[image: andreas-nesselthaler-pyramus-und-thisbe.jpg]
*Pyramus and Thisbe:  *The first tale of tragic love
Anyone seeking relationship advice might not want to consult the annals of
Classical Mythology which are rife with sad tales of love gone awry.    In
fact, tragic love is as integral a part of mythology as rapacious monsters,
perilous quests and self-fulfilling prophecies.  During these daily
journeys through the ethereal realm, we've already encountered Echo, who
literally faded into nothingness from the anguish of unrequited love for
Narcissus, and Pygmalion, who fell obsessively in love with the sculpture
he, himself, crafted.  Today's excursion brings us to Babylon, the capital
city of Babylonia, a region within Mesopotamia: the setting of one of the
earliest stories of ill-fated love:  that of Pyramus and Thisbe.     A
young man Pyramus and slightly younger woman Thisbe were neighbors in the
bustling city of Babylon, one of the first true cities to have taken root
in  the region historians now call "The Fertile Crescent."
Pyramus had often watched Thisbe through a chink in his parents's garden
wall. He saw her often playing chase with her brothers and tending to her
garden.  Thisbe was so pretty and cheerful that he soon fell in love with
her.  Eventually, Pyramus summoned enough courage to call to her through
the chink while she was sitting alone in her parents' courtyard.  Thisbe
was initially reluctant to approach the wall for her parents had warned her
to always avoid the neighbors behind it.  "We hate them and they us," her
father had once told her sternly. "They are monsters and there is nothing
good about them!"    While Thisbe stood transfixed before the wall, Pyramus
spoke softly to her.    "I won't harm you," the voice assured her.  "You
are very beautiful and I just want to see you more clearly."  Despite her
misgivings, Thisbe walked up to the wall because the voice was so soothing
and melodious.   "Are you a monster?   Will you devour me?" she nervously
asked.   Pyramus invited her to look at him through the hole.    When she
did so she discovered that Pyramus was a handsome young man.   She then
spoke to him and told him her name.  He told her his.  Thus started a
relationship that lasted for many months.   Every day they gathered by the
wall and spoke, sometimes for just minutes, at other times for hours.  They
soon fell in love and vowed to remain forever faithful to each other.
 They could only speak through the wall for they each knew of their
parents' mutual enmity and for the longest time didn't dare to try to see
each other.  Eventually, however, they agreed to meet the following
afternoon near some mulberry bushes just outside the city.   Thisbe arrived
first and moved to sit by one of the bushes when she saw a lion nearby
devouring a large bird.  The frightened Thisbe fled to a nearby cave and in
so doing dropped the cloak she had been wearing so as to conceal herself in
case anybody had been present to watch her leave the city.      While she
hid, the lion finished dining and approached the place Thisbe had once
occupied.   The lion sniffed the ground and licked the cloak, staining it
with the bird blood that had coated its mouth.  Unable to find other food
the lion soon left, leaving the cloak behind.       Pyramus arrived soon
after the lion's departure only to find Thisbe's bloodied cloak on the
ground.   The distraught Pyramus, having assumed that his love had been
eaten by some wild animal, collapsed to the ground and killed himself with
his sword.     Thisbe returned to the spot only a few moments later to
discover Pyramus' body.    Having seen Pyramus lying next to her bloodied
cloak, Thisbe realized that her love took his own life only because he
thought she had lost hers first.   In despair, she pulled the sword from
his chest and plunged it into her stomach.     It is said that the blood
gushing out from the bodies of these two self-slain lovers splattered on a
nearby mulberry bush and colored the berries red.  Up to that time,
mulberries had always been pearl white.    To honor the memories of this
ill fated pair, the gods transformed all mulberries would from that moment
always appear blood red.
This mythological story is unusual in that it involves neither sorcery nor
prophecy. The players were all too human: impelled by desperate love to a
secret gathering despite parental proscription.  It is heart wrenching to
hear how a simple misunderstanding not only prevented this gathering, but
also sharply curtailed two young lives.   No malignant monsters were
required to interfere with this true love.   Instead, mere circumstance was
sufficient to have precluded its consummation.

THE SOUTHWORTH PLANETARIUM
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Founded January 1970
Julian Date: 2458975.16
2019-2020:  CXLI


THE DAILY ASTRONOMER
Wednesday, May 6, 2020
Remote Planetarium 28:    The Sun Part II:  How We Know the Sun's Distance

___________________________________
TWO NOTES:
*-Don't hang up!*
In today's class we'll be using some mathematics in order to explain the
concepts involved.    We'll be as gentle as possible during these
applications.

*-The "syllabus" I provide on weekends has sometimes proven to be
unrealistic.  *
My initial intention was to explain how we know the Sun's distance, mass
and composition.    After working through the article, I realized that the
distance explanation would provide ample material for one day.   (I can
only input so many images before the system doesn't permit me to transmit
the article.)    Tomorrow we will focus on the Sun's mass and composition.
  On Monday, we'll discuss the Sun's life cycle.
________________________________________________________________


At some point in our childhoods, we all learn that the Sun is about 93
million miles away on average.  That its distance is not constant but
instead varies between 91.5 million to 94.5 million is a fact we learn in
later childhood or adulthood.    This value is one of those nifty little
facts that we  tend to shelve in the crowded back recesses of memory.     One
must wonder:* how could we humans possibly have determined this distance?*
  Earth's diameter is only slightly less than 8,000 miles.  Astronauts
haven't traveled farther than about a quarter million miles away from our
planet.    Of course, astronomers did determine this distance. Remarkably,
the first accurate measurement was made in the 18th century!

Before we explain the distance determination method, we should review some
concepts.

*Kepler's Third Law of Planetary motion. *
This relation equates a planet's orbital period with its average distance
   The square of a planet's period (expressed in years) equals the planet's
mean distance (expressed in astronomical units.)


   - *Astronomical unit:*  Earth's average distance from the Sun, which we
   now know to be 93 million miles.


This law, published in 1619, enabled future astronomers to determine each
planet's average distance from the Sun simply by measuring their orbital
periods.   We have the following table of planet distances in AU


   - MERCURY  0.387
   - VENUS  0.723
   - EARTH 1.000
   - MARS  1.523
   - JUPITER 5.203
   - SATURN 9.537
   - URANUS  19.191
   - NEPTUNE 30.07
   - PLUTO  39.5


While these values provide us with a ratio of the planet distances relative
to Earth's, they do not include absolute values.      The list shows us,
for instance, that Venus' mean distance from the Sun is about 72% that of
Earth's. However it doesn't tell us anything about Earth's true
heliocentric distance.

To determine this value, ingenuous 18th century astronomers traveled around
the world to observe a *transit of Venus.*

[image: transit-of-venus_2004_espenak_TV2004seq2w.jpg]

A transit of Venus occurs when the planet Venus appears to move directly
across the Sun from our perspective.   Such transits can only occur when
Venus passes through inferior conjunction while at or near a node (the
intersection point connecting the orbits of Earth and Venus.)     Although
Venusian transits are rare, two occurred in the 18th century:  1761 and
1769.    (Venusian transits tend to occur in eight year pairs separated by
more than a century.)         Astronomers went to stations at various
points on Earth to observe both transits in an effort to determine the
Sun's distance.      These observation teams went to places as far flung as
Tahiti and Newfoundland.     One expedition was led by Captain Cook,
himself, who traveled to Tahiti.   Also involved were Jeremiah Dixon and
Charles Mason, of Mason-Dixon line fame.

*How would a planetary transit enable them to make this determination? *

*Let's examine this "side view" of a Venusian transit:*

[image: drawings_summer_12key_6.jpg]
In this diagram, the Sun is to the left, Venus is the center circle with
Earth to the right.
When a transit occurs, Venus passes directly across the Sun because the
orbits of Earth and Venus are nearly perfectly aligned.     By examining
the geometry of the situation, we'll be able to understand the theory
behind this distance determination method:

[image: unnamed.gif]


*Don't hang up...yet!*
The top RE   is Earth's distance from the Sun
Rv is Venus' distance
Rv - RE   is the distance separating Venus and Earth.
d = the distance separating two points at which the Venusian transit is
observed.

Fortunately, Kepler's law tells us that Rv =  0.7 AU  and Rv - RE = 0.3 AU.

If different observers can measure the length of their respective transit
chords across the Sun, they can know the relative distance between the
chords.

A transit chord is just the apparent path Venus follows across the Sun.
[image: art_075_001.jpg]
The image above shows the transit chord during the 2012 transit.


[image: venustransit.jpg]
As we can see from the above highly exaggerated image, observers at
different latitudes will see different chords during the transit.    While
these observers cannot directly measure the chord lengths, they can measure
the amount of time Venus requires to traverse the Sun from their
perspective.  The longer the transit time, the longer the associated chord
will be.

By knowing the distance in miles between the observation points; the
distances in AU between the Sun, and the vertical angles, one can use
ratios to measure the distances from Earth to Venus to the Sun.        On
advice of counsel, I opted not to include the mathematical formulae.
We focused instead on the concept involved in making this determination.

Historical note:   The value they derived was about equal to 90 million
miles, very close to today's accepted value.



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