Tuesday, 20 August 2013

The Nights Are Drawing In

Well, by now it is noticeable. ABout two months from the summer solstice and a month to go to the autumnal equinox, it is getting darker earlier. If we look at the times of sunrise and sunset from Southampton Sunday-by-Sunday from August to December we get:

Date Sunrise Later by Sunset Earlier by Daylight shorter by
August 4 5.36am 10 mins 8.46pm 11 mins 21 mins
August 11 5.47am 11 mins 8.34pm 12 mins 23 mins
August 18 5.58am 11 mins 8.20pm 14 mins 25 mins
August 25 6.08am 10 mins 8.06pm 14 mins 24 mins
September 1 6.19am 11 mins 7.51pm 15 mins 26 mins
September 8 6.30am 11 mins 7.35pm 16 mins 27 mins
September 15 6.41am 11 mins 7.20pm 15 mins 26 mins
September 22 6.52am 11 mins 7.04pm 16 mins 27 mins
September 29 7.03am 11 mins 6.48pm 16 mins 27 mins
October 6 7.14am 11 mins 6.32pm 16 mins 27 mins
October 13 7.26am 12 mins 6.17pm 15 mins 27 mins
October 20 7.37am 11 mins 6.03pm 14 mins 25 mins
October 27* 6.49am 12 mins 4.49pm 14 mins 26 mins
November 3 7.01am 12 mins 4.37pm 12 mins 24 mins
November 10 7.13am 12 mins 4.25pm 12 mins 24 mins
November 17 7.25am 12 mins 4.16pm 9 mins 21 mins
November 24 7.36am 11 mins 4.08pm 8 mins 19 mins
December 1 7.47am 11 mins 4.03pm 5 mins 16 mins
December 8 7.55am 8 mins 4.00pm 3 mins 11 mins
December 15 8.02am 7 mins 4.00pm 0 mins 7 mins
December 22 8.07am 5 mins 4.02pm minus 2 mins 3 mins
December 29 8.08am 1 min 4.07pm minus 5 mins minus 4 mins

[* The clocks change from Central European Time (often called British Summer Time) to Universal Time (oftern called Greenwich Mean Time)]

But what is causing this?

In the sky, there is an equivalent of latitude known as declination - and this is measured in degrees. And the connection is that objects of a declination equal to the latitude pass overhead at some point in the siderial day - which is about 4 minutes shorter than the day we are used to (as a rough rule of thumb, in a 365-day year, the stars are im the same position 366 times).

So, if we take Southampton, at a latitude of 50 degrees 55 minutes, then we expect anything that has a declination of 50 degrees 55 minutes to pass overhead - these will be the constellations of Cassiopeia, Perseus, Auriga, Lynx, Ursa Major, Canes Venatici, Boötes, Hercules, Draco, Cygnus and Lacerta.

As we might expect, the more further north an object is, the longer it spends above the horizon. If we deduct 50 degrees 55 minutes from 90 degress, then we get 39 degrees 5 minutes, and anything further north than that is circumpolar, which means it is alwsys above the horixon. The north pole of the sky (near to the star Polaris) is 50 degrees 55 minutes above the horizon, due north, from Southampton, so anything less than 50 degrees 55 minutes from it (i.e. anything with a declination of more than 39 degrees 5 minutes) will be too close to go below the horizon.

That means that all of Camelopardalis, Cassiopeia, Cepheus, Draco and Ursa Minor and parts of Andromeda, Auriga, Boötes, Canes Venatici, Corona Borealis, Cygnus, Hercules, Lacerta, Leo Minor, Lynx, Lyra, Perseus and Ursa Major are circumpolar.

If we move to the other end of the United Kingdom - to Lerwick, which is 60 degrees 9 minutes north, then anything with a declination greater than 29 degrees 51 minutes will be circumpolar. This now brings in the remaider of Lacerta, Lynx and Perseus, more of Andromeda, Auriga, Boötes, Canes Venatici, Corona Borealis, Cygnus, Hercules, Leo Minor, Lyra and Ursa Major, along with parts of Aries, Cancer, Coma Berenices, Gemini, Leo, Pegasus, Pisces, Taurus and Triangulum.

It takes a bit of spherical geometry to work out how long an object at a certain declination will spend continually above the horizon from Southampton:

Declination Time above horizon
+23 degrees* 16h 9m
+22 degrees 15h 56m
+21 degrees 15h 43m
+20 degrees 15h 30m
+15 degrees 14h 32m
+10 degrees 13h 38m
+5 degrees 12h 47m
0 degrees 11h 58m
-5 degrees 11h 9m
-10 degrees 10h 18m
-15 degrees 9h 24m
-20 degrees 8h 26m
-21 degrees 8h 13m
-22 degrees 8h 0m
-23 degrees 7h 47m

[* Here we follow the convention of northern declinations being positive and southern ones being negative]

One thing that is noticeable is that the amount of time an object is above the horizon changes decreases at its slowest rate at the celestial equator - when the declination is zero. For example, an object with a declination of 39 degrees will be above the horizon continually for 23 hours 21 minutes, while an object just 1 degree south of that will be above the horizon for "only" 21 hours 50 minutes.

You will note that an object on the celestial equator is above the horizon continually for just 11 hours 58 minutes - this might seem odd, but it is half a siderial day.

It is sometimes said that the equinoxes are when night and day are equal. However, this year the autumnal equinox is on September 22, and the Sun is above the horizon for 12 hours 12 minutes - it is not until September 25 that the Sun is above the horizon for just 12 hours.

There are two effects causing this. Firstly, the Sun is not a point source - it is about half a degree across. So it takes time to rise and set - around the solstices it will be just over 4 minutes, and around the equinoxes just over 3 minutes.

The second effect is refraction. Have you ever done the experiment of putting a pencil in a glass of water, and seeing that it appears bent? This is an effect of the light slowing down a bit in water (it's the light that is bent, not the pencil), and a similar effect occurs in the atmosphere. A direct line from the Sun to you might pass through the Earth (just!) but the atmosphere is bending the light, so they Sun is a bit higher than it should be, and hence above the horizon. Both these effects lengthen the day a little bit.

Another thing to note is that as we approach the equinox, something changes. At the summer solstice, the Sun begins in Taurus (all images from Heavens Above).

Then on June 21 it enters Gemini.

Followed by Cancer on July 20.

Then Leo on August 10.

And Virgo on September 16.

Notice the line in all of these which the Sun lies on and the planets lie near - this is called the ecliptic. You'll see that in Taurus and Gemini it's quite shallow, with the declination not changing much, and by the time it gets to Leo the ecliptic gets steeper, so the Sun's declination is decreasing faster. We can see this by the dates the Sun reaches certain declinations:

Declination Date
+20 degrees July 23
+15 degrees August 12
+10 degrees August 27
+5 degrees September 10
0 degrees September 22
-5 degrees October 5
-10 degrees October 19
-15 degrees November 3
-20 degrees November 21

And if we look at the time it takes:

From To Days
+20 degrees +15 degrees 20
+15 degrees +10 degrees 15
+10 degrees +5 degrees 14
+5 degrees 0 degrees 12
0 degrees -5 degrees 13
-5 degrees -10 degrees 14
-10 degrees -15 degrees 15
-15 degrees -20 degrees 18

So, as you might expect, the Sun's declinaton changes fastest near the equinox - not only does the day get shorter, but it gets noticeably lower in the sky.

If the Sun's declination is changing faster, then something must slow to compensate - after all the ecliptic is inclined. There is a celestial equivalent to longitude, which is known as right ascension, and this is measured in units of time. In one siderial day, the sky rotates through 24 hours of right ascension. With 365 days in the year, you would expect the Sun's right ascension to increase by just under 4 minutes per day.

And it would - if the Earth orbited in a circle and the axis was not inclined.

However, the Earth orbits in an ellipse, as demonstrated in the 17th century by Johannes Kepler as one his three laws of planetary motion. The second and third tell us that when the Earth is closest to the Sun (perihelion) in early January then it is moving fastest, and conversely, when it is furthest from the Sun (aphelion) in early July then it is moving slowest. So the Sun is moving fastest along the ecliptic in early January and slowest along the ecliptic in early July.

And if the Sun's declination is changing faster than average then its right ascension is changing slower than average. The time between midday and midday remains the same from day to day. So, if the Sun's right ascension is changing slower than average, then it is at its highest, due south, slightly earlier than the day before - and this is the period around the equinoxes. And conversely, if the Sun's right ascension is changing faster than average, then it is at its highest slightly later than the day before.

And we see this effect with our rise and set times in the first table. Notice that the amount of time sunrise was getting later by did not match the amount of time that sunset was getting earlier by. That is because until about early November, the Sun is at its highest earlier each day. And so, as the day shortened, the change in setting time is greater than the change in rising time.

After early November the effect is reversed, and by the time we get to mid-December the Sun's declination isn't changing much, so the length of the day isn't changing much. But the time the Sun is at its highest is getting later, so this leads to a period from around mid-December to early January where both sunrise and sunset are getting later. Although the shortest day is December 21, the winter solstice, by that point we have already passed the earlest sunset. Look for the effect round Christmas and Hogmanay of the evenings starting to get a bit lighter while the mornings get a bit darker.

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