23.4°N in June and 23.4°S in December.
At
the equinoxes, anywhere in the world,
the Sun rises due east, 6
hours before noon, and sets due west, 6 hours after noon.
But
at the summer (June) solstice, in latitudes north of 66.6°N,
the
Sun never sets at all! (This defines the Arctic Circle.)
In
latitudes around 58°N,
the Sun rises in the north-east,
about 9 hours before noon,
and sets in the north-west,
about 9 hours after noon.
Similarly,
at the winter (December) solstice,
in the Arctic Circle the Sun
never rises;
in latitudes around 58°N,
the Sun rises in the
south-east, about 3 hours before noon,
and sets in the
south-west, about 3 hours after noon.
Now, the Moon follows
roughly the same path as the Sun
(ignoring its orbital tilt)
but
it takes only a month to trace the path which the Sun takes in a
year.
The Sun moves about 1°
a day (360° in 365.25 days)
The Moon lags behind the Sun by
about 12.2° a day,
so you can work out the date on which the
Sun will be at the point where the Moon now is.
This means you can estimate roughly how long the Moon will be above the horizon.
Having already calculated
the time at which it will cross the meridian,
you can now estimate
its rising and setting times.
This will not be very
accurate.
But it should be sufficient to determine, for example,
whether a particular night's observing will be affected by
moonlight.
Exercise:
Given the data in the previous
exercise,
estimate the times of moonrise and moonset
at
St.Andrews on January 1st 2001.
Click here for the answer.
And here's an example where you can deduce a great
deal
from very little information:
Exercise:
At a point with latitude near
58°N,
the Last-Quarter Moon is seen rising in the north-east.
What time of day is it?
What
time of year is it?
Click here for the answer.
Previous section:
The
Sun's motion, and its effect on time-keeping
Next
section: Refraction
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