The Autumn Equinox - an explanation of anomalies.
The Autumn Equinox occurred in 2009 at 22:21 UT on 22nd
September.
However, there’s a fair amount of confusion about precisely
what "the equinox" actually is. Well, the word itself tells it all,
doesn’t it? "Equinox" = "equal night", so surely the
equinox is one of the two days of each year during which the periods of daylight
and darkness are each twelve hours? Well, actually, no, that’s not the case at
all. Let’s see why.
Our clocks are mechanical devices designed to measure the
passing of time. The length of every day is the same as the length of
every other day, which common sense leads us to understand anyway. But the
Universe around us sees things differently!
But firstly, let’s clear up the definition of the equinox
– it is a moment in time, not a day or a date. The precise moment of the
autumn equinox this year (2009) occurs at 22:21 UT on 22nd September, and it’s
defined as the moment the Sun crosses the Earth’s equator on its annual
apparent journey from the Northern to the Southern hemisphere.
Secondly, the hours of daylight and darkness are not the same
on 22nd September. In and around Worcestershire, daylight runs from 05:55 until
18:07, i.e., 12 hours and 12 minutes, so the hours of darkness must be some 24
minutes shorter at 11 hours and 48 minutes. The day on which there genuinely are
12 hours each of daylight and darkness is 25th September. In some other places
these anomalies are even greater.
So why is the moment that the Sun crosses the equator known as
the equinox, with its implication of equal hours of daylight and darkness, when
that’s obviously not the case? Sorry, but what follows is pretty heavy
going!
Well, the answer is that they should be equal on that
day, but perversely they’re not! So why is this? The simple answer is
that it’s because the Earth’s axis is tilted by 23.5° relative to its solar
orbital plane, rather than zero, and because the Earth’s orbit around the Sun
is elliptical, not circular. But to understand why this is so, we need to delve
deeper.
So here goes. As I said earlier, we define the length of all
our days as the same, and that is the length of the mean solar day – the
length that every day would be if the tilt of the Earth’s axis were 0° and
the Earth’s orbit were circular. In this situation the Sun would cross the
meridian at 12 noon every day, and day by day would appear to move eastwards
along the celestial equator as the Earth moved in its orbit around the Sun.
But because the Earth’s axis is tilted by 23.5°, the Sun
appears to move along the ecliptic at 23.5 degrees to the celestial equator,
i.e., it moves south as well as east!
Now it’s not difficult to visualize that the Sun will move
further east in a given time period in the case of zero angle of tilt, than in
it would in the case of its moving along a line at an angle of 23.5°. So in the
latter case, the Sun crosses the meridian before the clock shows 12 noon. A
similar situation occurs on the following days, so the error will continue to
increase.
The Earth’s tilt has further influences on this
"day/night" length equinox inequality but the above is enough to give
you some idea of how this comes about. But the Earth’s slightly elliptical
orbit around the Sun also has an effect.
Kepler’s Second Law of Planetary Motion implies that the
Earth moves faster in its orbit when it’s closer to the Sun than it does when
it’s further away.
If the orbit were circular and the tilt were zero, the time
between noon on successive days would be equal. But because Earth’s speed in
its orbit varies, it has to rotate more in order for the Sun to cross the
meridian when it is closer to the Sun than when its further away, so the local
noon occurs later than the clock’s noon. And when the Earth is at its
furthest, local noon will occur before the clock’s noon.
We’ve seen the effect on the equinox of these two
separately, so let’s see the combined effects and see what happens near winter
solstice: both the effects conspire to make local noon later than clock's noon
near Winter Solstice. Hence, this shifts sunrise and sunset timings later (note
that without this effect, sunrise will become later and sunset will become
earlier). The overall effect is that sunset starts becoming later before actual
solstice even though the days are becoming shorter.
There is even more to it than this, but we're not going to go
into it here!
