[image: apollo-daphne-1280.jpg]
*Daphne:   *Flight from Apollo
Eros, better known as "Cupid," is famous for his ability to induce
passionate love with a simple arrow strike.   Anyone punctured by this
golden-tipped arrow will fall madly in love with the next person he/she
sees, even if the afflicted person harbored no affection for the subject
prior to the arrow assault.    What is less well known is that Eros' quiver
contains more than gilded-arrows.  He also possesses a store of lead-tipped
ones.      Anyone struck by one of those plumbean projectiles experiences a
deep revulsion toward the next person he/she sees.  Even if the subject is
enchantingly beautiful, exceedingly kind, mesmerizingly charismatic and has
memorized Pi out to 100 digits, the afflicted person won't be able to stand
to be within sight or sound of him/her.    And, yes, if you're punctured by
a lead arrow, you'll even be repulsed by a god.        Such was the case
with the poor dryad Daphne, gorgeous daughter of the River God Peneus.
Her tragic tale illustrates how the gods' petty vindictiveness so often
victimizes lesser beings who just happen to be in the wrong place at the
wrong time.       The story begins with Apollo, god of Sun, poetry,
prophecy and archery.     One day he approached Eros, the god of love and
sexual desire.  The son of Aphrodite and Ares, Eros remains forever
youthful, almost boyish.    It was this prepubescent appearance that evoked
Apollo's scorn.   "You may instill love with your arrows," Apollo mocked.
"Those arrows are more suited for true gods, not their pathetic offspring.
 The possession of such weaponry doesn't make you the superior archer ,for
I have just slain the Python, an act of which you are incapable."
 Though infuriated at this taunt, Eros walked away and said nothing.
Soon, however, he spied Apollo around a grove that the beautiful Daphne
also occupied.    He swiftly fired a golden arrow into Apollo and then
fired a lead arrow into Daphne.   Apollo fell madly in love with Daphne and
chased after her.  Daphne felt nauseated by the sight of Apollo and swiftly
fled.    Though they were equally quick, Daphne had had a slight head start
and initially maintained a lead over her lustful pursuer    Yet, she
quickly became fatigued and her pace slowed enough so that Apollo came
within an arm's length of her.   Before he was able to embrace her, Daphne
cried out to her father Peneus to transform her into a tree.    Though
distressed at having to lose a daughter, Peneus reluctantly agreed to do
so.   As her tender skin hardened into bark and her feet became rooted into
the ground, Apollo hugged the laurel tree into which she was transformed
and wept.   "Though I can never love you,"he cried, "I shall forever after
adorn myself with you."    For this reason, Apollo wore a laurel wreath
along his head and a laurel garland along his chest: a tribute to the nymph
he loved so ardently and who chose to become a tree rather than his
consort.

THE SOUTHWORTH PLANETARIUM
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Julian Date: 24591120.16
2020-2021:  XX


THE DAILY ASTRONOMER
Tuesday, September 29, 2020
Remote Planetarium 98:  Special Relativity  II - Matter and Energy

_________________________________________
Correction.
My sincerest apologies.
In yesterday's article, I wrote the following sentence:
*Accelerate up to 99.9999% light speed and a stationary observer will
experience about TWO YEARS for every since you experience.      *
Yes, a word is missing.  The sentence should have read:
 "Accelerate up to 99.9999% light speed and a stationary observer will
experience about TWO YEARS for every DAY you experience. "
____________________________________________


We begin today by reiterating the fundamental postulate of Special
Relativity:

*The speed of light is constant in all inertial reference frames.*

This single premise revolutionized physics for it became the basis of the
Special Theory of Relativity.   That theory united space and time which, in
Newtonian mechanics, had been regarded as separate aspects of physical
reality. Yesterday we focused on Special Relativity's most shocking
ramification:  time dilation.    Time literally dilates within a vessel as
it moves.   The higher the velocity, the greater the time dilation.     The
graph below relates a vessel's speed with the corresponding time dilation
amount.

[image: gr_timedial.png]

[Note:  the Time Dilation number is a ratio.   For instance, at the value
2.0, a stationary observer experiences twice as much time as the observer
within a moving vessel.]

One can see that time dilation is negligible for vessels moving at less
than half the speed of light (0.5), but quickly becomes more significant as
the vessel accelerates to much higher velocities.   The limit is light
speed, itself, which is the *highest attainable velocity *in a vacuum.
If a vessel were able to attain light speed, time within it would actually
stop.

The problem with vessels moving at such high speeds is *mass increase,* another
effect of Special Relativity.      The higher the velocity, the greater the
increase in the object's "inertial mass," defined as the object's
resistance to changes in its motion.     The faster an object moves, the
greater its kinetic energy and also its inertial mass.     The graph below
shows us the relation between the object speed and the mass increase
ratio.    [Note:A mass of "2" indicates that the relativistic mass has
increased to twice the resting mass.]

[image: main-qimg-5dfdc6bad9a1183ba5243c0807f9f144.jpg]

The faster the vessel, the more massive it becomes.  As the craft becomes
more massive, more energy is required to accelerate it to higher
velocities.    If the vessel were able to attain light speed, it would
become infinitely massive: an impossibility.        Photons can move at
light speed because they have no rest mass.


[image: 074dfa301cdb200bac45aaf274b1a1ad.jpg]
*The problem with warp.    *    The USS Enterprise's superluminal velocity
capability enables it to traverse vast interstellar distances in brief time
periods. Science fiction writers have wisely endowed spacecraft with the
ability to exceed light speed so as to move the plots rapidly along.
However, Special Relativity forbids any massive object from attaining such
speeds due to the effect of *mass increase *with increasing velocity.

This relation leads us naturally into the final part of today's lesson:
 the matter-energy equivalence.

[image: hasenohrl1.jpg]

The most famous physics equation of them all, except, perhaps   F = ma.
  This equation relates energy (E) to mass (m) and the speed of light (c)
squared. (Or c x c.)  One should note that c was chosen to represent light
because, as we all now know, light speed is *constant* in all inertial
reference frames.        This equation tells us that matter and energy are
equivalent.       Matter is merely crystallized energy.   Recall our
discussion pertaining to thermonuclear fusion within stellar cores.  Some
of the matter involved in these processes is converted directly into
energy, which powers the stars.  Although a minuscule amount of matter
(less than one percent) experiences this transmutation, it is sufficient to
sustain a star for millions, billions or, in the case of red dwarf stars,
trillions of years.

Special Relativity enabled astronomers to finally identify the stellar
energy generation method:  fusion, or the transmutation of matter into
energy.

Tomorrow, we conclude the three part series about Special Relativity with
"Light speed and length contraction."

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