[image: Guillaume_Guillon-Lethiere,_Philoctetes_on_the_Island_of_Lemnos.jpg]
*Philoctetes:  The bowman*
First, let's recall the circumstances preceding Heracles' death.   He and
his last mortal wife, Deianeira, were preparing to swim across the River
Evinos.  So swift was the current that Heracles, for all his strength, was
reluctant to convey his wife across, fearing that he might not be able to
retrieve her were she to become separated from him.     Within moments of
their arrival, the centaur Nessus approached them and offered to carry
Deianeira to the opposite shore, himself.    Although Heracles was weary of
Centaurs -for good reason as we'll learn at a later date-, he knew that
they were fiercely strong and could cope with such turbulent waters.
Despite his understandable misgivings, Heracles permitted Nessus to convey
Deianeira across.   Of course, as soon as they reached the opposite shore,
Nessus attempted to spirit Deianeira away.   Heracles promptly let loose an
arrow that struck the Centaur's side.    While Heracles frantically swam
across the river, Nessus, moments from death, persuaded Deianeira to take
some of his blood and use it as a love potion if she ever thought that
Heracles was losing his affection for her.      Nessus somehow convinced
Deianeira that giving her his blood was a genuine act of contrition, one
that he hoped would spare him an eternity in Tartarus.  (Centaurs were all
said to harbor a morbid fear of Tartarus due to their belief that it must
be teeming with other Centaurs.)  By the time Heracles arrived, Nessus had
died and Deianeira had concealed the phial of the Centaur's blood.  Years
later, when Heracles had taken Iole as a mistress, the lovelorn Deianeira
slathered his lion hyde cloak with blood.     As soon as he draped it over
himself, Heracles shrieked with agony.  The blood was a fell poison, not a
love potion.   He hurried to remove the cloak, only to find that some of
his flesh came away with it.   The blood seeped into his skin and induced
an anguish beyond anything he had ever experienced.  The pain was beyond
all endurance and he wanted nothing more than to die.    Unfortunately,
after having completed his twelve labors, Heracles had experienced an
apotheosis.  He became an immortal god.  He pleaded with Zeus to make him
mortal again so he could perish and be free of the excruciating torment.
Zeus acceded to the request.    He told Heracles that he needed to only lie
atop a funeral pyre and have someone light it.  Heracles and his followers,
all of whom were cowed by his thunderous shouts of anguish, quickly
constructed the pyre and Heracles hastily placed himself on it.   "Light
the pyre!" he demanded, his pain so intense he could barely speak.     None
of his followers dared to obey the command.   They all knew that Heracles
was a favorite son of Zeus and feared the consequences of lighting the pyre
that would end his life.   "We cannot do it, my lord," the bravest (or,
least timid) follower explained. "The fire will consume you whole and its
flames will torture you all the while."   Heracles screamed back  "The pain
of this blood poison is so great flames would be as spring breezes in
comparison.  Light the pyre, I beg you!"    They all remained obstinate in
their refusal.    Suddenly,   King Poens and his son Philoctetes were
walking by and saw the commotion.  They heard the famous Heracles begging
someone to light the pyre.   Unable to bear the sounds of such anguish,
Philoctetes placed the torch on the pyre, setting it ablaze.     In
gratitude, Heracles bequeathed Philoctetes his bow and poisoned arrows.
The gift was a great one, for the arrows always struck their intended
targets.     Soon thereafter, Philoctetes joined every other Greek man at
the palace of King Tyndareus, the father of Helen.   Like all the others,
Philoctetes tried to persuade the King to let him become Helen's husband.
Tyndareus ultimately chose Menelaus, but not before making every other
suitor vow to defend Helen's marriage against any interference.  So, when
Trojan prince Paris abducted Helen, Philoctetes and the others mobilized
their own armies to launch an assault on Troy.  Philoctetes gathered enough
men to fill seven ships.   As they sailed toward Troy, however, a snake
that stowed away on Philoctetes' vessel bit his ankle.    (Some insist the
snake was not a stow away, but was placed on the ship by Hera who wanted to
punish Philoctetes for helping Heracles.)   Philoctetes screamed in anguish
so loudly it disturbed his entire crew.  Moreover, the wound wouldn't heal
and it festered so badly a nauseating stench pervaded the entire ship.
 The vessel stopped at the island of Lemnos.  So, too, did the ship
commanded by Odysseus.   Having learned of Philoctetes' putrid wound and
having heard his despairing cries, Odysseus suggested that they abandon him
on Lemnos.    Though the crew was reluctant to proceed without their
captain, they knew that without him onboard, the remainder of the journey
would be calm and the stench would abate.    Odysseus allowed Philoctetes
to retain his bow and arrow and use it to kill whatever game he needed for
food.     And there the poor Philoctetes remained for nearly ten years
while the Trojan War raged without him.    Toward the end of that ten
years, realizing that the attack on Troy had turned into a protracted
struggle, the Greeks captured the seer Helenus, twin brother to the
unheeded prophetess Cassandra, and forced him under torture to reveal how
the war could be won.   He explained that the Greeks could only prevail
were they to use the divine Heracles' bow and arrows against the Trojans.
Odysseus and the Argive King Diomedes then sailed to Lemnos to collect the
bow and arrows. They both naturally assumed that Philoctetes had perished
long since, either from starvation or from the wound.  To their shock,
Philoctetes "greeted" them on their arrival.    Of course, he didn't as
much greet them as excoriate them for his abandonment.  His wound still
festered and he suffered ineluctable torments on the island and managed to
survive only because his arrows always struck every animal at which he had
aimed.   Odysseus immediately retreated to the boat with Diomedes and
hatched one of his cunning plans.     He instructed Diomedes to pretend to
begin an argument with him and then strike him in the face.  He was to then
rush to Philoctetes' side and profess everlasting hatred for Odysseus.
Diomedes was to claim he didn't know that Philoctetes had been stranded on
the island and wanted to use the bow and arrows to slay Odysseus by way of
avening the mistreatment.   Diomedes did as instructed. He screamed at
Odysseus, struck him (harder than Odysseus had wanted, frankly) and went to
Philoctetes.   Diomedes still needed all his cunning to
convince Philoctetes that his hatred for Odysseus was sincere and his wish
to slay him with the unerring arrows was genuine.    Philoctetes showed
Diomedes the bow and arrows.  Diomedes promptly gathered them in his arms
and prepared to leave.  He then heard Philoctetes bellow with pain and grab
his foot.    Diomedes halted.  When Odysseus had come forth, Diomedes did
not relinquish the weapons, but instead told Odysseus that they needed to
bring Philoctetes with them back to Troy.   "We cannot abandon the wretch
again, this time without any weapons," Diomedes demanded.      Odysseus,
having then looked pitifully down at the wretched Philoctetes, agreed.
He then explained the ruse, implored him to forgive them and accompany them
back to Troy.  Furious beyond measure, Philoctets took back his weapons
and, with the arrow fitted into the bow, ordered them to leave the island.
 At once, the ghost of Heracles, now a god, spoke to Philoctetes.  He
assured him that if he joined the Trojan War, the healer Asclepius would
cure his wound and the Greeks would win the Trojan War.     Philoctetes
complied immediately and traveled back to Troy.      Asclepius did, indeed,
heal his ankle wound.   Philoctetes then fought valiantly in the conflict,
killing three trojans, including Paris, himself, the famous Trojan prince
whose abduction of Helen precipitated the greatest war the world had ever
known up to that time.      Philoctetes is principally known now - albeit
by only a few- as the killer of Paris.  Of course, armed with those arrows,
Philoctetes enjoyed a tremendous advantage over him.

THE SOUTHWORTH PLANETARIUM
207-780-4249   www.usm.maine.edu/planet
<http://www.google.com/url?q=http%3A%2F%2Fwww.usm.maine.edu%2Fplanet&sa=D&sntz=1&usg=AFQjCNHulkHuLP13bOG2PkNrPazsGWFs2A>
70 Falmouth Street   Portland, Maine 04103
43.6667° N                   70.2667° W
Altitude:  10 feet below sea level
Founded January 1970
Julian Date: 2459057.16
2019-2020:  CLXXXV


THE DAILY ASTRONOMER
Monday, July 27, 2020
Remote Planetarium 72:   Proper Stellar Motions

Let's begin today's class with a demonstration.      Fold your hands on
your desk, close your eyes and count to seven.     Go ahead, we'll wait....
Welcome back.   During that seven second meditation, you traveled one
thousand miles through the Milky Way Galaxy.  Well, more precisely, the Sun
traveled through the galaxy and dragged the entire solar system, including
the planets, moon and other bodies, with it.   The Sun is moving through
the Milky Way at 143 miles per second: every second of every day.   At this
rapid clip, the Sun and the rest of the solar system completes one orbit
around the Milky Way every 225 million years, a period called a "galactic
year."        Every other star within the galaxy also moves quite rapidly.
 The velocity depends on location:  stars such as the Sun that reside along
the spiral arms travel more slowly than those clustered around the
nucleus.

Even though the stars we see in the sky are moving at speeds comparable to
that of the Sun, they each exhibit a different *proper motion*, defined as
the motion that displaces them relative to a set position, which, in our
case, is the First Point of Aries, or the Vernal Equinox.*      Three
factors determine a star's proper motion:


   - its distance
   - its transverse velocity
   - its radial velocity

*Distance:*
The closest stars tend to exhibit the highest proper motions.     The
relationship between distance and apparent motion is quite intuitive.
Think of watching a truck driving along a freeway.  If you happen to be far
away from the truck, its progression across your sight line seems slower
than it would if you were standing closer to it.    In the 19th century,
astronomers such as Friedrich Bessel chose to measure the parallaxes of
stars with the highest proper motion as they correctly assumed they were
the closest to our solar system.

*Transverse velocity:  *the component of velocity across the sight line.
Let's use a sports analogy.  Imagine you're watching a tennis match from
the center court.    During each volley, the tennis ball will exhibit a
high transverse velocity: it will move quickly from left to right according
to your perspective.    A star with a high transverse velocity will exhibit
a greater proper motion than one that is not moving as quickly along the
sight line.

*Radial velocity: * the component of velocity along the sight line.
To continue the sports analogy, now imagine you're one of the tennis
players. The ball's radial velocity will be much higher than its transverse
velocity as the ball moves directly away from  and then back toward you.
(As the players are striking the tennis ball so that it hits different
points within the opponent's court, it will also exhibit a transverse
velocity component as well.)    If a star has a high radial velocity but
zero transverse velocity, it will exhibit no proper motion at all.   The
star will appear to maintain the same position relative to the other
stars.   Of course, if the star is moving away from the Sun, its brightness
will decrease over time.  If it is moving toward the Sun, its brightness
will increase.

From our perspective, all these motions are relative to the Sun's, which is
following its own orbital path around the galaxy.   Because no star's path
is precisely the same as the Sun's, each star will exhibit both radial and
transverse velocities in varying amounts.    The actual proper motion is
determined by combining these two velocity components and the star's
distance.  A graphic below shows the relations between these factors and
the proper motion.

[image: Proper_motion.jpg]

Astronomers measure proper stellar motions in mill-arc seconds/year in
terms of *declination *and *right ascension*.
____________________________________
*Reminder:*
*Declination*:  a celestial body's apparent angular distance from the
celestial equator.  Measured in degrees, minutes, seconds
*Right ascension:  *a celestial body's apparent angular distance from the
point of the vernal equinox.  Measured in hours, minutes, seconds.
_____________________________________

The five stars with the highest proper motions:


   - Barnard's Star     declination  pm: 10328.12 mas/year
   - Kapetyn's Star     declination  pm: -5730.84 mas/year
   - Groombridge 1830   declination pm: -5813.62 mas/year
   - Lacaille 9352    declination pm:  1327.52 mas/year
   - Gliese 1              declination pm:  -2337.71 mas/year


[image: 61Cygni.jpg]
61 Cygni, the first star system whose distance was determined by
trigonometric parallax, exhibits a high proper motion.  Here we can observe
how much the two stars comprising 61 Cygni shifted over the course of 32
years.

Over long time periods, proper stellar motions will affect the appearance
of the constellations.   However, the proper motions are so small (on the
order of arc-seconds per year**) that the constellations will appear the
same even over thousands of years. Though the identities have varied,  the
star patterns adorning our sky look the same now as they have throughout
recorded history. Were you to travel back to ancient Egypt, you'd observe
Orion high above you and would be hard pressed to notice much of a
difference. Similarly, if you propel yourself forward thousands of years,
the same Orion would appear. (Assuming, of course, that Betelgeuse hasn't
gone supernova in the interim.)

Now, if you could see the sky tens of thousands of years from now, the
proper stellar motions would become more apparent. The constellations would
experience noticeable distortions. The following is an image of the Big
Dipper*** at different time periods.


[image: Big Dipper in the past and future]


This image illustrates that the Big Dipper will experience profound changes
in the distant future. Eventually, it will lose the Big Dipper shape
entirely. So, the constellations you see when you're a 100 won't be exactly
the same as those you saw when you were, let's say, 10. However, the
changes are so negligible, that it will seem as though no time has passed
at all, at least amongst the Pantheon of the Constellations.

[See a fascinating -and a bit eerie- time lapse sequence of Orion the
Hunter as its appearance changes over tens of thousands of years on the
planetarium web-site:
https://usm.maine.edu/planet/remote-planetarium-72-proper-stellar-motions ]


As we prepare to move onto galactic astronomy, it is helpful to remember
that none of the stars are stationary.  All of them are traveling within
the Milky Way at various velocities and directions.     When we observe our
night sky, the stars all seem stationary.   They are nothing of the sort.
  Were we able to watch millions of years pass over a single night, the
stars would be darting rapidly through the sky:  some vanishing, others
appearing;  very much like a swarm of bees.       Constellations would take
form and dissipate like clouds.    Like so much else, the "inert night sky"
is merely an illusion.


*Another example of astronomical ancestor worship.     The vernal equinox
point was once located in the constellation Aries the Ram.   Precession
shifted it into the Pisces region in 100 BCE.     However, astronomers
still refer to the vernal equinox point as the "First Point of Aries."
 They probably will continue to do so even when the vernal equinox enters
Aquarius in the early 28th century.

To subscribe or unsubscribe from the Daily Astronomer:
https://lists.maine.edu/cgi-bin/wa?SUBED1=DAILY-ASTRONOMER&A=
<https://lists.maine.edu/cgi-bin/wa?SUBED1=DAILY-ASTRONOMER&A=1>