|
Latest Sunrise, Earliest Sunset
and The Equation of Time
People are often puzzled by the fact
that the dates of earliest sunset and latest sunrise
do not coincide with the shortest day of the year
(which is on or around 21st December in non-tropical
northern latitudes). At latitude 25N, latest sunrise
occurs just before mid-January, and earliest sunset
is around the end of November. And at 50N, the date
of earliest sunset is approximately 13th December,
while latest sunrise is experienced at the end of
December.
Two quite separate factors contribute to this
apparently strange behavior:
1. The Earth's speed of movement round the sun is
not uniform. This causes variations in the sun's
apparent rate of passage through the constellations
- which is fastest during December/January, and
slowest around June/July. Thus, sometimes the sun
goes ahead of what may be called its 'normal' or
'mean' position; at other times it falls behind.
(Here, 'ahead' and 'behind' need to be carefully
defined; see below*).
2. The sun's week-to-week migration across the
starry firmament is tied to the Ecliptic Line.
However, times of sunrise, noon and sunset (being
determined by Earth's daily rotation) relate more
easily to the sun's Celestial Longitude - whose
labels (along the Celestial Equator) are direct
projections out from Earth's equator. But the
23½-degree angle between our equatorial plane and
the ecliptic - usually modifies the sun's speed of
progress parallel to the (more important) Celestial
Equator. The greatest reductions occur in late March
and late September. These seasonal fluctuations can
cause dawn and dusk to come early (or late)
Adding together those two contributing influences,
produces a double-waved curve with a minimum near
11th February (when the sun is said to be 14 minutes
'behind schedule'), and a maximum near 3rd November
(when it is just over 16 minutes 'ahead of
schedule'). Thus, times of sunrise (and indeed
sunset) from January to March are later than they
would be if Earth's orbit was circular and if our
spin-axis was 'upright'. And from September till
late December, those times are earlier than they
'should' be. (*However, remember that when sunset is
'later than normal', the sun is actually further
ahead than 'normal' in its migration across the
firmament - which is from west to east).
There is also a secondary maximum and minimum in May
and in late July respectively. This graph is known
as the Equation of Time - which may be described as
the daily and seasonal difference between sundial
time and clock time.
The Equation of Time
The total of these two effects gives the Equation
of Time, which is formally defined as the difference
between clock time and apparent solar time. The
Equation of Time takes the form of the curve
sketched below. It is zero on Apr 16, June 15, Sept
1 and Dec 25 and has maxima and minima near Feb 12,
May 15, July 27 and Nov 4.
The variation of the Equation of Time due to
Obliquity (filled circles) and the variation due to
Unequal Motion (open circles).
The Equation of Time (the total of the above two
effects).
--------------------------------------------------------------------------------
THE ECLIPTIC is the plane containing Earth's
orbit round the sun. It can be extended indefinitely
in all directions, so the ECLIPTIC LINE is where
that plane intersects the Celestial Firmament**.
This line occupies a well-defined position in the
sky (during the day as well as the night), being the
'track' followed by the sun (whose departure from it
is never more than 1.2" of arc). It is usually
marked on star charts.
** THE CELESTIAL FIRMAMENT is the inside surface
of an enormous imaginary sphere surrounding the
Earth. Positions of stars and planets etc. may be
projected onto this surface as if it were a screen -
just as in the interior of a gigantic planetarium.
The CELESTIAL EQUATOR is where Earth's extended
equatorial plane cuts through the firmament. Values
of CELESTIAL LONGITUDE are also called Right
Ascension; (their labels lie vertically above our
equator, but are fixed with respect to the
constellations).
|
