Orion in the Evening

One thing I'm always thankful for around Thanksgiving is that the seasonal wheel has turned so that the constellation Orion is again visible in the evening sky.  If you go outside some clear evening this month around 9:00 PM and look to the east, you can see Orion coming up above the horizon, laying on his side, becoming vertically upright as he approaches the meridian after midnight.

As longtime readers will recall, Orion is the reason for Classical Astronomy.  I first met this starry friend as a 7 year old in the winter of 1969.  My second grade teacher, Mrs. Tintera, showed us kids a picture of Orion and explained how to spot him in the sky.  I was hooked.  Every winter for the last 57 years I've loved seeing my old friend in the evening sky.  As my friend Dr. Parsons said, "I get excited every time I see Orion.  Every time."  My sentiments exactly.  

Orion is named in three Scriptures.  I've asked Mrs. Ryan to inscribe this verse on my tombstone:

Seek him that maketh the seven stars and Orion... The Lord is his name. - Amos 5:8

According to modern science, there's no such thing as Orion.  The constellations do not really exist as we see them, but are only just optical illusions, mere alignments of variably distant stars as they appear from the line of sight of Earth.  I don't care what the experts say, I believe in Orion, do you?

You won't be able to miss the blazingly brilliant planet Jupiter currently passing through Gemini and rising with Orion. Jupiter will be at opposition on January 10 when it will rise at sunset and only be visible in the evening sky until disappearing into the sunset next summer

Permanent Standard Time

Early this month during "fall back" to standard time from daylight savings, the perennial battle raged online about how to handle the issue.  Many people today agree that they hate all the seasonal clock changing and want to keep the clocks set year round.  But people are divided over whether it should be permanent standard time or permanent daylight savings.  

The issue boils down to the time of sunrise, whether the Sun comes up too early in the summer (daylight before people are accustomed to rise) or too late in the winter (darkness during the morning commute).  But it was because of this dilemma that the issue of clock switching was established in the first place.  So I posted this graphic on TwiX to help people visualize the choice.  We can either adopt one or the other or stick with the present clock switching.  Some people will be unhappy in any event.

The Analemma

Lately I've been transitioning Classical Astronomy away from the "what's up in the sky" approach to emphasizing natural methods of timekeeping from the Sun, Moon and stars.  This article picks up a thread from a couple newsletters ago, Up and Down the Seasonal Hill, how the annual apparent motion of the Sun along the ecliptic is in the pattern of a sine wave.  From this, the pattern of variable daylight is also sinusoidal, changing rapidly around the equinoxes and leveling out and remaining almost constant for a month or so on either side of the solstices.  

In the current period from late November through late January the Sun is in the "valley" of the seasonal hill, the southernmost declinations of the ecliptic.  Here in Cleveland, around latitude 40 degrees north, the duration of daylight is about 9 hours and 39 minutes on November 21, 9 hours and 10 minutes on December 21, the winter solstice, and back up to 9 hours and 42 minutes on January 21.  So the total hours of daylight only vary about a half hour over this two month period, compared to a three hour variation over a similar span around the equinoxes.  Daylight is shorter for latitudes north of 40 and longer for more southerly latitudes. 

Though the duration of daylight tends to change smoothly over the seasons like a sine wave, the actual times of sunrise and sunset have a bit of a twist.  For reasons that will (hopefully) become clear, the earliest sunset of the year takes place in early December, a few weeks before the shortest day.  And then the latest sunset of each year occurs in early January, a couple weeks after the shortest day.  

(Got that?  I know, right?  Wobbity wobitty wobbity.  Buckle up friends, we're about to get into some of the deep weeds of astronomy!)

Each year the Sun moves north to south over the seasons, measured as changing declination, the coordinate system of the sky, the counterpart of latitude on the Earth.  On the equinoxes, the Sun is at the celestial equator, declination zero.  Following its path along the ecliptic, the Sun heads north in declination over the spring, reaching a declination of 23.5 degrees north on the summer solstice.  The Sun then moves south along the ecliptic for 6 months, reaching a declination of 23.5 degrees south on the winter solstice.  (The ecliptic and the celestial equator are explained in detail in our Signs & Seasons curriculum.)  

In observing the annual seasonal motion of the Sun across the declinations of the sky, you might have thought that it would oscillate back and forth evenly between north and south like a celestial pendulum.  If only it was that easy!  Instead, the Sun traces out a figure-8 pattern as it moves from north to south.  This figure-8 is called the analemma.  

With Classical Astronomy, every time you think you're getting a handle on a new concept, there's always more!  The analemma is a good example.  

We're accustomed to mechanical and electronic clocks in which time the time of day is divided into neat and precise units of hours, minutes and seconds that recur every 24 hours.  By that reasoning, the Sun ought to arrive at the meridian every day at noon, local time.  But in reality, thanks to the analemma, there are some weeks and months of the year when the Sun runs fast compared to the clocks and arrives at the meridian a few minutes before noon, in the A.M. part of the day.  There are other weeks and months of the year when the Sun runs slow compared to the clocks and arrives at the meridian after noon, in the P.M. part of the day.   

This apparent anomaly happens because of the eccentricity of the Earth's orbit and the 23.5 degree obliquity of the Earth's axis.  These factors each contribute components that add together to produce the analemma. The actual position of the Sun is compared to the mean sun, a theoretical ideally uniform motion of the Sun as if it moved at a constant rate along the celestial equator. The difference between the mean sun and the actual Sun is called the equation of time, which is the sum total of these two components for any date of the year, as shown the following graph.  

So basically, as the Sun changes in declination, there are corresponding changes in the equation of time.  The graph above shows the analemma as the equation of time plotted out for each declination.  The equation of time is also called "sundial error" since it shows the difference between the clock and the sundial.  But in Colonial America, when sundials were more common, the equation of time was called "clock error."  It's all in your perpective.

The equation of time must also be taken into account for celestial navigation, and has been giving fits to sailors for a very long time....

The difference between the sun’s position and the position where the sun ought to be if it were a decent, self-respecting sun, man calls the Equation of Time. – Jack London, from Voyage of the Snark (A.D. 1911) 

The eccentricity component is the result of the Earth speeding up in its orbital motion as it approaches perihelion, its closest position to the Sun.  This is due to Kepler's Laws of Motion, which are the basis of Newton's Law of Universal Gravitation.  Essentially, due to gravity, the Earth (or any planet) moves faster when it's closest to the Sun.  As a result, the Sun appears at a point on the ecliptic ahead of the mean sun, where it would appear if its motion were constant like a clock.  

The Earth passes perihelion on January 3, when its declination is about 23 degrees south, as shown in the graph above.  The Sun's position runs progressively faster as the Earth approaches perihelion and remains ahead of the mean sun until the Earth'sorbital motion slows with the approach to aphelion, its most distant point from the Sun, round about July 4, near 23 degrees north as shown in the graph above.  At that time the Sun runs slow and the eccentricity component of the equation of time now lags behind the mean sun. 

The obliquity component is due to the tilt of the Earth's axis and its north and south poles toward the ecliptic which causes the seasons.  For this reason, the Sun's path along the ecliptic appears tilted to the celestial equator, which is referenced to the Earth's axis.  Because of obliquity, the Sun runs slower than the mean sun around the equinoxes and faster around the solstices.  

In the example of the vernal equinox, the Sun's ecliptic path is tilted to the celestial equator in early spring, so the Sun's path has a horizontal component toward the east and a vertical component toward the north while the mean sun only has a horizontal component toward the east.  This results in a lag of the actual Sun, so that it reaches the meridian earlier than the mean sun, therefore running faster than the clock.

However, by later spring, approaching the solstice, the Sun's ecliptic path levels off, becoming more horizontal.  Now here's another twist -- with the higher declination, the intersecting circles of right ascension are closer together, just like how the terrestrial circles of longitude converge toward the poles.  So the Sun moves more quickly through right ascension and thus catches up to the mean sun.  (Don't worry if these new concepts are hard to follow, we're almost to the punchline.)    

So anyway, due to obliquity, during the spring the equation of time forms the upper right section of the figure-8 in the graph above when the Sun moves faster than the clock.  A reverse process happens in the summer, forming the upper left section in the graph above where the Sun is slower than the clock.  The lower right section represents fall and the lower left corresponds to winter.  And the combined components of the equation of time for both eccentricity and obliquity are represented in the final combined analemma on the right of the graph above.

So who cares anyway?  Why do we need to know this?  Because the equation of time and the analemma affect the time of sunrise and sunset, which is especially significant here in the shortest days of the year.  During December, the days are growing shorter but the Sun is running ahead of the clock, arriving at the meridian and then at the sunset horizon a little sooner than we might expect.  As seen from Cleveland, the sunset is the earliest of the year on December 8, at 4:56 PM, varying by mere seconds for several days before and after.

Here's the tricky part.  The Sun sets at 5:00 PM on November 23 and sets only a few minutes earlier each day until December 8, and gets back to 5:00 PM again on December 21.  So the sunset time is fairly constant for nearly a month.  But the shortening of the daylight appears in the sunrise, which varies by 24 minutes during over this one-month period.  Here's a table of select sunrise/sunset times for Cleveland from the Time and Date site:

Date        Sunrise      Sunset

Nov 23    7:25 AM    5:00 PM
Dec 1       7:34 AM    4:57 PM
Dec 8      7:40 AM    4:56 PM
Dec 15     7:41 AM    4:56 PM
Dec 21     7:49 AM    5:00 PM

And as you can see from the table above, the time of sunrise occurs later and later as the shortest day approaches.  This trend continues for a couple weeks after the shortest day.  After the winter solstice, the equation of time runs slow through late December and into January.  Thus, the Sun rises later than one would expect and also reaches the meridian later.  In Cleveland, the date of the latest sunrise is January 3, when the Sun rises at 7:53 AM.