[image: Agave.jpg]
*Agave: Dionysus' Ill-fated Aunt*
Merely being related to a god won't necessarily protect one from the god's
wrath.  In fact, deities tend to punish relations more severely than others
for their transgressions.  Case in point: the Theban woman Agave,. sister
of Semele, the mortal mother of Dionysus.    Semele and Zeus fell in love
and conceived Dionysus.  Hera, Zeus' wife, grew to hate Semele and, while
disguised as a old woman, persuaded Semele, who was seven months'
pregnant,  to ask Zeus to reveal himself in his natural form.  Zeus, who
had sworn by the River Styx to comply with any of Semele's requests, sadly
transformed into a thunder cloud.   The resultant lightning discharge
immediately struck and incinerated Semele.  Just before Semele's
incineration, Zeus reached into her body and removed the infant, which he
placed in his thigh until the gestation was complete.  The child was
therefore named "Dionysus," meaning :"twice-born."

Semele's sisters Agave, Autonoe and Ino widely disseminated the story that
their dead sister had never been Zeus's consort.  Instead, her lover was a
mere mortal and she falsely claimed that Zeus fathered her child.  They
then said that her immolation was condign punishment for her blasphemous
claim.   When Dionysus attained godhead, he vowed to avenge his mother's
memory on her siblings.      He traveled to Thebes where his mother's
sisters still lived.  Agave's son, Pentheus, had become king of Thebes.
  Dionysus cast an insanity spell on the Theban women, all of whom fled to
the wilderness surrounding Thebes.  Once outside the city, all the women
began dancing and wailing in a bacchanal frenzy.     Dionysus when
disguised himself as an old beggar and informed King Pentheus that the
city's women had become engaged in wild sexual exploits in the surrounding
countryside.   King Pentheus left Thebes at once to investigate, although
it is not known if he intended to punish the women for their lascivious
behavior or if he had hoped to join them.       On first seeing Pentheus,
Agave and the other women believed him to have been a lion and promptly
attacked him.    In this mad mindset, Agave dismembered her own son with
savage abandon.    She then stuck his head on a pole and marched back to
Thebes while triumphantly holding it aloft.   Only when she encountered her
father Cadmus, Thebes' founder, was her sanity restored and she realized to
her horror what she had done.

THE SOUTHWORTH PLANETARIUM
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Founded January 1970
Julian Date:  2459250.18
2020-2021:  LXXXIII


THE DAILY ASTRONOMER
Thursday, February 4, 2021
Exploratorium XVI:   Mercury's Perihelion Shift

*Location*
            Mercury's orbit

*Time*
            Any given perihelion

Today, we visit Mercury, or, at least Mercury's orbit.    Our aim is to
understand why a minute shift in the planet's perihelion position provided
verification for Albert Einstein's General Theory of Relativity.

Well, doesn't this one look like that Christmas present consisting of 1,435
irreplaceable components and emblazoned with the divorce-precipitating
phrase "some assembly required."  However, if we approach this question
slowly and methodically, Alexander, we might be able to extract the threads
from this Gordian knot.    Admittedly, this question does contain many
moving parts, which, to mix metaphors, we'll take in turn.

                  [image: unnamed.gif]
The above image shows a two complete Mercurian orbits and one partial
orbit. The perihelion point on each is designated by P.    The perihelion
positions shift after each orbit due largely to he gravitational influence
of the other planets and, to a lesser extent, the Sun's influence.
 General Relativistic effects account for a  small part of the shift,
amounting to about 43 arc-seconds.

Mercury describes an elliptical orbit around the Sun, as do all the
planets. We can think of an elliptical orbit as being similar to an
"oval."   Each ellipse contains two focus points, one of which the Sun
occupies.     During each orbit, Mercury attains its least distance from
the Sun, a point called "perihelion."    The orbital position at which
Mercury reaches perihelion doesn't remain static. It shifts along its orbit
by 574" per Julian century.**     Most of this shift (531.6")  is
attributable to the gravitational tugs of other planets.

We ascribe a meager fraction (0.0254") to the Sun's oblateness.
 Oblateness measures the ratio between a spherical body's equatorial
diameter (through the middle) and the polar diameter (the line connecting
opposite poles.)  The equatorial  and polar diameters are equal in
perfectly spherical body, but in an oblate spheroid the equatorial diameter
is greater. The body has a "bulge."   The Sun's oblateness is minuscule:
about nine millionths, meaning that its equatorial diameter is about 10
kilometers greater than its polar diameter: a trifle, considering its
equatorial radius is 696, 350 kilometers.***     Though the Sun is nearly a
perfect sphere, that slight bulge is sufficient to induce a 0.0254" shift
in Mercury's perihelion value.

The planetary and solar factors in the shift of Mercury's perihelion
position have been well known since the 19th century, when the Sun's mass
and actual distances between the Sun and planets were determined.
However,  as early as 1859, Urbain Le Verrier**** noted that the observed
precession of Mercury's perihelion was greater than it should have been.
 He and other astronomers based these predictions on Newtonian principles.
  The anomalous rate of precession, as it is called, amounted to nearly 43",
far too large to be within an allowable margin of error.

Many theories attempted to account for this discrepancy.    One of the
principal theories involved the Sun's oblateness, which some assumed to be
far greater than the currently accepted value, which is far too small to be
responsible for this anomalous rate of precession. (A term that sounds so
deliciously sophisticated that we just had to mention it again.)     As it
turns out, Einstein's General Theory of Relativity explained the
discrepancy.    General Relativity describes gravity as being caused by
massive objects distorting their local space-time geometry.  Newton's
description says nothing of the sort and presumes that space is static and
unaffected by any object's motion within it.     General Relativity
essentially says that the Sun is bending space-time enough to account for
this extra precession.  To adopt an analogy that will likely imperil my
hopes of becoming the next Nobel Laureate, think of the Sun as 'dragging'
space time enough to cause some 'crumpling' around Mercury: enough to push
its perihelion point ahead more than it would were space-time undistorted.

[image: hqdefault.jpg]

It was Einstein, himself, who proposed the Mercury perihelion shift issue
as one means by which to test his General Theory of Relativity.    This
verification required meticulous calculations involving the kind of
mathematics harsh enough to laugh at sincere sorrow and slap grandmothers.
  Prior to this verification, someone asked Albert Einstein what he would
think were the General Relativity theory to fail this Mercury perihelion
test.  (It didn't.)   Einstein replied, "I would feel sorry for the Lord.
The theory is correct."

One has to admire his confidence.



*British astrophysicist Sir Arthur Eddington (1882-1944) led an 1919
expedition to Principle Island in West Africa to observe a total solar
eclipse.  Photographic plates of the star field around the eclipsed Sun
showed that the stars within the Sun's 'vicinity' were deflected by an
amount Einstein's General Relativity predicted.     General Relativity
describes gravity as the "indentations" that material objects induce in
their local space-time regions.     Therefore, the apparent positions of
the stars around the Sun will experience a slight deflection related to the
presence of this indentation.

**Well, of course we'd attached a footnote to that 574" per Julian century
horror.      574" means 574 arc-second.    We recall that a circle contains
360 degrees.   Each degree can be divided into sixty equal sections, each
of which comprises an arc-minute (denoted by  ' ).  Each arc-minute can,
itself, be divided into sixty equal arc-seconds.  (denoted by ").    A
"Julian Century" relates to the old Julian calendar (named for Julius
Caesar) which defined each year as consisting of 365.25 days, as opposed to
the modern Gregorian calendar which acknowledges that an Earth year's
duration is closer to 365.2422 days.  The Julian Century equals one hundred
Julian years and is often used in astronomy to denote a precise unit of
time, as opposed to any of the other current year measurements, which are
all messes.

***The issue of the Sun's oblateness is one that hasn't wholly been
resolved.  As the Sun is a plasma, not a solid, astronomers still aren't
certain if the Sun;s oblateness is a constant the precise measurement of
this oblateness.    It is certain that the Sun's oblateness is slight, as
evidenced by the comparatively small contribution its oblateness makes to
Mercury's perihelion shift.





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