[image: antigone-small.jpg]
[image: Lytras_nikiforos_antigone_polynices.jpeg]
*Antigone: * *The abiding love of a daughter/sister*
When Oedipus, King of Thebes, realized that he had, indeed, killed his
father and married his mother, as the oracle had foretold, he punctured
both of his eyes in a mad fit of remorse and self-disgust. He then promptly
abdicated and swore to forever after abjure human society.  However, the
citizens of Thebes allowed him to remain in their city as a private citizen
for many years thereafter.  They had been moved by both the rapid
renunciation of his kingship and his self-mutilating gesture of
contrition.    (They also didn't forget that years earlier he had saved
them all from the dreadful Sphinx.)   He spent those years mostly in
seclusion with his four children/siblings:  Eteocles, Polyneices, Ismene,
and Antigone. The first two were his sons/brothers, the others his
daughters/sisters.    He continued raising them as best he could despite
both his enfeebled condition and the absence of their mother, Jocasta, who
had committed suicide after learning that her husband Oedipus was also her
son.   During the period following Oedipus' downfall, Creon, Jocasta's
brother, served as regent.    Creon had reluctantly permitted Oedipus to
remain in Thebes in deference to the citizens who still harbored affection
for him.   And, in any case, the plague that had devastated Thebes and had
led to the revelations pertaining to Oedipus' marriage lifted soon after he
abdicated the throne.    All seemed well for those many years until another
plague struck the city.    Believing this latest blight to have been caused
by Oedipus' continued presence, Creon banished him from Thebes at once.
 To Oedipus' disgust, neither of his sons opposed the banishment.   Before
he departed, Oedipus cursed them both.   His love for his daughters,
however, remained undiminished, for Antigone had agreed to accompany him in
his banishment while Ismene offered to remain in Thebes to attend to his
affairs.     Oedpius and Antigone wandered far from Thebes and for years
found no refuge.   Citizens all over Greece had learned of Oedipus and
officials from most cities barred him entrance for fear that in doing so
they would incur divine disfavor.   Finally, King Theseus of Athens (yes,
that Theseus!) provided Oedipus and Antigone refuge.     Theseus had
matured into a wise older man who grew to be as compassionate as he was
courageous.  He, too, had heard of Oedipus and well knew that he was widely
reviled and therefore wretched.  Under Theseus' protection and with
Antigone at his side, Oedipus lived peacefully during the very last phase
of his life.   Just prior to his death, Oedipus received a visit from his
daughter Ismene.  She had come to him to report that an oracle had
proclaimed that Oedipus would eventually perish in Athens.  His internment
would bestow great power onto the city and in death he would be revered as
he had never been in life.  Comforted by this news, Oedipus lapsed into a
sleep from which he never awoke.      After performing the death rituals in
honor of their father/brother, Ismene and Antigone returned to Thebes.
 They arrived to discover that one of their brothers was about to declare
war on the other.     A few years after Oedipus' banishment, Eteocles and
Polyneices had reached the age at which both were eligible for the
kingship.  Creon had agreed to relinquish the throne to one of the
brothers, provided that he was allowed to select his successor.    Even
though Polyneices was the older and consequently entitled to the succession
through primogeniture, Creon decided that the brothers should each rule in
alternate years.  Creon secretly believed Eteocles to have been the wiser,
kinder and more temperamentally inclined to be king than his elder
brother.  However, not wishing to ignite a civil war, he opted for an
alternative he hoped both brothers would favor.     He did, however, give
the first year's rule to Etoceles.  After that year elapsed, Etoceles
refused to relinquish the throne to his brother.  Polyneices fled Thebes in
a fury and quickly mobilized an army to launch an assault on Thebes.
 Polyneices and six others divided the army into seven divisions.  Each
division was deployed to one of the seven gates surrounding the city.
(Antigone and Ismene, who managed to reach Thebes just prior to the war's
inception, remained neutral and isolated.)  The ensuing war, known as the
"Seven Against Thebes" was, even by the standards of conflict, ferocious,
bloody and ultimately indecisive.  While the invading army couldn't
penetrate the gates, the defending army couldn't force them to abandon the
assault.   Finally, it was decided that the two brothers should fight one
another.  The winner would earn the throne for life.     Alas, during their
struggle, Eteocles and Polyneices were both slain.      The two armies,
which had disbanded before the brothers' fight, did not reassemble.
Creon assumed the throne again.  He declared that while he would
posthumously bestow every honour onto Eteocles, Polyneices would be left
outside the gates to rot.  "Let the birds devour the traitor's corpse!" he
declared. "And any of those who attempt to bury him will be put to death at
once!"     Antigone and Ismene, both devastated at the loss of their
brothers, were horrified by this declaration.  They loved both brothers and
knew that if a dead person's body was left uninterred, his shade would
wander the world in utter desolation forever. Nobody was particularly fond
of the underworld, but at least there one was part of a large community.
The ghost of an unburied person was doomed to eternal isolation.  Antigone
confided to Ismene that she was going to venture outside Thebes to inter
her brother's body.  Ismene, though sympathizing with her sister, tried
unsuccessfully to dissuade her.  "We are but women, dearest sister.  It is
not for us to decide such matters. If you do this, I shall lose a sister as
well as both brothers."    Ismene's protest only strengthened Antigone's
resolve.  In the middle of the night, Antigone fled the city and quickly
found Polyneices lying dead in the precise place he fell during his combat
with Eteocles.   She hurriedly dug a shallow grave with her hands next to
the corpse.  Once the hole was completed, she took her brother in her arms
and kissed him tenderly.   Antigone then dragged him into the grave and
covered him with a thin layer of dirt.    Though she had intended to
perform a death ritual, she was instead convulsed with sobs and could say
nothing.  Her cries drew the attention of sentinels who saw what she had
done and detained her.     Antigone was brought immediately before Creon.
  The King first asked Antigone if she had been aware of his proclamation.
When she told him she had, he angrily demanded to know why she defied the
order.  "I abided by the rule of the gods," she answered, "which shall
always prevail above the law of men."    At this, Ismene ran into the court
and tearfully declared that she had helped to bury her brother.  "No!"
Antigone shouted, glowering murderously at her sister.  "She had no part in
it.  She chose a coward's life and I chose a noble death.     Be gone with
her!"   After Ismene was escorted away, Creon pronounced a sentence of
death.   "You are to be buried alive at sunrise.   Prepare yourself."
Antigone was brought back to her home under guard.  That night, while the
soldiers remained stationed outside her door, Antigone hanged herself.
In one version of her story, Haemon, Creon's only son, was so distraught at
her suicide that he killed himself.  He had been passionately in love with
Antigone and was determined to marry her.   Haemon's mother then also
committed suicide after finding her son's body.   Creon's household was
destroyed and he lived the rest of his life in misery for attempting to
withhold from Polyneices the rites to which all mortals were by divine
order entitled.




THE SOUTHWORTH PLANETARIUM
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2019-2020:  CLIV


THE DAILY ASTRONOMER
Tuesday, May 26, 2020
Remote Planetarium 41:   Stellar Motions

[image: iStock_OrionSword-XSmall-200x300.jpg]
*Stars move.*
However, when admiring the stars on any clear night, one perceives them as
stagnant.   Well, honestly, if one watches the stars at the same time of
year once every decade, they still seem boringly inert.  Look at the
constellation Orion.  Were one to venture outside in early February to find
the great hunter, one would find him high in the south around 8:00 p.m.
For an entire human lifetime Orion would be thus situated;  due south
around 8:00 p.m. in early February.    The Orion of one's youth is
identical to the Orion's of one's old age.   Moreover, the Orion of your
great great grandfather's youth seems the same as that of your great great
grandchild's last days.    From these observations one can well understand
the ancient belief that the stars were immutable, immortal and immobile.
Astronomers have only recently - by astronomical time frames- discovered
that they are nothing of the sort.   They move through the galaxy at speeds
exceeding a hundred miles per second.   They're also constantly changing
and, like everything else in the cosmos, their time within it is finite.
(Topics for another day.)

Our focus today is stellar motions. We will divide these motions into two
categories: proper and improper.  Proper motions are intrinsic motions,
whereas improper motions are merely those that we perceive.    We also
refer to proper motion as "space motion."  We identify three main types of
improper motion, diurnal, annual and precessional.

   - *IMPROPER MOTIONS:*     diurnal (daily), annual  and precessional
   - *PROPER MOTION:*   space motion

*DIURNAL MOTION*
The simple westward motion of stars caused by Earth's rotation.   Our
planet rotates once every 24 hours or every 1440 minutes.      Since one
rotation covers 360 degrees, a star will shift by one degree every four
minutes or about fifteen degrees per hour.

[image: maxresdefault.jpg]
The image above shows a time lapse photograph of the night sky.    We can
see direct evidence of Earth's rotational motion.    Each star follows a
circular pathway, the size of which depends on its angular distance from
the celestial pole.

If Earth could somehow occupy the location in its orbit (impossible), the
stellar motions would be merely diurnal.  We would see the same stars at
the same time of night each night.    However, not only is Earth rotating,
it is also revolving around the Sun. As a consequence, stars also exhibit

*ANNUAL MOTION*
During each rotation, Earth moves approximately one degree ahead in its
orbit.    As a consequence of this shifting, stars will rise four minutes
earlier each day, unless, of course, they're circumpolar.    We can use
this four minute daily shift to help us follow stars throughout the year.
Namely, we can employ the *"Two Hour Rule.*"   At the article's beginning
we mentioned Orion being due south at 8 p.m. in early February.   Let's be
a bit more specific.  Orion will be due south at 8 p.m. on February 2nd.
 Each February 2nd for the rest of our lives we can expect to see Orion the
Hunter due south at 8 p.m.   Now, when will Orion be due south on March
2nd?    Well, we know that stars rise four minutes earlier each day.    So,
in one week, a star's rise time will decrease by 28 minutes or nearly half
an hour.   In two weeks, the rise time is reduced by one hour.  We can then
see that a star will rise two hours earlier each month.

If Orion is due south at 8 p.m. on February 2nd, it will be due south at 6
p.m. on March 2nd, 4 p.m. on April 2nd, noon time on May 2nd, and so
forth.  However, Orion will be due south at 10:00 p.m. on January 2nd,
midnight on December 2nd and 2:00 a.m. on November 2nd.    One can also
determine the time that Orion reaches the due south position (called *upper
culmination*) at any other time.  For instance, on February 9th, Orion will
be due south at 7:30 p.m.   on February 16th, 7:00 p.m.

One may use this rule to track any star or constellation through the year.
Just remember, however, that the amount of time a star spends above the
horizon depends on its *declination, *or angular distance north or south of
the celestial equator.  The higher north the star, the greater its amount
of time above the horizon.

*PRECESSION:*
Have you ever seen a top spin?   If you have, you might have noticed that
the axis "precesses." As the top rotates on its axis, the axis describes a
wide circle so that it is constantly  pointing in different directions.
Our planet's axis also undergoes precessional shifting due primarily to the
gravitational pulls of the Sun and moon.

[image: download.jpg]
One of Earth's precessional cycles lasts about 26,000 years.     During
this time period, the north celestial pole (NCP) will be aligned toward a
variety of different stars.   Currently, the NCP is oriented toward
Polaris, hence the name "North Star."   Precessional wobbling will continue
to move the NCP toward Polaris until it reaches its minimum angular
separation distance of 27' in the year 2102.    The graphic below shows the
NCP's path over the next 26,000 year period.

[image: 800px-Precession_N.gif]
Around the year 4000, Errai, a star in Cepheus will become the new "north
star." In about 13,000 years, the bright star Vega will have that
distinction. Although, as we can see from the graphic, Vega will not be
nearly as close to the NCP as Polaris is now.

Not only will the precessional cycle alter the NCP's position, it will also
affect the *zodiac.  *Recall that the zodiac refers to the thirteen
constellations through which the Sun appears to travel each year.   While
these constellations will always remain part of the zodiac -until proper
stellar motions disfigure the constellations beyond all recognition- their
positions relative to the seasonal points will vary over time.   The actual
shift equals one degree every 73 years.     Presently, the Sun appears to
occupy the constellation Pisces on the vernal equinox, the first  day of
spring.      The Sun's vernal equinox point had been in the constellation
Aries the Ram.   In 68 BCE, this point shifted from the Aries into the
Pisces region.     For this reason, the vernal equinox is also called "The
First Point of Aries."   The Vernal Equinox point will move into Aquarius
in AD 2597!

Another example:  the summer solstice point was in Gemini the Twins until
1989, when it then shifted into the Taurus the Bull region.
Throughout the 26,000 precessional cycle, the four seasonal points will
eventually occupy every point of the zodiac.

The diurnal, annual and precessional stellar motions are all a consequence
of Earth's motion.   Finally, we will look at proper motions and the space
motions of the stars.

*PROPER MOTION*
Stars move through space in three dimensions; four, if you count time
because you believe in the hyperspatial space-time continuum.
 Consequently, we can divide stellar motions into two components: radial
velocity and transverse velocity.

*Radial velocity* refers to motion either toward or away from an observer.
Think of being a batter in a baseball game.  When the pitcher throws the
ball, it exhibits a high negative radial velocity as it is approaching
you.  If you hit the ball, its radial velocity will be highly positive.
 The* transverse or tangential velocity* will be very low because the ball
won't be moving much to either the left or the right when it is approaching
you and when you hit it away.     Now, further suppose that while you're at
the plate, a runner is on first base.   When you hit the ball, the man on
first will be running toward second.  The runner will exhibit a high
transverse velocity because he will be moving toward your left. However,
the runner's radial velocity will be low because he'll be moving away from
you at a very small angle.

[image: Proper_motion.jpg]
The actual* space motion* can be calculated by combining the radial and
transverse velocity components.   The *proper motion *is largely a result
of the transverse velocity.

The Sun is moving through the galaxy at a speed of  200 kilometers per hour
through the galaxy.  Although the stars within our region of the galaxy are
moving at comparable speeds, their directions differ so that some stars are
approaching us, others are receding and others are traveling along paths
nearly parallel with the Sun's trajectory.     Moreover, the transverse
velocities of the closest stars are greater than those of the more distant
stars.      For this reason, the 19th century astronomers chose to measure
the parallax of the stars with the highest proper motions as those were
correctly judged to have been the nearest ones. Astronomers measure proper
motions in terms of *right ascension * and *declination.  * Right ascension
measures a celestial object's apparent distance from the vernal equinox
while declination measures the object's distance north or south of the
celestial equator.

The stars comprising the constellations will eventually disperse as a
consequence of this proper motion  However, these motions are on the order
of milli arc-seconds per year even for the fastest moving stars such as
Barnard's Star or Groombridge 1830.  Constellation disintegration requires
tens to hundreds of thousands of years.   The image below shows how the Big
Dipper (an asterism within Ursa Major) appeared 100,000 years ago, how it
looks today and how it will appear in 100,000 years from now.   The five
central stars comprising this asterism are actually part of the Ursa Major
Moving Cluster and are thus moving together through space.  The two stars
at either end are not physically associated with them and so will be moving
away from them thousands of years in the future.
[image: unnamed.gif]

The upshot of this entire lesson is that nothing remains still.  Earth
rotates, revolves and precesses. The Sun and the billions of other stars
within the galaxy move quickly through the galaxy.       Even though we
might see Orion due south in early February each year of our lives, the
hunter's position relative to the seasons will change and eventually his
component stars will tear him apart:  far, far in the future.

Tomorrow, an investigation into stellar properties.
______________________________________
*A QUESTION ABOUT PARSECS:*
Subscriber JV asked the following question regarding information contained
within "The Closest Stars" class. (RP 39)
*"Why do astronomers use the dimension parsec if they have the seemingly
perfectly good light year?  And why 3.26 light years per parsec? Seems an
odd number."*
Excellent question!   I apologize for not having included this information
in the class, itself. The term "parsec" is a contraction of the term
"parallax second."     In this regard, we are referring to the geometric
measurement of arc-second.    A quick review:

[image: anunit.gif]
A circle consists of 360 degrees.     One can divide that degree into 60
arc minutes.   One can divide that arc minute into 60 arc-seconds.   The
same divisions apply to angular measurements within the sky, as well.
 The Sun and moon each subtend about half a degree or approximately thirty
arc-minutes.(This value is not constant as the separation distances between
the Sun and Earth and Earth and the moon are constantly changing.*)
An arc-second, however, is quite small. If someone 4 kilometers away from
you holds up a dime, it will subtend an angle of one  arc-second in your
line of sight.   Imagine you had a disc equal in diameter to one
astronomical unit, about 93,000,000 miles.   That disc would subtend an
arc-second at a distance of 3.26 light years, what we call a parsec.


[image: 600px-Parsec_(1).svg.png]
By designating the "parsec" we can simplify the mathematics of the stellar
distance calculation.    The SD distance above equals the distance
separating the Sun from the star.   We know the tangent of the angle equals
ES (the Earth Sun distance) divided by the distance SD.    We can rearrange
this relation so that SD equals the Earth-Sun (ES) distance divided by the
tangent of the angle.   Fortunately, the tangent of very small angles
approximately equals the values of those angles.   This all reduces to:

DISTANCE =   1/p"     where p" is the parallax angle in arc-seconds.  The
distance in this relation is expressed in parsecs.
___________________________________________________



*The Sun's minimum angular diameter is 31.6' and its maximum is 32.7'.  The
moon's minimum angular diameter is 29.4' and its maximum is 33.5.'

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