[image: 1200px-Atalanta_Vatican_Inv2784.jpg]
*Atalanta:   The Pride of the Arcadian Forest*
It is rather tedious, isn't it?   You know, the story of the helpless
female held captive by some malignant male until a kindly god, noble
paladin or well timed wind gust intervenes on her behalf.     One would
think that the mythological universe teems with frail ladies dependent on
strong men for shelter and protection.    In fact, it doesn't.  While we're
up here among them, we'd be well advised not to come to cross purposes with
the female sirens, furies or fates.   Also, we should be on our best
behavior in the presence of the formidable Athena or the furious Hera.
 And, while we're at it, let's be polite to the Dryads and Graeae ladies,
as well.    Lastly, let's give a wide berth and offer a gracious smile to
Atalanta, the perfectly self possessed and prepossessingly beautiful
warrior/huntress.
Atalanta's story begins promptly at her birth.  Her father, Iasus, king of
Arcadia, so desperately wanted a son that when his daughter was born, he
took her immediately to a mountainside and exposed her.   Fortunately, a
she-bear soon happened upon the abandoned infant and nursed her.   The
bear's milk imparted a preternatural strength onto the baby who matured
quickly under the animal's care.     When she was about five years old, the
young girl was found by hunters who adopted her and gave her the name
Atalanta, meaning simply "huntress."   Under the tutelage of her adoptive
family, Atalanta developed hunting skills surpassing all those who taught
her.   She devoted herself fully to the hunt and chase and in so doing
became swifter than any other mortal.     So blissful was Atalanta in her
life, she determined to remain forever unmarried.  Not only did her
temperament incline her toward chastity, but she also heard an oracle
warning her that any marriage would come to a disastrous end.    She didn't
need a man for happiness as life, itself, brought her fulfillment.   Such
was her speed and physical prowess that she required no protector, either.
 On one occasion, two centaurs, Rhoecus and Hylaeus, spied Atalanta and
sought to rape her.    Instead of fleeing, which would have been in vain as
she could not outrun even the slowest centaur,  Atalanta stood fast and
slew both pursuers with her arrows.    Being so strong and quick, she
naturally craved adventure.   She pleaded with Jason to let her sail on the
Argo and join in the pursuit of the golden fleece. Jason, who well knew of
her skill, reluctantly declined the offer.  Jason wasn't stupid.  He
immediately recognized the dangers inherent in having a crew of more than
forty men and only one woman. Later on, however, Atalanta was permitted to
join the famous Calydonian Boar Hunt.  This hunt was organized by
Calydonian king Oeneus, whose kingdom was being ravaged by a giant boar.
During the annual harvest, Oeneus had neglected to pay tribute to Artemis,
goddess of the hunt and wild animals.  Artemis punished this neglect by
casting a boar into this kingdom.  This creature was so ferocious it
rapidly slew any soldiers that dared confront it.    The boar so frightened
the populace that nobody  ventured outside.   Crops failed and people began
to starve.     In desperation, Oeneus called for volunteers from around
Greece to from a hunting party to seek out and kill the monster.     This
party included the king's son Meleager and his two uncles, Toxeus and
Plexippus, the queen Althea's brothers.       Meleager first saw Atalanta
when all the warriors gathered for a feast prior to the hunt.   Though most
of the men, including Toxeus and Plexippus, were displeased at having a
woman in her party, Meleager fell passionately in love with her.   He kept
near Atalanta during the hunt out of devotion. For her part, Atalanta
regarded him merely as a hunting companion.     The party sought the boar
over many days until they finally surrounded it.    The ravenous beast
quickly killed three of the party before Atalanta struck it with her
arrow.     Meleager then went forth and killed the wounded boar with his
dagger.     Although the kill was technically his, the love-besotted
Meleager presented the boar skin to Atalanta as she had drawn the first
blood.   Incensed, Toxeus and Plexippus came forward and ripped the skin
from Atalanta's grasp.   Meleager then engaged his uncles in combat,
killing them both.      In so doing, Meleager doomed himself.  Years
earlier, when Meleager was just a week old, the three Fates had appeared in
his home and told his mother Althea that though her son would grow to be
brave and famous, he would only live until the log presently burning in the
hearth had been reduced to ashes.   Horror struck, Althea doused the log
with water and hid it in her closet.    When word reached her that Meleager
killed her two brothers, Althea furiously took out the log and set it
blaze.    By the time the log was reduced to ashes, Meleager had died in
the arms of Atalanta who was distressed to have helplessly watched her
brave comrade perish.    The next morning Althea was so distraught at what
she had done that she hanged herself.
Atalanta soon became famous for her exploits at the Calydonian Boar Hunt.
 As a consequence, many men wanted to marry her.   Still determined to
remain unwed, Atalanta devised a scheme she hoped would keep her single
forever.  Any man who wanted her as a wife would have to race her across a
strip of land extending for many miles.  The first man to win would become
her husband.    Many men tried to beat her in a race and they all failed
miserably.     Finally, a clever man named Milanion devised a scheme of his
own.  He appealed for help from Aphrodite the goddess of love and beauty.
She was all too delighted to assist him in his efforts to win Atalanta for
Aphrodite despised chaste women who were resistant to love's allure.  The
goddess gave him three golden apples so beautiful that every mortal who
looked on them would want to possess them.    Milanion challenged Atalanta
to a race.   She quickly accepted secure in the belief that she would again
prevail.     Soon after the race started, Atalanta ran ahead of Milanion.
He then tossed one apple in front of her.  Dazzled, she stooped to pick it
up, thus allowing him to pull ahead.     When Atalanta came abreast of him,
Milanion tossed the apple off to the side.    Yet again Atalanta couldn't
resist and ran away to fetch the apple.   As they neared the end, Atalanta
caught up with him again.  When they were both within a few strides of the
finish line, he dropped the apple in front of her.   By the time she
stooped down to retrieve it, Milanion crossed the line and won the race.
Per her agreement, Atalanta took Milanion as husband.     The marriage,
though brief, seemed relatively happy.  The couple joyfully hunted together
through the fields and forests of Arcadia.   However, Milanion forgot to
offer a sacrifice to Aphrodite out of gratitude for her assistance.
So, one day, while Atalanta and Milanion were walking by the temple of
Athena, Aphrodite smote them with a curse of intense desire.    They made
love in the temple much to Athena's chagrin.    She transformed them both
into lions for it was then believed that lions could only mate with
leopards.  By making them both lions, they could no longer satisfy their
mutual desire.   In this new form Atalanta became unwed again while
remaining strong, fast and formidable.  Perhaps to her view, the marriage
didn't end disastrously after all.


THE SOUTHWORTH PLANETARIUM
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Founded January 1970
Julian Date: 2458976.16
2019-2020:  CXLII


THE DAILY ASTRONOMER
Thursday, May 7, 2020
Remote Planetarium 29:   The Sun Part II:   How We Know the Sun's Mass and
Composition

Let's imagine the following scenario: While you're standing out in your
yard,  a planetarium astronomer drives up in his Lamborghini Aventador
SVJ.  He leans out of the window and asks, "Pardon this intrusion, but I
was wondering if this month you would kindly give me the money you had
intended to spend on your rent or mortgage?"    You pause to consider the
request.  Yes, like all planetarium astronomers, this debonair boulevardier
can beguile with a smile and entrance with a glance. On the other hand, you
recognize that giving him the rent or mortgage money would place you in an
uncomfortable position.    If you miss a payment, the bank might initiate
foreclosure proceedings or your landlord might threaten eviction.  Though
you have fallen deeply in love and it breaks your heart to have to do so,
you regretfully decline.   "Hmmm, that's the fourth decline today," the
planetarium astronomer mumbles with bewilderment as he drives off in a
huff.

Why did you decline?
Didn't you know that dashing astronomy guy would have paid off your entire
mortgage or paid your rent each month for the rest of your life if only you
had acceded to his request?!   Yes, you thought that you might have lost
your home had you given him the funds you had set aside for your monthly
payment.     Fact it, you wouldn't have lost your home at all.   In
retrospect your decision seemed rather foolish...no offense.     Then
again, you had no knowledge of what he intended to do for you.

So, bearing that matter in mind, let's regard the ancient rituals once
performed around the winter solstice.      From our modern perspective,
these ceremonies seem, well, rather foolish.     The intent of these
rituals was, in part, to facilitate the Sun's ascent back to the high arcs
it followed during the previous warm season.   Our ancestors realized how
Sun dependent they all were.  (Someday their smug dependents will hopefully
come to the same realization.)   They knew that if the Sun's descent
continued after the winter solstice, it would soon vanish from the sky
altogether, plunging their world into perpetual darkness.    We know that
the Sun will always ascend after reaching the winter solstice point because
we are aware of Earth's tilt.

[image: hqdefault.jpg]
*Earth's tilt: *Not to scale, thank heavens!

The rituals were performed by people who knew nothing of this tilt and so
weren't aware that the Sun would always rise again even without their
encouragement.  The discovery of Earth's tilt and revolutionary motion
allayed our winter solstice anxiety.     However, we still knew little
about the Sun until relatively recently. Humanity knew that it was reliant
on the Sun, but knew nothing about how it generated its energy or how long
it would last.  (We'll address that issue on Monday).   As we learned
yesterday, it was only in the latter part of the 18th century that human
determined the Sun's average distance of slightly more than 90 million
miles.   This distance determination was our first step in truly
understanding not only the Sun's dimensions, but its nature, as well.   The
Sun subtends half an angle in our sky.  In order to appear that large from
a distance of 93 million miles, our Sun must be enormous. It is!  The Sun
is a sphere with a diameter exceeding 840,000 miles!     Were it hollowed
out, the Sun could accommodate 1.2 million Earth-sized spheres.   See the
image below.

[image: 0ebcdd9157af0ccd6b37afc775bab10ba7c64818.jpg]

All the planets are minuscule compared to their parent star.        It is
little wonder at all that the Sun, not Earth, occupies the solar system's
center.     Being so large, the Sun must also be unfathomably massive!
 And, indeed, it is.     Yet, how is it possible to "weigh" the Sun?
Using mathematics and physics, of course.

First, we have to introduce the following equation:

[image: sun_massEqn2.png]

The left side refers to the force of gravity between any two objects. For
our purposes,  M equals the Sun's mass; m = Earth's mass;  r = Earth's
orbital radius;  and G is the "gravitational constant," a value indicating
the strength of the gravitational force exerted between massive objects.
 G =  6.67 × 10-11 N m2/kg2 (where N is Newtons)

The right side refers to the centripetal "force" of Earth as it revolves
around the Sun.
v = Earth's orbital speed;  m = Earth's mass;  r  = radius of Earth's orbit

The gravitational force equals the centripetal force so we can equate these
two formulae.

A little algebraic manipulation reduces the equation to the following:

[image: sun_massEqn3.png]
By knowing Earth's orbital velocity, radius and the gravitational constant,
we can accurately measure the Sun's mass.

The  Sun's mass  in kilograms is 2×1030

Or, to put it another way, the Sun is 330,000 times more massive than
Earth.   We will learn how important this mass value becomes when we try to
determine the Sun's lifetime.

*CHEMICAL COMPOSITION*

Philosopher Auguste Compte (1798-1857) has joined the sad rank of
philosophers who are best known for their mistakes.   The astronomical
world knows Compte primarily because of a now laughable prediction.   In
his 1835 publication "Cours de la Philosophie Positive" he wrote


*On the subject of stars, all investigations which are not ultimately
reducible to simple visual observations are ... necessarily denied to us.
While we can conceive of the possibility of determining their shapes, their
sizes, and their motions, we shall never be able by any means to study
their chemical composition or their mineralogical structure ... Our
knowledge concerning their gaseous envelopes is necessarily limited to
their existence, size ... and refractive power, we shall not at all be able
to determine their chemical composition or even their density... I regard
any notion concerning the true mean temperature of the various stars as
forever denied to us.  *


Fortunately, Compte was mistaken.    Astronomers have managed to determine
the chemical compositions, densities and temperatures of the stars.
Before we end today, we'll discuss the means by which they identified the
chemicals within the Sun.  Making this determination required examination
of the Sun's spectra: the light it emits.

Let's first examine the visible light spectrum:

[image: wavelength-nm.jpg]

If we could split the visible light apart into its component colors we
would notice a smooth continuous spectrum extending from red to violet.
 To remember the color sequence, think of the name  Roy G.  Biv
 Red-Orange-Yellow-Green-Blue-Indigo-Violet.     A light source that does
not pass through any other medium would produce a spectrum similar to the
one seen above.

The Sun's light originates in its core and passes through the outer
layers.   As the light traverses the Sun's outer region, some of the
photons are absorbed by atoms within that medium.         When an atom
absorbs a photon, one of the atom's electrons is elevated into a higher
energy orbit.   The atom then becomes "excited."

[image: download.png]
In this idealized model, the electron absorbs an incoming photon and is
elevated to a higher energy orbit.     The electron orbits are NOT as
depicted, however.   The more accurate term is "electron energy level."


Each atom absorbs photons at specific wavelengths. Consequently each atom
produces its own "barcode" along the visible light spectrum.
The image below is provides an idealized example of such a spectrum;


[image: sun_spectrum_1.jpg]

The black lines correspond to the wavelengths of light that atoms within
the Sun's outer layers absorb.        Astronomer Cecilia Payne Gaposchkin
(1900-1979)  studied stellar spectra and concluded that stars consist
primarily of hydrogen and helium.   Her 1925 doctoral thesis in which this
conclusion appeared was largely dismissed as it was at variance with the
prevailing belief of the time that stellar material was similar to that
comprising Earth.
[image: download.jpg]
*Dr. Cecilia Payne Gaposchkin*

We know today that hydrogen and helium are the primary constituents of the
Sun and other stars. The Sun also shows trace amounts of other materials,
as well. The chart below shows the relative abundances of elements within
the Sun.  We can see that hydrogen is dominant followed by helium.

[image: main-qimg-de945d40ad04f2146022770eeaa1572d.webp]

Knowing the Sun's size, mass and chemical composition are the next steps in
our effort to truly understand how the Sun works and how long it will
last.  We'll continue with the Sun on Monday.

Tomorrow, another horrible quiz!

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