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
Tuesday, May 26, 2020
Remote Planetarium 41: Stellar Motions
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.
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.
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.
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.
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.
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.
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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:
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.
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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.
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*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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