Like Sun, Like Moon

The Earth orbits the Sun once every 365.256363 (mean solar) days relative to the distant stars.  The Earth’s orbital speed ranges from 18.2 miles per second at aphelion, around July 4th, to 18.8 miles per second at perihelion, around January 3rd.  In units we’re perhaps more familiar with, that’s 65,518 mph at aphelion and 67,741 mph at perihelion. That’s a difference of 2,223 miles per hour!

As we are on a spinning globe, the direction towards which the Earth is orbiting is different at different times of the day.  When the Sun crosses the celestial meridian, due south, at its highest point in the sky around noon (1:00 p.m. daylight time), the Earth is orbiting towards your right (west) as you are facing south. Since the Earth is orbiting towards the west, the Sun appears to move towards the east, relative to the background stars—if we could see them during the day.  Since there are 360° in a circle and the Earth orbits the Sun in 365.256363 days (therefore the Sun appears to go around the Earth once every 365.256363 days relative to the background stars), the Sun’s average angular velocity eastward relative to the background stars is 360°/365.256363 days = 0.9856° per day.

The constellations through which the Sun moves are called the zodiacal constellations, and historically the zodiac contained 12 constellations, the same number as the number of months in a year.  But Belgian astronomer Eugène Delporte (1882-1955) drew up the 88 constellation boundaries we use today, approved by the IAU in 1930, so now the Sun spends a few days each year in the non-zodiacal constellation Ophiuchus, the Serpent Bearer. Furthermore, because the Earth’s axis is precessing, the calendar dates during which the Sun is in a particular zodiacal constellation is gradually getting later.

Astrologically, each zodiacal constellation has a width of 30° (360° / 12 constellations = 30° per constellation).  But, of course, the constellations are different sizes and shapes, so astronomically the number of days the Sun spends in each constellation varies. Here is the situation at present.

Constellation
Description
Sun Travel Dates
Capricornus
Sea Goat
Jan 19 through Feb 16
Aquarius
Water Bearer
Feb 16 through Mar 12
Pisces
The Fish
Mar 12 through Apr 18
Aries
The Ram
Apr 18 through May 14
Taurus
The Bull
May 14 through Jun 21
Gemini
The Twins
Jun 21 through Jul 20
Cancer
The Crab
Jul 20 through Aug 10
Leo
The Lion
Aug 10 through Sep 16
Virgo
The Virgin
Sep 16 through Oct 31
Libra
The Scales
Oct 31 through Nov 23
Scorpius
The Scorpion
Nov 23 through Nov 29
Ophiuchus
Serpent Bearer
Nov 29 through Dec 18
Sagittarius
The Archer
Dec 18 through Jan 19

 

The apparent path the Sun takes across the sky relative to the background stars through these 13 constellations is called the ecliptic.  A little contemplation, aided perhaps by a drawing, will convince you that the ecliptic is also the plane of the Earth’s orbit around the Sun.  The Moon never strays very far from the ecliptic in our sky, since its orbital plane around the Earth is inclined at a modest angle of 5.16° relative to the Earth’s orbital plane around the Sun.  But, relative to the Earth’s equatorial plane, the inclination of the Moon’s orbit varies between 18.28° and 28.60° over 18.6 years as the line of intersection between the Moon’s orbital plane and the ecliptic plane precesses westward along the ecliptic due to the gravitational tug of war the Earth and the Sun exert on the Moon as it moves through space.  This steep inclination to the equatorial plane is very unusual for such a large moon.  In fact, all four satellites in our solar system that are larger than our Moon (Ganymede, Titan, Callisto, and Io) and the one that is slightly smaller (Europa) all orbit in a plane that is inclined less than 1/2° from the equatorial plane of their host planet (Jupiter and Saturn).

Since the Moon is never farther than 5.16° from the ecliptic, its apparent motion through our sky as it orbits the Earth mimics that of the Sun, only the Moon’s angular speed is over 13 times faster, completing its circuit of the sky every 27.321662 days, relative to the distant stars.  Thus the Moon moves a little over 13° eastward every day, or about 1/2° per hour.  Since the angular diameter of the Moon is also about 1/2°, we can easily remember that the Moon moves its own diameter eastward relative to the stars every hour.  Of course, superimposed on this motion is the 27-times-faster-yet motion of the Moon and stars westward as the Earth rotates towards the east.

Now, take a look at the following table and see how the Moon’s motion mimics that of the Sun throughout the month, and throughout the year.

 
——— Moon’s Phase and Path ———
Date
Sun’s Path
New
FQ
Full
LQ
Mar 20
EQ
EQ
High
EQ
Low
Jun 21
High
High
EQ
Low
EQ
Sep 22
EQ
EQ
Low
EQ
High
Dec 21
Low
Low
EQ
High
EQ

 

New = New Moon
near the Sun
FQ = First Quarter
90° east of the Sun
Full = Full Moon
180°, opposite the Sun
LQ = Last Quarter
90° west of the Sun

 

EQ
= crosses the celestial equator heading north
High
= rides high (north) across the sky
EQ
= crosses the celestial equator heading south
Low
= rides low (south) across the sky

 

So, if you aren’t already doing so, take note of how the Moon moves across the sky at different phases and times of the year.  For example, notice how the full moon (nearest the summer solstice) on June 27/28 rides low in the south across the sky.  You’ll note the entry for the “Jun 21” row and “Full” column is “Low”.  And, the Sun entry for that date is “High”.  See, it works!

Pole Stars

Currently, Polaris (Alpha α UMi) shines at magnitude 2.0 and lies just 0.7° from the North Celestial Pole (NCP).  Precession of the Earth’s rotation axis will bring the NCP to within 0.5° of Polaris in March 2100, its minimum distance.

The situation for the South Celestial Pole (SCP) is not such a happy circumstance.  The nearest naked-eye star to the SCP at present is neither near nor bright.  Sigma Octantis at magnitude 5.5 is not easy to see with the unaided eye, and being 1.1 degrees away from the SCP doesn’t win it any awards.  Besides, precession is moving the SCP farther away from Sigma Oct, not nearer.

One wonders, will precession someday bring us a south celestial pole star worthy of the name?  Even, perhaps, comparable to Polaris?  Here’s what our stargazing descendants can look forward to:

Cha = Chamaeleon; Car = Carina; Vel = Vela

So, around 8100 A.D. Iota Carinae and around 9220 A.D. Delta Velorum will serve admirably as southern pole stars every bit as good as Polaris does now in the northern hemisphere.

Now, for the northern hemisphere…

Cep = Cepheus

Up until the year 10,000 A.D., no northern pole star will be as good as Polaris is now, though 4.8-magnitude 9 Cephei will be very close to the north celestial pole around 7400 A.D.

Thought you might enjoy seeing what deep sky objects will come close to the celestial poles, so those are listed in the above tables as well.

Epoch and Equinox

We use the term epoch (of a given date) to refer to the actual measured coordinates of a star that takes into account precession, nutation, and proper motion. The term equinox means that the coordinates have been precessed to a given date, but that other factors affecting a star’s position have not been applied. So, equinox 2000.0 is not the same as epoch 2000.0.

Example: Barnard’s Star

Epoch 2000.0 coordinates: α = 17h 57m 48.49803s, δ = +4° 41′ 36.2072″ (the actual position of Barnard’s Star at 0h UT on January 1, 2000, accounting for precession, nutation, and proper motion)

Equinox 2017.1 coordinates: α = 17h 58m 39.20689s, δ = +4° 41′ 33.5614″ (coordinates have been precessed from epoch 2000.0 above to today’s date, but nutation and proper motion have not been applied)

Epoch 2017.1 coordinates: α = 17h 58m 37.85s, δ = +4° 44′ 37.8″ (the actual position of Barnard’s Star on January 19, 2017, accounting for precession, nutation, and proper motion)

Sometimes, the epochal coordinates are further adjusted to account for aberration and atmospheric refraction.  The latter tends to “lift” stars towards the zenith—the closer to the horizon the greater the lift.

Eugène Delporte and the Constellation Jigsaw

Belgian astronomer Eugène Joseph Delporte (1882-1955) discovered 66 asteroids from 1925 to 1942, but he is best remembered for determining the official boundaries of the 88 constellations, work he completed in 1928 and published in 1930.  The constellation boundaries have remained unchanged since then.

The International Astronomical Union (IAU), founded, incidentally, in Brussels, Belgium in 1919, established the number of constellations at 88—the same number, coincidentally, as the keys on a piano—in 1922 under the guidance of American astronomer Henry Norris Russell (1877-1957).  The IAU officially adopted Delporte’s constellation boundaries in 1928.

All the constellation boundaries lie along lines of constant right ascension and declination—as they existed in the year 1875. Why 1875 and not 1900, 1925, or 1930? American astronomer Benjamin Gould (1824-1896) had already drawn up southern constellation boundaries for epoch 1875, and Delporte built upon Gould’s earlier work.

As the direction of the Earth’s polar axis slowly changes due to precession, the constellation boundaries gradually tilt so that they no longer fall upon lines of constant right ascension and declination. Eventually, the tilt of the constellation boundaries will become large enough that the boundaries will probably be redefined to line up with the equatorial coordinate grid for some future epoch. When that happens, some borderline stars will move into an adjacent constellation. Even now, every year some stars change constellations because proper motion causes them to move across a constellation boundary. For faint stars, this happens frequently, but for bright stars such a constellation switch is exceedingly rare.