Since we've now infiltrated the celestial realm with our impertinent inquiries, each class will include a daily deity or other mythological being that we could actually encounter while ascending through the boundless skies. Naturally, they'll loiter high above the text, though not nearly as high as they'd probably prefer to be. Today's is Janus, the god of endings, beginnings and doorways. Janus is both retrospective in his contemplation of the past and hopeful in his anticipation of the future. He contains two heads to enable him to see both that which lies ahead and that which recedes into the distance. On both countenances he wears an expression of stoic resignation for he is powerless to exert any influence over the past or future. Instead, he merely reflects on what has transpired and awaits future occurrences. Sound familiar?
THE SOUTHWORTH PLANETARIUM
207-780-4249 www.usm.maine.edu/planet
70 Falmouth Street Portland, Maine 04103
43.6667° N 70.2667° W
Altitude: 10 feet below sea level
Founded January 1970
Julian Date: 245940.16
Julian Date: 245940.16
2019-2020: CXVI
"When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars."
-Walt Whitman
THE DAILY ASTRONOMER
Tuesday, March 31, 2020
RP 2: A Slice of Sky for Walt Whitman
RP 2: A Slice of Sky for Walt Whitman
I: The Cosmos Box
Let's assume that we just received a massive present: the true gift for the person who has everything. A box containing everything. A Universe-in-the-box. Exquisitely wrapped, perfectly proportioned , though a bit weighty, this rectangular enclosure of all extant things contains a googleplex of moving interconnected parts. We pour it out and survey the myriad components scattered along your thick pile carpet. Before we hoist out the assembly guide tome and place it on the table with a continent-perturbing thud, we see what's before us. What does it take to make a Universe?
Stars, planets, moons, asteroids, comets, centaurs, gases, dust, galaxies, nebulae, black holes, protons, neutrons, electrons, space and time (complete with interconnecting locks), galactic clusters, globular clusters, and, of course, more than 90 elements, hydrogen and helium being predominant. Oh, and lest we forget the one component on which everything else is predicated: energy. Unfathomably large quantities of energy. While we don't have the option of adding more energy, that which the box already contains won't vanish. It will merely change form and in so doing will power the cosmos entire.
What a mess!
Our mission is to try to sort it all out.
To organize it, dissect its parts, and puzzle out how it all fits together. This aim necessitates the introduction of enough constructs and contrivances to aggravate a pub's worth of poets. If we're going to have any hope of understanding the Universe -or, to be more accurate, to understand the parts of the Universe we can understand- we have to slice the sky into segments, Mr. Whitman. If it is any consolation, sir, the sky itself shrugs off such imprints and remains beautifully whole to those who simply venture outside to observe it.
II: Celestial Grids
Earth is the center of the Universe.
We'll give you a moment to absorb that statement. In fact, we'll repeat it.
Earth is the center of the Universe!
We added an exclamation point, meaning that it now has to be true.
True in the sense that for our purposes we can regard Earth as occupying the cosmic center, at least for a little while. We acknowledge, of course, that Earth doesn't actually maintain a special place in the Universe. (Probably for the best. Such notions go right to our heads.)
With Earth securely set in the cosmic center, we then turn our attention to the sky above. What do you notice? It all seems like a field of luminescent pinpoints along a thin curved membrane. In fact, the night sky was once regarded as a threadbare burlap tapestry draped over the world. This covering obscured the brilliant light pervading the heavens. The stars were the worn sections that permitted the light to shine through. (This model has since been revised.)
CELESTIAL EQUATOR
The question becomes: how can we patriarchal thugs impose a semblance of order onto the sky so we can start tracking the motions of stars, moons and planets? Well, imagine Earth was encircled by a bright ring akin to that which encircles Saturn. It is poised directly above the planet's equator at such a height as to allow everyone on Earth to see it. Earthbound observers would see it as a luminous arc extending from due east to due west. Where it would appear in the sky would depend on the observer's latitude.
Let's summon three volunteers: Oliver Cromwell, Rasputin and Gaius Caligula. (Hey, the after world is self isolating, too, so we have to take what we can get.)
Oliver will go to the equator; Caligula to the Tropic of Capricorn (23.5 degrees south) and Rasputin to Moscow (ha ha.)
Oliver sees the celestial equator pass due east to due west and pass directly overhead, along a point we define as the zenith. Being on the equator, Oliver is standing directly beneath the "ring" and so will see it right above him.
Caligula is standing somewhere along the 23.5 south parallel, called the Tropic of Capricorn. (We'll explain that in time.) He also sees the ring extending between due east and west. However, he is 23. 5 degrees south of the ring and so it doesn't pass directly above him. Instead, it passes 23.5 degrees below the zenith. Since he is in the southern hemisphere, the ring will therefore pass 66.5 degrees above his northern horizon (90 - 23.5 = 66.5 degrees) at its highest point, which is due north.
Meanwhile, Rasputin is in Moscow, which is almost at 56 degrees north. (To make the math more nerve-friendly, we'll call it 56 degrees.) Rasputin also sees the ring extend from due east to due west. However, as he is 56 degrees north of the ring, it will attain its greatest height at 34 degrees (90-56) above the point due south.
We call this ring the "Celestial equator."
We know that if it were real it would:
-Be visible everywhere
-Pass from due east to due west at every location
-Its position would depend on the observer. Those in the northern hemisphere would see it attain its greatest height due south. Those in the southern hemisphere would see it attain its greatest height due north.
-The Celestial equator's highest angle would be equal to 90 degrees minus the observer's latitude:
Right now, we're going to pretend you're in Portland, Maine (latitude 43 degrees...almost.) Here, the celestial equator would still pass due east to due west and would attain its highest angle of 47 degrees due south. Now, hold that thought because we're going to give you an assignment in a moment.
MERIDIAN
Now that we have an arc connecting due east and west, we should have another that extends between due north and due south. We'll call it the "meridian," and it will be wholly observer dependent. That means that your due north and south follow you everywhere you go and that your due north and south are not the same as mine. Your meridian will intersect the celestial equator only once: at the point of highest aspect, or where the celestial equator is at the greatest height above the horizon.
Splendid. Celestial equator connecting due east and due west. Meridian connecting due south and due north.
In Portland, they intersect where the celestial equator passes 47 degrees above due south.
DECLINATION
Before proceeding, we must devise a way to measure a celestial object's angular distance north or south of the celestial equator. We'll adopt a convention that geographers use to measure a terrestrial object's distance from Earth's equator. Whereas they use the term "latitude," we'll use the term "declination."
-The declination of an object precisely on the celestial equator is 0 degrees.
-The declination of an object at the north celestial pole (the pole directly above Earth's north pole, and, yes, I know I didn't have to say that) is 90 degrees. The declination of an object the south celestial pole is -90 degrees.
-Any object north of the celestial equator is assigned a positive declination and any object south of the celestial equator is assigned a negative declination.
ECLIPTIC
Now, for your assignment. First, you must remain in Portland for an entire year. (No worries. Portland's the microbrew capital of the planet. You'll cope.) Each day around noon time*, you must watch the Sun crossing the meridian and note its angle relative to the southern horizon at each passage, properly known as "upper culmination." To render matters a bit simpler, let's have you begin on the vernal equinox, the first day of spring (On or around March 21.) On this date, as well as on the autumnal equinox, the Sun precisely follows the celestial equator, rising due east, setting due west, and attaining its maximum angle at 47 degrees.
You continue to watch the Sun's upper culmination each day thereafter. You'll note that the Sun's angle when crossing the meridian will be progressively higher each day until the summer solstice around June 21st. After the solstice, which we should properly term the "June solstice," the Sun's upper culmination angle will decrease gradually as it passes the autumnal equinox point and then reaches the winter, or December solstice around December 21st. At this time, the Sun will ascend each day and its upper culmination angle will increase. You will have completed the assignment once you observe the Sun's meridian passage the day before the vernal equinox.
Compile your records, noting the Sun's due south angle each day at upper culmination and note it relative to the date. Then produce a graph showing this angle each day of the year.
Now, if you are not overly enthusiastic about this assignment, we will be delighted to tell you the results of your observations had you actually made them.
The horizontal line extending through the middle of the star chart above represents the celestial equator. The yellow undulating curve shows the Sun's position relative to it on each date. Notice that we've marked each seasonal date starting with the autumnal equinox at the right hand side and left hand side. (These two ends should be connected as they represent the same date.)
You would have also noted that :
-at the June solstice point the Sun was 23.5 degrees north of the celestial equator. Or, the Sun's declination equalled 23.5 degrees So, in Portland, Maine, when the Sun crossed the meridian on the June solstice, it was 47 + 23.5 = 70.5 degrees above the southern horizon, its highest possible altitude.
-at the December solstice point the Sun was 23.5 degrees south of the celestial equator. Or, the Sun's declination equalled -23.5 degrees. The Sun's upper culmination angle on that date was therefore 47 - 23.5 = 23.5 degrees.
The graph you drew (or would have drawn) represents the ecliptic: the Sun's annual path through the sky.
That construct leads us naturally to tomorrow's class:
about that menagerie of mythological misfits known as the "zodiac."
*The Sun does NOT cross the meridian at precisely noon time every day of the year. Actually, the Sun only crosses the meridian at noon on four different days, when the "Equation of time" is zero. This occurs in mid April, June, very late August/very early September and in December. At other times, the Sun crosses the meridian either before or after noon.
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