September 2013 Night Sky Calendar

by Uber Professor  Dr. Xavier Cinnamon Trinket

["September," derived from the Roman word "Septimus," as it represented the seventh month in the Roman Calendar, until the Julian reformation of 46 BC, in which January replaced March at the year's first month.*]



I shall expect praise.

Convey at once to



Nothing personal, but the usual DA night sky calendars are appallingly inadequate in every regard:  the content is sparse, the information unreliable; the presentation unprofessional;  the arrangement haphazard and the writing, well, I shall decline comment as I don't wish to injure the DA's sensitive feelings.     So, when it came to my attention that your usual host wished to extend his vacation by another day to savour his leisure in the Lake Region area (i.e. sleep it off), I naturally volunteered my services.   After all, I am now the most academically credentialed individual to ever be in hiding from the law and require constant intellectual engagement to sustain me during my exile. (Crafting this calendar provided me with 11.3 minutes of such stimulation.)    And, of course, this substitution will furnish the readers with much superior fare than that to which they have lamentably become  accustomed.  I regret that all subsequent submissions shall seem,  when contrasted with the piece I here offer, lacking.   I would therefore encourage readers to make allowances for your usual host, who cannot be blamed for being an inferior specimen.  


Now that the preliminaries have ended, I intend to use every single event as a occasion for pure pedagogy.   We shall fully engage our minds to the task at hand.  Well, honestly, this composition requires less than one percent of my brain,  as I am simultaneously contemplating a 40,000 word response to Kant's little rant; working out the details for all conceivable hyper dimensional Pythagorean solids, determining the coefficient of static friction between two exotic solids only found in the phosphorus fern jungles of Branimatrix seven (a bit more complicated affair than merely measuring the tangent of the critical incline angle) and calculating the next moves in the eight chess matches currently milling about in my little iridescent violet brain cells.


Incidentally, I shall not confer medal awards onto any event, a practice your usual host considers endearing, but which I regard as frivolous.   Bah!  I am afraid your usual host is full of himself.   




ZHR = 6 r value = 2.6

While ordinarily classified as a "minor meteor shower," the Aurigid meteor peak in 2013 is expected to be marginally more active than usual, so the above-stated ZHR is likely to be less than what we shall observe during this event. [The ZHR is called the "Zenithal Hourly Rate," an idealized value which assumes that an experienced observer can observe all meteors as they radiate away from a zenithal radiant. This means, of course, that the radiant -the shower's apparent origin point- is poised at the zenith, the point directly overhead.] The Aurigid shower has exhibited increased activity in 1935, 1986, 1994, and 2007. No comparable increase is predicted for this year, but as the moon is a thin waning crescent, meteor observers will not have to contend with lunar light obscuration.

The r-value specifies the ratio of bright to faint meteors. Generally, an r-value between 2 - 2.6 indicates a higher ratio of bright meteors; while an r-value of 2.9 or higher is assigned to showers with a higher proportion of faint meteors. We can therefore expect a smattering of bright meteors related to the Aurigids, so named, incidentally, as the radiant is within the Auriga constellation. Interesting note is that the shower was once named the "alpha Aurigids," for the radiant appeared close to the Alpha star, Capella. Subsequent investigation has shown, however, that the radiant is closer to the constellation's central region.




It is hardly surprising that the "Equation of Time" issue baffles your usual host, who tends not to include it in his calendar version.    The "Equation of Time" is not a formula or equation, but a correction factor relating the idealized "mean" Sun and the "true" Sun, the latter referring to the observed Sun and its intersection of the meridian, the vertical arc connecting due south and due north.     The "mean" Sun traverses this arc every 24 hours: the time separating successive "noons."  The true Sun is either ahead of or behing this true Sun depending on various factors, discussion of which I shall avoid so as to maintain this calendar's simplicity.     


On February 11, the Equation of Time reached a minimum for 2013, its value equaling -14.25 minutes.   Therefore, on that date, the mean Sun reached the meridian at noon, but the true sun would not cross the meridian for another 14 minutes, 15 seconds.   


Today, the Equation of Time is zero, indicating a convergence between the true and mean noons, or meridian passages of the actual Sun and idealized one.   Such factors are of utmost importance in almanac computations.     As a curious side note, such equation factors are necessary on any planet with an axial tilt (obliquity) greater than zero and an orbital eccentricity (departure from circularity) greater than zero,


Earth's current eccentricity is 0.017 and its obliquity is 23.4 degrees, approximately.**


2013 September 2


[Lunar phase: Waning crescent 8% illuminated Moon rises 3:17 a.m. Mars rises 2:52 a.m. 46 degrees from Sun.]

The proximity of two worlds often excites interest in sky watchers, particularly when the bodies attain a minimum apparent distance, a configuration called an "appulse." One shall observe Mars and the Moon in the eastern pre-dawn sky. Note that civil twilight shall commence at 5:37 a.m. Soon thereafter Mars shall no longer be visible due to this light obscuration. The Moon, of course, remains visible throughout the day.

[This event provides us with an opportunity to discuss the slight, but distinct difference between "topocentric" and "geocentric," in reference to astronomical configurations. Topocentric refers to the positions of bodies relative to a planetary surface, which, in this instance, is Earth. Geocentric refers to the position relative to the planet's center. These terms cannot be used interchangeably owing to Earth's extent, with a radius approximating 6,378 kilometers. When great precision is required, as it should always be, even in one is in pre-school learning the 99 basic Pythagorean theorem proofs, topocentric values are preferred.]





[Lunar phase: Waning crescent 8% illuminated Moon rises 3:17 a.m]

Known as M44 or Praesepe, the Beehive Star Cluster subtends an angular diameter of 95 arc-minutes in the night sky, as opposed to the Moon's approximate 30' angular diameter.  One could state that the Moon will be nearly 12 Moon-diameters to the SSW of Praesepe in the eastern early morning sky.   

The Beehive Star Cluster, a quaint sobriquet attesting to its resemblance to a swarm of honey bees  (genus Apis), is one of more than 1,100 cataloged open, or galactic, star clusters, within the Milky Way Galaxy.   A few traits define such clusters and distinguish them from the other principal cluster type known as "globulars."    Galactic clusters contain, at most, a few thousand member stars of comparative youth confined within a sphere usually no more than twenty light years in diameter, with a 2-3 light year wide core.  

At  distance of 577 light years, Praesepe is the 6th closest star cluster to the solar system.    Its member population exceeds 1010 members and has a combined mass of 500-600 solar masses (One solar mass equals the mass of the Sun.)   Though it appears to be of uniform brightness, the Preasepe Cluster has experienced "mass segregation." by which the more massive -and therefore brighter- members migrate toward the center. A physical process somewhat similar, in principal, to the tendency of multiple liquids in a sphere to differentiate themselves according to density.      The core is approximately 22 light years in diameter, making it amongst the larger galactic clusters.


A curious note:  galactic star clusters are relatively plentiful in spiral galaxies, but absent in elliptical galaxies.   Elliptical galaxies have depleted their gaseous reserves; the reserves necessary for galactic cluster formation.   Any galactic clusters that did form in elliptical galaxies will have long since dissipated.   Unlike the much more massive globulars that retain their members over billions of years, galactic cluster members will eventually disperse. 






The analysis of any population requires not only thorough observations of the specimens, but also necessitates the establishment of a system to distinguish them.  Moreover, this system must enable us to draw inferences about the specimens based on that information.   Toward this end, stellar astronomy developed the magnitude system in which one could categorize the stars according to brightness.  (Here, we hasten to point out that we're referring to apparent, not intrinsic brightness:  how bright the object "appears to be" as opposed to its actual brightness.)    We credit Claudius Ptolemaeus (Ptolemy) with the introduction of the magnitude system, though we have sufficient evidence to conclude that Hipparchos of Nicene actually crafted the scheme nearly three centuries before.  Claudius Ptolemaeus merely included the information in his own writings.


The original system separated stars into six categories according to brightness:    15 were classified as magnitude 1; 45 as magnitude 2; 208 as mag 3; 474 as mag 4; 217 as mag 5 and 49 as magnitude 6.  (We can infer from these values that the last two categories were somewhat incomplete.)


Implicit within the word 'magnitude' was the erroneous assumption that the brightness necessarily related to size.   (In modern day, we do have a mass-luminosity relation which equates a star's mass and its energy output, but this is an entirely different matter altogether.)  For instance, Tycho Brahe assumed the first magnitude stars to have subtended a 2 arc-minute angle; while magnitude 3 stars had an angular width of 1 arc-minute.    This correlation predated the understanding that stellar distances placed them light years away from Earth, as opposed to the current notion that stars were proximate objects of undetermined remoteness.


 The modern magnitude system was based on this scheme, although the increased database and expanding knowledge required a more quantitative system: one that precisely specified the brightness difference ratio between magnitudes.    Understanding that ratio truly began with 19th century astronomer Argelander, whose principal contribution involved celestial cartography.    Until that time, most star charts emphasized the constellation patterns and characters they represented, while the component stars were deemed of secondary importance.    Argelander, in his 1843 publication Uranometria Nova, lent a greater prominence to the stars, themselves.   The stellar population included in the work increased to 1,871.  Argelander adopted the Ptolemaic/Hipparchan system, and expanded it to accommodate the extra stars.  He also attempted to calibrate the system to account for brightness variations within each category, for the human eye can perceive brightness differences smaller than the whole magnitude ratio.


In 1872, Eduard Heis produced his Atlas coelestis novus, a publication containing 5,421 stars.    Gifted with unsual eyesight, Heis incorporated even fainter stars into his catalog, and by necessity, created the magnitude designation of 6,7 to accommodate the fainter stars.


Meanwhile, as these catalogs expanded the known stellar populations, other astronomers struggled with the brightness ratio represented by magnitude differences.    In 1835, CA Steinheil asserted that the various stellar brightnesses represented light intensity ratios of 2.83: so that a magntiude 1 star was 2.83 times more intense that a magnitude 2 star.   Three decades later, Professor Fechner formulated his 'psychophysical law" stating that the what the eye experiences as an equal difference in brightness is not a constant difference but a constant percentage of the light quantity."  (He based this realization by observing that the brightness difference within a cloud bank does not change when the clouds were viewed through dark glass.)


Steinheil constructed a highly sophisticated photometer enabling him to determine brightness differences quite precisely. He concluded the brightness ratio difference to be between  2.2 - 2.5.    He opted for the latter value as the uniform brightness difference, or, more correctly, the actual brightness ratio therefore between stars with magnitude 1 - 6  would be 3125/32, or 97.6.   NG In 1850, N G Pogson proposed that the ratio 2.512 be adopted as it equals the fifth root of 100, close to the 3125/32 ratio.


This value was adopted and remains the ratio factor for the magnitude system.  A magnitude 1 stars is approximately 2.5 times brighter than a magnitude 2 star; 6.25 times brighter than a magnitude 3 star; 15.6 times brighter than a magnitude 4; 39 times brighter than a magnitude 5; and 100 times brighter than magnitude 6.






[Lunar phase: waning crescent; illumination percentage:  1%  Rise time: 5:18 a.m.]

An event of academic importance, as the Moon and Regulus will appear to be 12 degrees from the Sun in the eastern twilight sky.   That having been said, of course, one might observe the star and moon provided one has an obstructed eastern horizon.   Both rise during Nautical twilight,*** and civil twilight begins at 5:39 a.m.  Regulus is the 21st brightest star in the night sky, as its magnitude is 1.3.




[Illumination percentage: 0% Precise phase time - 11:35 a.m. UT; 7:35 a.m. EDT]

The proper term is "solar conjunction," referring to the configuration in which the Sun and Moon have equal right ascension values. "Right ascension," measures a celestial body's apparent angular displacement from the vernal equinox, on an hour scale from 0 -24h.

The new moon is at conjunction and consequently not visible to Earth-bound observers. With this new moon commences Lunation Cycle 1122.

The Lunation Number refers to the Brown Lunation Cycle, defined as that which began on January 17, 1923. It was in that year that Ernst William Brown (1866-1938)'s more precise lunar theory was incorporated into leading astronomical almanacs. Each lunation number counts all cycles since 1923's first new moon.

Interestingly, for those who consider lunar motion computations amusing, even Brown's considerable improvements on lunar ephemerides (computational tables listing positions, phase angles, and distances of the moon) did not account for various small uncertainties dubbed "secular variations," that confounded Brown and his contemporaries until they were discovered to be uncertainties within Earth's rotational rate, itself. From this realization came Dynamical Time, a time flow that is impervious to external influences as it relates to the frequency of light from a certain transition of the Cesium-133 atom.




[Venus magnitude: -4.0; Spica magnitude 1.0; Venus set time - 8:32 p.m.; Spica set time - 8:22 p.m.]


    The appulse of Venus and Spica presents us with an opportunity to use magnitudes as a means of determining comparative brightness. Here, I would refer you to the Essay about Magnitudes written for September 3. This evening, Venus' magnitude is -4.0 and Spica's is 1.0. [Realize that Venus' magnitude is hardly constant, for it is determined by four factors, two of which are variable. The two constant factors are its size and albedo, the second of which measures the percentage of light it reflects back out into space. Venus' albedo is 0.67***, indicating that it reflects 67% of all incidental sunlight. The variable factors are its "heliocentric distance," the separation distance between Venus and the Sun; and "geocentric distance," the distance between Venus and Earth.]


The magnitude values indicate that Venus is considerably brighter than Spica, but we must understand the actual brightness difference. As it happens, here we contend with whole numbers, so we needn't resort to the equation. Instead, we remember that the brightness factor is 2.512 between whole ratios, so that a magnitude 1 object is 2.512 times brighter than a magnitude 2 object. As the difference between Spica and Venus is precisely five magnitudes, the brightness difference is 2.512 multiplied by itself five times. Conveniently, we know that 2.512 is the fifth root of 100, so Venus will be 100 times brighter than Spica.






Planetary astronomy is often regarded as a complex affair as it involves observations of moving objects from a moving platform.     The situation would be simpler were Earth stationary, as it can never be.    Predicting planet position requires us to know not only the planet's location relative to the Sun, but also Earth's location relative to the planet.        Hence, the difference between "sidereal period," the time a planet requires to complete one orbit relative to the distant stars, or, more correctly, the first point of Aries (vernal equinox position) and synodic period, the time a planet requires to be in the same part of the sky relative to Earth.


 Those astronomers who predict planet positions are more interested in the synodic period than the sidereal one.   Of course, successive planetary oppositions -the point at which Earth is between the Sun and the superior planet- are separated by these synodic periods.    For inferior planets, synodic periods also separate successive inferior conjunctions (the passage of the planet between the Sun and Earth.)


 We here list the Sidereal  (SL) and Synodic (SC) periods for each planet


MERCURY             (SL = 88 days; SC = 116 days)

VENUS                  (SL = 225 days; SC = 584 days)

MARS                   (SL = 687 days; SC = 780 days)

JUPITER                 (SL= 11.86 years; SC = 399 days)

SATURN                (SL = 29.46 years; SC = 378 days)

URANUS               (SL = 84.0 years; SC = 370 days)

NEPTUNE             (SL = 165 years; SC = 367 days)

PLUTO                  (SL = 248 years; SC = 367 days)


One might note the apparent incongruity of the 2nd and 4th planets having synodic periods greater than the outer planets.   We know that a planet's period is related to its distance as stated in the Keplerian harmonic law (The square of a planet's period is proportional to the cube of its semi-major axis, or mean distance.)    However, we resolve this incongruity at once by explaining that period to be sidereal, not synodic.    We see at once that the Sidereal periods do increase with increasing planetary distance. A brief analysis reveals that this relation isn't linear.


As Earth completes one orbit, the superior planet will have moved through part of its own orbit.    What matters most to the synodic period is the percentage of  the orbit completed.    Mars, the planet with the greatest synodic period (780 days) has to complete an entire sidereal period before completing one synodic period.    Neptune and Pluto hardly shift in their orbits during one Earth year.   Neptune moves through approximately 1.2% of its orbit each Earth year; Pluto moves through only 0.4% of its orbit.  So, their positions on Jan 1, 2013 are nearly the same on Jan 1, 2014, one need only add two days to obtain the synodic period.


Determining which period one should use to predict planetary phenomena requires one to know if the event is Earth-dependent; or Earth-independent.    In other words, does the event involve Earth.


An Earth-independent event would include "Mercury at aphelion," when Mercury attains its greatest distance from the Sun during a given orbit.  Such an occurrence does not involve Earth at all, so one can use the sidereal period to approximate the time separating successive Mercurian aphelia.   Mercury was at aphelion on June 28th and will reach aphelion again on September 24: 88 days later.

An Earth-dependent event would include "Mercury at inferior conjunction"  (At inferior conjunction, Mercury passes between Earth and the Sun.)  Mercury was at inferior conjunction on July 9 and will be again on November 1: 114 days.  Not precisely equal to the synodic period due to other factors, but we see that we must use the synodic period to approximate the time span between these successive Earth-dependent events.


Planetary astronomy becomes slightly easier when one knows the difference between sidereal and synodic periods and also when to apply both.





"Obliquity" does not merely apply to the planets, but is used in reference to the Sun, as well. The Sun is inclined at a 7.25 degree angle relative to Earth's orbital plane: an imaginary construct defined as "the ecliptic." Today, the Sun's north pole is inclined 7.25 degrees toward Earth; On March 6, the north pole was directed away from Earth to the greatest extent, again of 7.25 degrees. Ironically, in December and June, around the time when Earth experiences its two solstices, the Sun's angle is equinoctial: its north pole is neither inclined toward or away from Earth.




[Mars magnitude 1.6 Mars Rise time: 2:48 a.m. ang dia: 4.1"]

Praesepe subtends an angle of 90 arc-minutes, equal to 1.5 degrees. Mars, on this date, subtends 4.1 arc-seconds. [1 degree equals 60 arc-minutes; one arc-minute contains 60 arc seconds.] Consequently, it is inadequate to merely indicate that Mars appears "within" or "around" this star cluster. Instead, one must specify the angular separation between the planet and cluster center. Here, we must indicate "angular separation," as opposed to physical separation. We realize that whereas Praesepe is 577 light years away, Mars, at a current approximate distance of 2.261 Astronomical Units, is merely 18.8 light minutes from Earth***** The proximity is illusory, a consequence of the celestial sphere's apparent lack of depth.




[Lunar phase: Waxing crescent Illumination percentage: 11% Moon set - 8:28 p.m.]

Now, we recall that the difference between appulse and occultation is all a matter of location and geometry. While for your viewing area, Spica and the Moon's minimum separation distance is 1.1 degrees

In this region, observers will see a "close approach" of Spica and the Moon, but within a localized area, one will observe the direct passage of the Moon in front to this star. Observers within Northern Africa, Europe, the Middle East, portions of Greenland, and easternmost Canada will watch Spica's sudden disappearance behind the Moon. As the Moon's lacks any true atmosphere, when a star or planet moves behind it, it vanishes at once If the Moon had an atmosphere comparable to Earth's, any occulted object would gradually vanish as it passed behind various atmospheric layers.

The Moon has occulted Spica often this year: Jan 5, Feb 2, March 1, March 28, April 25, June 18th, September 8th and will occult it again on October 5 and November 29th, the last two events will be visible in North America.




Another occultation event, this one visible in southernmost South America and along a swath extending across the South Pacific. Again, as was true with Spica, when the Moon moves in front of Venus, the latter will vanish immediately: an instantaneous event that mathematical astronomy enables us to precisely predict.

Here, we find a splendid opportunity to discuss why only certain celestial objects experience this occultations while many others do not. The difference is quite simple: the occulted stars, like the planets, are confined to the ecliptic region: a path centered on the ecliptic: the undulating annual arc the Sun appears to describe each year. As the Solar System is essentially a disc, most solar system objects do not venture far from the Earth's orbital plane - another definition of "ecliptic." The Moon is similarly confined to the ecliptic area, though not precisely to the ecliptic owing to its orbital inclination. Therefore, it can occult planets (this year saw two lunar occultations of Jupiter -Jan 22 and Feb 18- and one lunar occultation of Venus - Sept 8) And, also stars surrounding the ecliptic (this year we've had multiple occultations of Spica, as well as Zeta Tau, Alpha Librae, and Graffias)   Four first magnitude stars Spica, Aldebaran, Regulus and Antares- are within 5.5 degrees of the ecliptic and therefore can be occulted by the Moon. These occultations occur in cycles. In 2013, the Moon occults Spica 14 times, but doesn't occult Aldebaran, Regulus or Antares.




[ZHR = 5; r = 3.0]

The peak of this comparatively minor meteor shower affords us the splendid opportunity to expose yet another of your usual host's myriad errors. In a previous article, which I read under duress, he stated that the light emission we perceive as a meteor results from ablation, the excitation of meteoroid atoms within the descent path. Well, I tell you that definition most certainly doesn't apply to "ablation," which pertains to the erosion of particles from an object's surface. Any process that draws material from an object's surface, such as evaporation or sublimation (the direct phase change from solid to gas without the intervening liquid stage) is considered "ablation."

"Excitation" occurs when the ablative process excites the electrons within the atoms. The energy elevates the electrons to higher levels. They return to their original states by emitting the imparted energy as photon: the photon energy****** must be equal to the energy difference between the elevated level and that to which the electron returns after this emission.

I hasten to add that one should not envisage the atom as being similar to a solar system in appearance, with a comparatively massive central nucleus surrounded by electrons orbiting within a series of concentric circles. That misconception derives from the Bohr Model of the Atom, a model that basic quantum theory has shown to be utterly false. Electrons do not occupy specific points in space-time and woe betide those who think otherwise.

The Epsilon Perseid shower appears to originate from a region around the star Epislon Persei. Were one to trace the trajectories of the shower's members, one would observe that they appear to emanate from the space around this star. This convergence is illusory, a consequence of our limited perception. The meteoroids actually move in paths parallel to Earth;s surface.




[Lunar phase - waxing crescent; illumination percentage - 18%

Moon set time: 9:06 p.m]

We ponder the disproportionate satellite population between Earth and Saturn, the sixth planet from the Sun. Our pesky little planet has merely one attendant world, while Saturn has (***forbidden***) moons, 62 of which have thus far been discovered. When one observes the Moon and Saturn together in the western evening sky, one must wonder why Earth and the other inferior planets have a paucity of moons, while they are abundant in the outer solar system.

We offer the following list of natural satellites for each planet.

Mercury - 0

Venus - 0

Earth - 1

Mars - 2

Jupiter (**forbidden) of which 67 have been discovered

Saturn (**forbidden) of which 62 have been discovered

Uranus - 27

Neptune - (**forbidden) of which 14 have been discovered

We readily observe the difference between the inferior planet total - 3; and the outer world total (*******). Also, we hasten to point out that the three inferior planet moons were accidental. Earth's moon formed after a sizeable proto planet collided with the infant Earth, vaporizing both the errant body and a substantial portion of the largely molten Earth. (That it was molten prevented Earth from being annihilated altogether.) The resultant amalgam solidified beyond Earth and established a receding orbit around it. The two Martian moons, Phobos and Deimos, were quite obviously captured asteroids and not coeval with Mars, meaning that they shared the same approximate origin periods.

The outer worlds, being profoundly more massive, were consequently more gravitationally powerful and therefore capable of either capturing renegade bodies or for retaining those smaller bodies forming out of the nebular cloud with them. The moon population thrives in the outer solar system; but languishes close to the Sun.




Will prove an utter disappointment.




[Moon set time: 10:38 p.m.; Lunar phase - waxing crescent; illumination percentage - 38%]

The name, "Antares," imprecisely translated as "rival to Mars," is hardly the star's first title. Persian astronomers assigned it the name "Satavis,"the western observer, and designated it one of the four Royal Stars, along with Aldebaran (Tascheter, the Eastern observer), Regulus (Venant, the Northern observer) and Fomalhaut (Hastrang, the Southern observer.)

Persian astronomers conferred this distinction on these four stars as they were, and still are, nearly a quarter of the sky apart from each other, or, 6 hours of right ascension. (Right ascension measures a celestial object's angular displacement from the Vernal Equinox, or the First Point of Aries. The right ascension range extends form 0 - 24 hours; with each "hour" equal to 15 degrees.

Even though the positions have each stars have changed since the 3000 BC period, dramatically through precession, negligibly through proper motion, the approximate equi distance between them remains constant. Aldebaran's RA is 4 hours 30 minutes; Regulus' RA is 10h 8m; Antares - 16 h 29 m; and Fomalhaut - 22 h 57 m)

Antares no longer serves the role of Royal Persian star, but remains prominent in the western evening sky.




[Moon set - 11:36 p.m.; lunar phase - first quadrature; illumination percentage - 50%]

An exposition pertaining to illumination percentages, for they are misleading statistics, indeed. A sphere in three dimensional space will, if subjected to a light source, be constant half illuminated. A brief contemplation should suffice to convince you of this reality. Our perspective, alas, does not permit us to observe the entire illuminated half apart from the opposition period, otherwise known as "full moon."

As the Moon completes an orbit around Earth, the illuminated portion it presents to us varies from 0% at conjunction (new moon) to 50% at both quadratures (first and last quarter) and 100% at opposition. The illumination percentages I cite at the beginning of each moon event refers to Earth bound perspective.




The dread that "13" inspires is hardly ubiquitous. While "13" has developed sinister connotations in various cultures, other numbers are similarly ominous in others. "17" is feared in many parts of Italy; The Chinese harbor no love for "4" as the Mandarin word for four sounds quite similar to "death," and the western world's lucky number "7" induces disquiet amongst the Chinese as the seven lunar month is the Festival of the Feeding Ghosts.

By bestowing supernatural properties onto numbers, humanity sustains the irrational notions that plagued it through the medieval period and for generations prior: the advent of the scientific method, which is still in in infancy on Earth, should have long since dispensed with these antiquated numerological beliefs.

A perfect instance is Friggatriskaidekaphobia, the irrational fear of Friday the 13th, a strange foreboding that still permeates your culture. However, an investigation into the Gregorian calendar since its 1582 inception shows that Friday occurs the 13th more than any other day. During the first four centuries following the Gregorian calendar reform, Friday was on the 13th of the month 688 times: The 13th occurred on a Sunday and Wednesday 687 times; on a Monday and Tuesday 685 times; and on Thursday and Saturday 684 times.

Those who obstinately retain their unjustified fear of Friday the 13th should derive comfort from its frequency and realize that numbers are abstract concepts and therefore should no more inspire fear than they evoke good fortune.

Provided your receptive to its teachings, astronomy can save you from such medieval psychological torments.




Were we able to illuminate the ecliptic, this evening we would observe Mercury intersecting it after having spent some time "north" of Earth's orbital plane. (The extension of cardinal directions into space is tricky; as one must define the plane according to a set standard. The North implies the Northern hemisphere of your planet.)

When a planet reaches the descending node, it is moving "below" (another uneasy directional word) the plane. This intersection means little for observers, apart from knowing that if one observes a planet at a node, then one is by association viewing a fragment of the ecliptic.

Mercury is a tricky world; for it is the fastest of the planets as a consequence of its proximity to the Sun. Its high velocity and location render it elusive to Earth-bound observers.

We understand the velocity-position relation as the second Keplerian planetary law, which, states that each planet moves in such a way along its orbit that a line drawn from the Sun to the planet sweeps out equal areas in equal time intervals. Johannes Kepler, the quintessential mathematician, opted for the term "radius vector," of course. Any vector connecting a planet and Sun will, in a given time interval of, let's say for simplicity, the duration of 9,192,631,770,000, periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom, draw out equals areas of space. Saturn travels slower than Mercury, but the former is so far away that the radius vector will sweep out a great deal of space even through its motion is slow. Mercury is quite close to the Sun, but moves so quickly, the swept out spatial area will be equally vast.

This Keplerian relation is, of course, a consequence of the angular momentum conservation law discerned by Sir Isaac Newton.




[Moon rise - 4:32 p.m; set - 3:00 a.m. 09/16; lunar phase - waxing gibbous; illumination percentage - 82%]

An ellipse is a closed curve such that the distance between the two foci and any point on the curve is constant. (Refer to the orbital elements essay on September 17.) As a planet's orbit is elliptical and the Sun occupies one focus (Kepler's first law), a planet's distance from the Sun varies continuously. Along a planetary, or, in this instance, a lunar orbit, is a point of least distance and greatest distance. For planets, these positions are perihelion (least distance) and aphelion (greatest distance.) For the moon, it is perigee (least) and apogee (greatest).

The moon is at perigee today, at a distance of 57.60 Earth radii, a measurement unit often employed for the Moon. We define Earth radius as 6,371 km. (That unit is particularly problematic as Earth is not perfectly spherical, but is instead a geoid that approximates to an oblate spheroid.)

The Moon's apparent angular diameter does increase at perigee, for the simplest reason that it is closer than at other times in its orbit. This difference is slight: the tides are more profoundly affected, as the differential gravitational force varies with the cube of the distance, as opposed to the gravitational force which is inversely proportional to the distance squared. Moon reaches apogee on September 27.




[Ecliptic longitude 174 degrees.]

A manifestation of orbital motion perceived as solar migration along the ecliptic: the apparent transition of the Sun from one constellation pattern to another. The Sun appears to proceed into Virgo the Maiden, the second largest constellation by subtended area (1294 square degrees; Hydra, with an 1302 square degree area, is largest.) Associated in mythology with Persephone, the abducted daughter of Demeter (Ceres), goddess of the harvest and grain, Virgo is the longest ecliptic constellation and therefore will host the Sun until October 30, when the Sun migrates into Libra the Scales.

We adopt your usual host's practice of listing the thirteen constellations comprising the ecliptic: Virgo the Maiden; Libra the Scales; Scorpius the Scorpion; Ophiuchus the Serpent Charmer; Sagittarius the Archer; Capricornus the Seagoat; Aquarius the Water Bearer; Pisces the Fish; Aries the Ram; Taurus the Bull; Gemini the Twins; Cancer the Crab. and Leo the Lion.

Apart from Ophiuchus, who remains unrecognized by the astrological community, these patterns also comprise the zodiac: a sequence of characters who placement during one's birth allegedly determines a human's defining traits: an arbitrary, mystical summation of one's flaws and attributes that can be regarded as comparable to psychoanalysis in terms of legitimacy and assessment accuracy.




As elementary as celestial mechanics truly is to those who grew up with matrix calculus amusement blocks, one does encounter exceeding difficulty when attempting to describe planetary orbits and predict positions, velocities, phase angles, magnitudes and the other factors. Fortunately, we have the basic orbital elements to assist us in our efforts to calculate planetary motions.

These six elements are:

The Semi major axis - the planet's mean heliocentric (sun-centered) distance;

Orbital Eccentricity - the value specifying an ellipse's departure from circularity. For an ellipse, the range is 0 - 1; 0 indicative of a perfect circle; 1 is a parabola. Most planets have comparatively low eccentricities, although Mercury is somewhat elongated with a 0.206 eccentricity.

Orbital inclination - the angle a planet's orbit subtends with respect to the Ecliptic

The Longitude of the Ascending Node - the angle the ascending node subtends in reference to the vernal equinox. The point at which the planetary orbit intersect the ecliptic en route to the region north of that plane.

The Argument of Perihelion - the angle between the perihelion (closest point in the orbit) to the Ascending Node position.

The Time at which the Planet reached Perihelion.

Were the solar system constructed for simplicity, such factors would be ignored. As it is, the resultant interplay of planets and the Sun makes the matter considerably more complicated. However, if one obtains the values cited above, one can start the process of understanding planetary motion and crafting ephemerides to predict planet positions.



(Your congenitally lazy usual host added yet another day to his extended vacation.)


*We remember, of course, that the term "BC," Before Christ or "BCE," Before the Common Era, a convention chosen by those preferring to detach calendar reckoning from ecclesiastical association, are comparatively modern designations, having been devised in AD 525 by Dionysius Exiguus (470-544) to replace the system using AUC, ab urbe condita, designating years from the "founding of the city," a quasi mythological event involving the encampments of Romulus and Remus on the banks of the Tiber River.    Incidentally, Romans did not make frequent use of this AUC designation, preferring, instead, to specify the years according to the tenure of the two counsels.   The AUC popularity derives more from medieval scholars who adopted it when translating Roman texts.



**Both factors vary with time, with Earth's orbital eccentricity varying within a range of 0.005 - 0.058 over a rough 413,000 year period.     The eccentricity value is currently decreasing,   The obliquity varies between 22 degrees, 13 minutes and 44 arc-seconds to 24 degrees 20 minutes and 50 arc-seconds over the next million years.    This range, itself, varies over longer periods.   


***One must differentiate between geometric albedo, the reflection percentage of visible light; and bond albedo, the percentage of all electromagnetic radiation reflected. Venus' bond albedo is 0.9.


***We designate three twilight phases:    Astronomical, Nautical and Civil.    Astronomical twilight occurs when the Sun is between 18 - 12 degrees of the horizon.    Nautical twilight corresponds to the time when the Sun is between 12 - 6 degrees of the horizon; and Civil Twilight is the time period when the Sun is between 6 - 1 degrees of the horizon.      On September 4, astronomical twilight begins at 4:27 a.m.; nautical twilight begins at 5:04 a.m. and civil twilight starts at 5:39 a.m.


*****Computation details. An astronomical unit, defined as the mean Earth-Sun distance, is 149,597,871 kilometers. Mars' Au distance is 2.261 AU, yielding a distance of 338,240,786 kilometers. Next, we know the exact speed of light propagating through a vacuum, which is 299,792,458. (This value is exact because we define the kilometer by this light standard according to the International System of Units.) The resultant quotient of the distance by rate produces the speed in light-time.


******A photon's energy is proportional to its frequency, or inversely proportional to its wavelength. All photons propagate at light speed, so an energy increase within a photon doesn't induce an acceleration, but, instead, heightens its frequency.

 2013 SEPTEMBER 18


[Venus mag: -4.1; Saturn mag: 0.7]

Let us embrace this splendid opportunity to calculate relative planetary brightnesses!   A lovely way to begin this second part of our night sky calendar.   After all, if one can observe both worlds this evening, and make a note of their comparative brightnesses, one can relate it to the value we're about to calculate.

We first calculate the difference between the magnitudes      0.7 - (-4.1) = 4.8. 

Next, we multiply that value by 0.4  = (4.8)(0.4) = 1.92

Finally, we raise 10 to the power of that number = 83.1

Thus, we can conclude that Venus is 83 times brighter than Saturn.


Oh, how exquisitely lovely!

We'll do that calculation again on September 25th.


Incidentally, Venus and Saturn will be 42 degrees from the Sun and therefore still visible just after the conclusion of astronomical twilight.  Of course, one would need a western sky free of obstruction to observe them both when Astronomical twilight ends.





The proper term is opposition, when the Moon's longitude is 180 degrees.    Quite importantly, we must remind readers that the full moon is an instantaneous phenomenon, as the Moon moves continuously.  The notion that the "moon will be full tonight" is a gross misconception your usual host cheerfully propagates.   The moon is either waxing gibbous, the phase just preceding the full moon, or waning gibbous, the phase that immediately follows.

We also must address a controversy pertaining to the "Harvest Moon," a quaint term that humanity will inevitably forget once it out-evolves agriculture,   By some estimations, the Harvest Moon refers to the full moon closest to the September equinox (The term "September equinox" is preferable to "Autumnal," as the latter is hemisphere-specific.)  By other reckoning, one can only confer the "Harvest moon" designation on the full moon occurring after this equinox.     Thus, the uncertainty:  the harvest moon is today according to some, or October 18 according to others    It is an indifferent matter for me, hence my admirable lack of emotion in discussing the issue.






Another curious term which will become obsolete once humanity wrests itself away from its Ptolemaic prejudices.    No planet can ever be stationary, any more than it can reverse its own course.   Planets are massive objects and, just by simple inertia, impeding their progress would require substantial force, let alone halting their motion and causing them to actually move in a retrograde fashion.  

As humans observe all planetary motion from a mobile station, many perceived motions will be illusory: a combined effect of actual object and observer movements.   Were the observers inert, all planets would maintain a consistent orbit, varying only as their heliocentric distances changed.  (The velocity increases with decreasing distance and decreases with increasing distance.)   

As Earth approaches, intersects, and then moves just beyond the radius vector connecting a planet and Sun, the planet appears to halt, commence retrograde motion and then halt again before resuming prograde motion.   This peculiar behaviour inspired Claudius Ptolemy to contrive his convoluted system of epicycles, deferents, and perfectly circular orbits: a scheme necessitated by the contemporary paradigm that celestial motions had to be circular and centered on Earth.

The Copernican system, which displaced Earth from its centralized station and into its proper orbit, did, at least, offer a rational explanation for retrograde motion.  Although, even Copernicus retained the circular orbits.    It would be left to Johannes Kepler to reveal that planetary orbits were elliptical.  





("Autumnal Equinox" for the Northern Hemisphere;  "Vernal Equinox" for the Southern Hemisphere.)

Technically, the moment -like the Full Moon, also instantaneous- when Earth is 180 degrees from the March Equinox: the point diametrically opposite that it occupies at the First Point of Aries.      The term derives from the Latin terms "aequus," meaning "equal" and and "nox," for "night."      As it implies an equality of day and night duration, this term is quite misleading. 


On the September Equinox, we do not experience this equality,   The discrepancy arises from a few factors:  first, the Sun is not a point source and Earth's atmosphere refracts its light, causing a distortion and horizontal elevation of its image (it appears above the horizon just after setting).  Secondly, as Earth is not perfectly spherical, the surface onto which the light is cast is uneven.   


In Portland, Maine, the Sun rises at 6:29 a.m. and sets at 6:38 p.m. today


At the "Great Intersection," the point in the South Atlantic where the Prime Meridian crosses the Equator, the Sun rises at 5:49 a.m. and sets at 5:56 p.m. local time.  Still not equal.


In the Northern Hemisphere, autumn begins; in the Southern Hemisphere, spring commences.   At the North Pole, the Sun has almost set.  Atmospheric refraction causes the solar disc image to protrude above the horizon for the next few days.    At the South Pole, the Sun is above the horizon.   





[Moon rise - 9:40 p.m.;   Lunar phase - waning gibbous; illumination percentage - 73%]


A galactic star cluster with an estimated distance of 390 - 440 light years, and an angular extent of 110 arc-minutes (1 degree 50 arc minutes), the Pleiades is an asterism with the constellation Taurus the Bull, a pattern associated with early winter, the season when it is most prominent.   

One could consider the waning gibbous moon to be slightly more than 3 Pleiades-diameters south of this cluster.  


The lunar light obscuration, still significant when at 73% perceived illumination, will not be sufficient to obscure the cluster.





[Mercury mag:  -0.1;  Spica mag: 1.0]


Yes, I promised we'd repeat the calculation we performed in September 18th.    First, however, we note that this appulse represents the closest approach of a planet and 1st magnitude star for 2013.     Such close approaches can, and periodically do, occur as a few first magnitude stars, such as Spica, Regulus, and Antares, are close enough to the ecliptic to have close approaches with, and, quite rarely, by occulted by planets.

{Venus occulted Regulus in 1959 and will do so again in 2044.]


Now, as for that calculation;


Determine the magnitude difference   1.0 - (-0.1) = 1.1

Multiply the result by 0.4  = 0.44

Raise ten to the power of that product = 2.75

Mercury is currently almost three times brighter than Spica.





[Rise time:  11:17 p.m.   Illumination percentage:  50%]


What a splendid time to address the misconception pertaining to lunar rotation.   The notion that as the Moon directs the same region toward us constantly, it must not rotate.  How else, some wonder, could we only see 50% of the moon? [Due to libration, we actually see 59% during each orbit.] 


The Moon does rotate, but does so in such a way so that its rotational and revolutionary periods are equal, approximately 27.3 days.  The equality of the revolutionary and rotational periods is called "synchronous rotation." a phase-locked state that is certainly not unique to the Earth-moon system. 

[Phobos and Deimos are tidally locked to Mars; and many of Jupiter and Saturn's moons are similarly locked.]


Therefore, the term "dark side of the Moon," is a falsity, for all regions of the Moon are subjected to sunlight, except for the deepest region of some polar craters.





[Distance = 63.39 Earth-radii]


Please refer to the section on September 15 about Perigee for more information about variations in the moon's distance.  I would expound more, but I think it would be inappropriate to make this calendar excessively long.





[Moon rise - 12:10 a.m.; Moon set - 2:53 p.m.      Lunar phase - Waning crescent;

Illumination percentage - 36%]




 Readers will notice a couple of differences between my Planet Section and that of your usual host.  First, I categorically refuse to assign a "pick planet tiara" to any of these worlds.   Such designations are pointless, subjective and arbitrary.  Secondly, unlike the planets featured in previous articles, these planets will not run to the bathroom, powder their noses, smoke cigars in back room closets, dance on stage, glower enviously at other planets, pirouette in plate tops, perform back flips on horses, cram their heads into Lions' mouths, or engage in any other asinine anthropomorphic behaviour.  Planets are, as we all know, spheroids moving under the influence of a centralized force and are incapable of both human emotions and feats of acrobatics.




[Mag  Sept 1: -1.0 (not visible);  Mag Sept 30: 0 (visible)  decreasing]

Approximate percentage of orbit completed - 32%]

Sidereal period - 88 days

Synodic period - 116 days   (refer to September 7th essay for more information pertaining to these two periods.)


The namesake of Mercurius, a Roman counterpart to the Greek Hermes, Mercury is the closest planet to the Sun, at an average distance of 0.39 AU, which approximates to 36 million miles.    Visible by mid month - the end of September, but always within nautical evening twilight (the time period when the Sun is between 6 - 12 degrees below the horizon.)  It brightness diminishes during this visibility period and one would be advised to search for it between September 15 - 25.


As Mercury is quite close to the Sun, it remains quite close to the Sun from our vantage point: its maximum elongation angle never exceeds 28 degrees.   Consequently, Mercury is most often observed during one of the three twilight periods-


Astronomical  (when the Sun is between 18 - 12 degrees of the horizon)


Nautical (12 - 6 degrees of the horizon)


Civil (6 - 0 degrees of the horizon.)


One can infrequently observe Mercury in just before astronomical twilight in the early morning or just after astronomical ends in the evening.   The next occurrence of "Mercury out of twilight" happens in mid November, when Mercury rises a few minutes before astronomical twilight commences.


Notable events:  This month Mercury reached the descending node on September 14th; and will be at aphelion on September 24th




[Mag  Sept 1: -4.0 Mag Sept 30: -4.2 (visible)   increasing.]

Approximate percentage of orbit completed - 13%]

Sidereal period - 225 days

Synodic period -  584 days   (refer to September 7th essay for more information pertaining to these two periods.)


Named for Venus, the Roman goddess of physical love and beauty, the counterpart to the Greek Aphrodite, Venus is the second planet from the Sun.    Its average heliocentric distance is approximately 67million miles.  


One will observe Venus in the western evening sky this evening.  Its brightness increases throughout the month as its distance from Earth decreases.  We recall earlier in the article when we discussed the four factor determining planetary brightness:   size, albedo, heliocentric distance and geocentric distance.  The last two factors are variable, while the first two are constant.     We can use this opportunity to discuss the inverse square law, and how it applies to light emission and reflection.


We observe planets as they reflect sunlight.   The brightness varies because the intensity of the incidental sunlight and that of the reflected light also vary.    The inverse square law indicates that this brightness diminishes with the square of the distance:  if one doubles the distance from a light source, its brightness isn't reduced to a half of its original value, but to a quarter:  1 divided by the square of two.     We can readily see that the brightness is quite distance sensitive.


We employ the sphere to explain this sensitivity: for one can imagine light as radiating away from a spherical source, such as the Sun.   Along the Sun's surface is a shell of energy.   As the shell expands, the same amount  of energy covers a sphere whose surface area increases with the square of the distance.  (A sphere's volume varies with the cube of its radius, but its surface area varies with the square.)   The farther away one measures this energy, the more attenuated it becomes.   


Venus is the brightest planet as it is comparatively close to the Sun and also to us, although on occasion Mars will be closer.    However, Mars does not reflect as much of its incidental sunlight back into space as Venus does.    Mars' geometric albedo is 0.17; Venus' is 0.67, meaning that Mars reflects approximately 17% of the sunlight into space; whereas Venus reflects 67%.   Also, Mars is much farther from the Sun than Venus and therefore the incidental sunlight will be less intense.





[Mag  Sept 1: 1.5 Mag Sept 30: 1.4  (visible)   increasing.]

Approximate percentage of orbit completed this month - 4.5%]

Sidereal period - 687 days

Synodic period -  780 days   (refer to September 7th essay for more information pertaining to these two periods.)


Iron oxide accumulation lends this planet surface a ruddy red color, reminiscent of blood.   The planet's distinctive crimson hue caused war-weary humans to associate it with blood shed, battles, death and mayhem.  Through these associations, it came to be known as Mars, the God of War; Greek counterpart of Ares.        


One will locate Mars in the eastern morning sky; it rises around 2:30 a.m. at month's beginning; and at 2:00 a.m. by month's end.    We refer to 2013 as a Non Martian Opposition year, as Mars will not be at opposition at all this year.  (Opposition occurs when Earth passes between Mars and the Sun.)   The last opposition was March 3, 2012; the next opposition will be April 8, 2014.   As it true with all superior planets, Mars is easiest to observe around oppostion, as it remains visible all night and will be at its brigthest.   This year, Mars never rises before midnight and for the remainder of 2013, is the dimmest of the "visible planet," meant in this instance as those planets humans can observe without optical enhancement.  


One perplexing issue about Mars is surface gravity: the magnitude of the gravitational attraction that one experiences on another object's surface.  On Mars, the surface gravity is 0.38, meaning that one's weight on Mars is 38% that on Earth.     That, in and of itself, is not confusing.  However,  Mercury's surface gravity is also 0.38, equal to Mars.  One might wonder how Mars' surface gravity can be equal to Mercury's when the former is more massive than the latter?


We address this seemingly nonsensical matter by explaining that a body's mass is not the only factor involved in surface gravity. So, too, is size, or, more precisely, volume.     The simple surface gravity calculation indicates that a planet's surface gravity is proportional to the body's mass and inversely proportional to the square of the planet's radius.


We see that Mars is more massive than Mercury (Mars is 10.7% as massive as Earth; Mercury is only 5.5% as massive), but Mars is also bigger (15.1% as large as Earth by volume; Mercury's volume is 5.6% of Earth's.)     Recall that the magnitude of the gravitational force diminishes with the square of the distance:   and, when you stand on a planet, each particle within that planet exerts a gravitational force on you.   If one were to make the planet smaller while maintaining the mass, the surface gravity would increase because the distance between you and all the planet's particles would decrease.    Conversely, the separation distance between you and the planet's particles would increase if the planet's volume increased.  Therefore, the surface gravity would decrease.


So, if you weigh 100 pounds on Earth, you would weigh 38 pounds on Mars and on the less massive planet, Mercury.






[Mag  Sept 1:  -2.0  Mag Sept 30: -2.2  (visible)   increasing.]

Approximate percentage of orbit completed this month - 0.7%]

Sidereal period - 11.86 years

Synodic period -  399 days   (refer to September 7th essay for more information pertaining to these two periods.)


Jove, the Greek Zeus, the lord of the Gods who defeated Cronos and the Titans, the namesake of the planet whose mass exceeds the combined mass of all the other planets.   Jupiter rises after midnight on September 1st, and before midnight on September 30.   Jupiter brightness increases throughout the remainder of 2013 and is the second brightest of the "visible planets."  (27 times brighter than Mars;  6.25 times brighter than Mercury at month's end; 10 times brighter than Saturn; 6.25 times dimmer than Venus.)


Jupiter is the closest Jovian world, defined as a planet predominantly gaseous with a solid, rock-dense core; and a comparatively high rotation rate.      Its sidereal rotation rate -defined as the time required for Jupiter to have completed one orbit relative to the distant stars- is 9 hours 55 minutes; as opposed to the comparatively lethargic turn of Venus, with a rotation period of 243 days.    Saturn also rotates rapidly, its sidereal rotational period is 10 hours and a half; Uranus and Neptune are marginally slower - 17 hours 14 minutes and 16 hours 6 minutes, respectively.


Here, we must specify the difference between rotation periods and rotation rates, which are variable along a planet's surface.    Again, we confront the apparently counterintuitive: if the body rotates as one mass, i.e. doesn't experience differential rotation -as the Sun does- how can the rotational rates differ on its surface?  The answer is elementary:  a sphere's circumference varies with latitude.  (Granted, the planets are essentially oblate spheroids, but the principal is the same.)    The circumference is greatest along the equator, and at a minimum at the poles.    Any point on the planet must travel a certain distance during each rotation. An equatorial point travels a greater distance than one at any other latitude.  


One can approximate the velocity with a simple equation relating the speed with the latitude: it is equal to the equatorial velocity multiplied by the cosine of the latitude.      On Jupiter, the equatorial velocity is 12 kilometers per second (26784 miles per hour; compare to Earth's equatorial velocity of 1036 miles per hour).   Around the Great Red Spot, centered around 22 degrees South latitude, the rotation velocity would be 11.12 kilometers per second (24,833 miles per hour.)



[Sept 1: mag 0.7 Sept 30: magnitude 0.6;

Approximate percentage of orbit completed this month -

Human eye sensitivity is quite limiting astronomically, as evidenced by the antiquated belief that Saturn defined the Solar system's boundaries. Only when humans developed enhancement mechanisms did they start to identify the myriad bodies beyond the Saturnian orbit. (Astronomers periodically included Uranus on their star charts, but erroneously classified it as stellar instead of planetary.)

This month, one will observe Saturn in the western evening sky.     We expect it to become obscured in the western twilight by October, only to return to visibility in late November.


We recall our discussion about the inverse square law: the diminishment of an object's brightness with increasing distance.      We remember, also, that a planet's brightness varies with changing distance from the Sun (the original light source) and from Earth, the station where the reflected light is observed.     As Saturn is rather remote, by planetary standards, is in a marvel that it can be so bright.    We can ascribe this brightness, in part, to its extensive ring system: the array of particles that have established equatorial orbits around Saturn.    The material within these rings are often highly reflective, similar to water ice.   The cumulative effect of this ring reflexivity is a brightness increase within one magnitude:  its contribution varies due to the "ring aspect," the angle the rings subtend relative to the Earth-Saturn sight line.   This variation results from Saturn's obliquity (26.7 degrees) that will occasionally cause the rings to "disappear," as they will appear edge-on.   





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