[image: download.jpg]
*Eris: Goddess of Discord*
Almost everything in and under heaven was presided over by a god or
goddess.   During our daily celestial voyages we are likely to encounter
some of them.  Perhaps Morpheus, god of dreams or Iris, goddess of
rainbows, to name but two.    During today's ascent we've discovered a
goddess we'd be best advised to avoid:  Eris, goddess of strife and
discord.   She was the ultimate unwanted relative at the reunion: the one
inclined to fight without the slightest provocation and who antagonized
others for the sheer sport of it.     It is little wonder that Eris was the
only goddess not invited to the splendid wedding feast of Peleus and
Thetis.   Eris avenged this exclusion by tossing a golden apple into the
wedding assembly.   She attached the label "to the fairest" on it, knowing
full well that many goddesses would seek claim to it.  Indeed, the three
most powerful goddesses, Hera (Zeus's wife and the goddess of marriage),
Athena (goddess of war and wisdom)  and Aphrodite (goddess of love and
beauty) all wished to possess it.     Initially they wanted Zeus to decide
who was the most worthy goddess to claim the apple. He wisely refused to
choose and instead selected a young Trojan shepherd named Paris to select
which goddess would receive the apple.     The three goddesses presented
themselves to Paris and each offered him a bribe to influence his
decision.   Athena promised him profound wisdom. Hera offered him
widespread political influence.  Aphrodite, who really knew the hearts of
young men, instead offered him the world's most beautiful woman.
 Predictably, Paris gave Aphrodite the apple, and in so doing incurred the
implacable hatred of the other two goddesses.    The problem was that the
most beautiful woman in the world was Helen, wife of Menelaus, king of
Sparta.   So Paris, with Aphrodite's much needed assistance, abducted Helen
which precipitated a 10-year skirmish between the Greeks and Trojans.
Ironically, by trying to avoid discord by excluding Eris, the Olympians
ended up causing more strife than the world had hitherto known:   the
Trojan War.

THE SOUTHWORTH PLANETARIUM
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Founded January 1970
Julian Date: 245947.16
2019-2020:  CXXI


THE DAILY ASTRONOMER
Tuesday, April 7, 2020
Remote Planetarium 7:  Orbs and Orbits

___________________________________________________________
*TODAY'S HELPFUL INFORMATION*
The Planets (in order of increasing distance from the Sun)
MERCURY
VENUS
EARTH
MARS
JUPITER
SATURN
URANUS
NEPTUNE
PLUTO  (Yes, we're including it.  More on that matter on another day).
____________________________________________________________

[image: 28546.jpg]

Before we delve into astronomy, let's simply admire the artistry of
planetary orbits.  The image above depicts the orbits as they would appear
were they actually visible and multi colored.   We're seeing the closed
curves along which the planets travel under the Sun's gravitational
influence.      Isn't it interesting that some of the solar system's most
elegant constructs, the orbits, are actually invisible?   Isn't it all the
more remarkable that a few humans managed to determine the shapes and
properties of these orbits?

Allow me to introduce one of these extraordinary humans:
[image: 78.jpg]

*Johannes Kepler  (1571-1630)*
Though celebrated as the grand patriarch of astronomy, the German
astronomer Johannes Kepler was first and foremost a mathematician and
mystic.     He became one of astronomy's most important figures through his
analysis of Tycho Brahe's extensive observational records of the planet
Mars.  Tycho Brahe was the bona fide astronomer who devoted twenty years of
his career to observing Mars from various observatories, most notably
Uraniborg on the island of Hven.   However, when he went into exile
following a dispute with new Danish king Christian IV, Brahe constructed an
observatory at Benátky nad Jizerou in what is now the Czech Republic.  At
this time, Brahe hired Johannes Kepler to serve as his assistant and
according to historians they both enjoyed eighteen months of a stormy
professional relationship.  Brahe was known to act imperiously toward those
he regarded as inferiors.  Yes, that's right, all of us.   Conversely, if
you met Kepler today, he'd likely buy you a drink and chat non stop for
three hours.  After a year and a half, Brahe died, which greatly improved
relations between Kepler and himself.     Kepler then inherited Tycho's
treasure trove of Martian observations.    His disagreeable personality
notwithstanding, Brahe was a meticulous observer whose records were all the
more impressive as his life predated the invention of the telescope.

Kepler devoted another twenty years to studying these records and in so
doing developed his three planetary laws, our only subject today.     We
regard these laws in turn.

*1.  EVERY PLANETARY ORBIT IS AN ELLIPSE WITH THE SUN AT ONE FOCUS.*

Don't panic at the graphic below.     We'll work through it.
[image: Ellipse-1.png]

We're going to have a contest between you and your best friend.    First,
we're going to put each of you on a different stool and then will draw an
ellipse around you.   You will be on a stool at F1 and your friend will be
at the stool  F2     Now, you both have to walk in a straight line from
your stool to a point on the ellipse and then back along a straight line to
the other stool.   Your aim is to figure out a way to walk a shorter
distance than your friend walks.   However, you needn't bother.  The
distances will always be the same.     That is the property of the
ellipse.    You and your friend were each sitting at a focus of that
ellipse.  Each ellipse has two foci.      Every planetary orbit is an
ellipse and the Sun occupies one focus of that ellipse.

Kepler's revelation that planetary orbits were elliptical represented a
profound departure from all previous models which depicted planetary orbits
was circular.

*WHAT DOES THIS MEAN?*
-Planetary orbits are not circular, so a planet's distance from the Sun is
always changing.   The planet's closest point to the Sun is called
"perihelion."   The planet's farthest point from the Sun is called
"aphelion."

*2.  THE RADIUS VECTOR CONNECTING THE SUN AND THE PLANETS SWEEP OUT  EQUAL
AREAS IN EQUAL TIMES.*
Don't hang up!   All this statement means is that the closer a planet is to
the Sun the faster it moves.

[image: glo_kepler2.gif]

Imagine that a paint-coated string connects the Sun to each planet.  As the
planet revolves, it leaves a large painted area in its wake as seen in the
above image.   Let's imagine that we allow each planet to move for an hour
and then measure the regions each of them painted.  We would find that
these areas would all be equal.    From this observation we determine that
the closer planets have to be moving more quickly than the more distant
planets.
If we study this list of a few of the planet's average orbital velocities
we can recognize the inverse relationship between distance and orbital
speeds.

*MERCURY*  107,082 miles per hour
*EARTH *  66,615 miles per hour
*JUPITER*  29,236 miles per hour
*SATURN * 21,765 miles per hour


*3.  THE HARMONIC LAW:   THE SQUARE OF A PLANET'S PERIOD IS PROPORTIONAL TO
THE CUBE OF ITS SEMI MAJOR AXIS!*
WAIT!  DON'T HANG UP!

The* planet's period *is just the amount of time a planet requires to
complete one orbit.

The *semi-major axis* is just the planet's average distance from the Sun.

*WHAT DOES THIS MEAN?*
If we can know how much time a planet requires to complete one orbit, we
can know the planet's average distance from the Sun.  The proportionality
means that when one value increases, the other value increases, as well.
 Now, we can turn the proportionality into an equality by measuring the
period in Earth years and the semi-major axis (average distance) in
astronomical units.     An astronomical unit equals Earth's average
distance from the Sun which is approximately 93 million miles.

[Side note:  *What is the difference between a proportionality and an
equality?    *
Let's happily pretend that I am going to give you a bag of coins, all of
which are of the same value.         We know that the amount of money I
give you is proportional to the number of coins you receive.    You'll have
more money if I give you 30 coins than if I give you  10.    Yet, you don't
know how much money you'll actually receive.  In order to know how much I'm
giving you, you must know the coins' value.   You'll have more money if I
give you dimes than if I give you pennies.    In this example, the coin
value is the "constant of proportionality." Without this constant, we only
have a proportionality:   your income increases with an increasing number
of coins.     If this constant is known, we have an equality.    Your
income increases by ten cents for every dime you receive.]

The Harmonic Law was immensely powerful for it provided astronomers with a
means to determine planetary distances as a ratio of Earth's distance.
Let's look at the approximate periods and distances of the four inner
planets


*MERCURY*      Distance  =  0.4 AU    Period =  0.24 years

*VENUS  *          Distance  = 0.7 AU     Period =  0.61 years

*EARTH      *      Distance = 1.0 AU      Period =  1.0 years

*MARS      *         Distance  =  1.5 AU     Period 1.88 years


While Kepler's Third law enabled us to know the planetary distances as
ratios to Earth's, it didn't reveal the absolute distances, a topic we'll
discuss next week.

Tomorrow, we'll take what we've learned about orbits and apply them to
Earth's tides.   We'll also use what we've learned about Earth's orbit and
tilt to understand the placement of various geographical markers.






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