[image: 220px-Centaur_nymph_Marqueste_Tuileries.jpg]
*Nessus:   Hercules' Killer*
We have mostly avoided Hercules in these mythological introductions for the
benefit of those who find them intolerably tedious.   Were we ever to
encounter Hercules himself during our daily excursions through the
boundless celestial sphere, the introduction would run into the hundreds of
pages.  Hercules, or, Heracles as the Greeks named him, was the strongest,
bravest and most adventurous of all mythological entities.   From the time
he was a day old infant and strangled two serpents to his twelve famous
labors, his recruitment by Jason to join the Argonauts, and myriad other
quests, Hercules did more with his life than almost everyone else
combined.   During these adventures, many strove earnestly to kill him,
most notably the goddess Hera who loathed Hercules for having been one of
the many children her husband Zeus sired with other women.
Ironically, Hercules' actual killer died many years before Hercules died.
To explain, we must introduce the centaur Nessus.
Though a particularly loathsome soul, even by the abysmally low centaurian
standards, Nessus the centaur was, however, diabolically clever.      He
was serving as a ferryman across the River Euenos when Hercules and his
wife Deianeira came upon him on the river bank.   Nessus offered to convey
them across the river.  Though Hercules was distrustful of centaurs, owing
to the ferocious battle he had fought with the centaurs during his fourth
labor, Nessus seemed friendly and trustworthy.    Besides, the river
current was so swift that even Hercules for all his strength would have
found it difficult to cross while carrying his wife.  He accepted Nessus'
offer and allowed Deianeira to go first, as Nessus wasn't able to carry
them both simultaneously.  As soon as Nessus and Deianeira reached the
opposite bank, the centaur tried to kidnap her.   Seeing this attempted
abduction, Hercules swiftly let fly an arrow that struck the  centaur's
side.  As the arrow tip had been dipped in Hydra's blood, the Centaur was
mortally wounded. While such poison arrows could kill a human instantly,
the Centaur was stronger and lasted for a few moments after having been
mortally wounded.   While Hercules swam madly across the river, Nessus somehow
persuaded Deianeira to take some of his blood in a phial and conceal it.
"Centaur blood is a powerful love potion," he told the inexplicably
trusting Deianeira.  "If you ever find your husband's love is weakening,
smear this blood on his cloak and he will fall desperately in love with you
again.   I offer this blood as an act of contrition for my attempted
outrage.  But, take my blood at once before your husband arrives so he
won't know of it."
Deianeira had just managed to collect the blood and hide it by the time
Hercules reached the shore and ran his sword through Nessus' corpse.
Years later Deianeira had indeed sensed that Hercules' love for her was
waning.   He had become taciturn in speech, morose in mood and seemed
callously indifferent.   Still being passionately in love with Hercules,
Deianeira felt  so tormented by his distant manner that she found the phial
of blood and smeared it on Hercules' cloak while he slept.   The next
morning he awoke and his wife anxiously waited for him to put on the cloak
and rekindle his love for her.  Instead, when he draped the cloak over
himself, Hercules screamed in agony.  He frantically removed the cloak and
much of his flesh came away with it.   The blood had soaked into his body
and he was tormented by an excruciating pain that he had never before
known.  His anguish was so intense he actually begged to die, but, of
course, the gods conferred immortality on him after he had completed his
twelve labors.   He desperately offered to relinquish his immorality just
to stop the agony.    Zeus, who, after all, was Hercules' father,
reluctantly consented to rescind the immortality.  Hercules then quickly
constructed his own funeral pyre and lit it.  Realizing what she had done,
Deianeira threw herself onto the same flames that consumed Hercules.   The
Goddess Hera, Hercules' arch nemesis, placed Nessus in the stars as an
honor for doing what thousands before him had been unable to do:  kill
Hercules...at least indirectly.  We know of this constellation as
Sagittarius the Archer, the low southern constellation that will rise into
prominence as we move into summer.

THE SOUTHWORTH PLANETARIUM
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Julian Date: 2458974.16
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THE DAILY ASTRONOMER
Tuesday, May 5, 2020
Remote Planetarium 27:  The Sun   Part I: Putting the Sun in its Place

Let's try this thought experiment.
Pretend you're living on a happy planet on which astronomy never
developed.   You then spend a blissful day and night observing the sky.
 What do you notice?   Every celestial object, including the Sun, seems to
revolve around our planet.   One can see the stars, Sun, moon and planets
moving each night east to west.   However, by watching the sky over many
nights, one notices that the planets exhibit different motions. They move
west to east over many nights.   Mercury and Venus travel along their
respective paths much more quickly than Mars, Jupiter or Saturn.
(Remember, without any astronomers, we won't know of any planet beyond
Saturn.)   Saturn moves the slowest, Mercury the fastest.  We reason that
the slower a planet moves in our sky, the longer its orbit must be.   The
Sun also exhibits such a motion relative to the stars.  It requires more
time than Venus to complete a cycle relative to the zodiac constellations,
but less time than Mars.   (Note: its revolutionary period is about 365
days.)
Conclusions:

*Earth must occupy the Universal center.*
The planets follow rigid orbits, or spheres centered on Earth.   The moon
closest to Earth, followed by Mercury, Venus, the Sun, Mars, Jupiter and
then Saturn.  The stars,  do not exhibit any of the independent motions
we've observed in the other bodies.   The stars occupy the most distant
shell at an indeterminate distance.

[image: 4115860027_32d8cc9dd5_b.jpg]

Being part of the perfect celestial realm, all the planets are spherical
and their orbits circular.    No mechanism surpasses the solar system for
the elegance of its design and the regularity of its mechanisms.

Oh, but wait!
Over a long time period you notice the planets exhibiting a strange motion.
First, the speed of their motion isn't constant, as you would expect it to
be were the orbits perfectly circular.  Also, and more disturbingly,  at
various times, the planets appear to stop before reversing course so as to
move east to west.   Eventually, this "retrograde motion" will cease.  The
planet will stop again before resuming prograde motion.         Let's
assume you decide to track the motion of Mars as it progresses through this
retrograde loop.    You note the planet's position at regular intervals and
then chart its progress.

[image: Ma2011-2Tezel_La900.jpg]

Brilliant!  The most beautiful retrograde loop imaginable.  Aesthetics
apart, however, such motion does present a problem.   How can only possibly
explain this weird planetary behavior while maintaining Earth's position at
the solar system's center?   Why would a planet moving around Earth
describe such a loop?

Well, here we should allow one astronomer to make an appearance:

[image: 5f515d00d793167e4cae799bc77ff8601ac1798d.jpg]
 *Claudius Ptolemy* (circa 1st century AD), the mathematically ingenuous
fellow who developed a geocentric model that will explain the retrograde
motions you've observed.  He formalized a system developed by two equally
clever mathematicians: Apollonius of Perga and Hipparchus of Rhodes.
This system included such clever contrivances as deferents, epicycles and
equants.  See below:

[image: unnamed.gif]
All the celestial bodies revolving around Earth except for the moon and the
Sun travel along epicycles. An epicycle is a small, perfect circle
surrounding an equant that travels along a rotating shell (deferent)
centered on Earth.    As the planet moves around the epicycle, it will
sometimes appear to be moving in the same direction as the shell and at
other times will appear to move backward.       This model, which you
decide to call Ptolemaic out of appreciation for Ptolemy's contribution,
explains the retrograde motion and the apparent planetary speed changes
while maintaining Earth's position in the solar system's center.

How lovely that this situation is working itself out so nicely.
Well. Eventually, you decide that you want to predict future planetary
positions based on this Ptolemaic model.    You naturally believe that such
a mathematically intricate and geometrically perfect system should enable
you to make perfect predictions.      Perhaps it should, but it doesn't.
 Discrepancies develop between predicted and actual planet predictions.
  Granted, only you know about this problem.   The others who rely on you
for planet information remain blissfully oblivious to this troubling
systematic problem.

Perhaps we can allow another astronomer to intervene:

[image: 0f53d30d1fb41b3d99cf34d5351e8f5ff8aa0b34.jpg]
*Copernicus* (1473-1543) was actually a Polish clergyman and mathematician,
not an astronomer, per se.     Though history regards him as one of the
world's greatest intellectual revolutionaries, Copernicus did not intend to
revolutionize astronomy.  He instead meant only to develop a system that
would enable him to calculate Easter more accurately.     The mathematical
method he developed to improve these calculations necessitated switching
the positions of the Sun and Earth.   In the Copernican model, the Sun
occupied the solar system center and so became "heliocentric," meaning
Sun-centered as opposed to "geocentric" meaning Earth-centered.

*The Copernican system neatly explains retrograde motion:*


[image: download (1).jpg]
As Earth revolves around the Sun, it will pass a more distant planet such
as Mars.   From our perspective on Earth, Mars will appear to stop, reverse
course, top and then resume its prograde motion relative to the more
distant stars while Earth approaches, catches up to and then passes Mars.
This effect is similar to watching a car on the freeway as you drive past
it.  The car actually appear to reverse course against the more distant
objects.

Alas, we find that, well, the planet position predictions don't improve at
all!  Sometimes the planet predictions are evenly slightly less accurate
that those based on the Ptolemaic model.   Hmmm....Before we decide to
place Earth back in its exalted position, let's bring forth one more
astronomer.   Well, he is more a physical scientist.

[image: J28JVRESdaX6rEUQ5jbbJQ-320-80.jpg]
*Galileo Galilei * believed in the heliocentric model because such a system
was consistent with his telescopic observations of the solar system.   He
noticed satellites revolving around the planet Jupiter.   (We now call
these satellites "Galilean moons.")   Also, when he observed the planets
Mercury and Venus through his telescope, they exhibited phases, just as the
moon does.       See below:

[image: 482_m_GalileosPhases.jpg]
On these sketches of Galileo we see Saturn (upper left), followed by
Jupiter and Mars.  Below, many different phases of Venus.     Only in the
heliocentric model do the Venusian and Mercurian phases make sense.

We need only two more people;   Tycho Brahe (1546-1601) and Johannes Kepler
(1571-1630).   The first was the grand patriarch of astronomers.  He
devoted twenty years to studying the planet Mars.    Kepler was a
mathematician who devoted twenty more years to studying and analyzing
Brahe's observations.    He developed the three planetary laws, one of
which states that every planetary orbit is an ellipse with the Sun at one
focus.      Copernicus retained the circular orbits in his heliocentric
model, hence the inaccuracy.   Kepler replaced the perfect circles with
slightly elongated ellipses, rendering his model more accurate than the
Copernican or Ptolemaic.

The accuracy of Kepler's system and the observations of Galileo have
destroyed our lovely geocentric model.     The Sun is firmly set in the
solar system's center.  Earth has been relegated to the lower status of
planet, a "moon of the Sun."

Of course, as we will come to learn this week.    Putting the Sun in its
proper place was only the first step.     We'll have much more to do before
we can know how we came to know so much about our parent star.

Part II tomorrow.

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