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[Stamped:]
RECEIVED
O R A
MAY 03 1993

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Victor G. Szebehely
Richard B. Curran Centennial
Professor of Engineering
University of Texas at Austin
c/o University of Texas Press
P.O. Box 7819
Austin, TX 78713-7819

April 4, 1993

Dear Professor Szebehely,

I have read your textbook <u>Adventures in Celestial Mechanics</u> with interest and thought you might be able to offer an educated opinion on the enclosed paper. It details a computer analysis of the plenetary orbits that, though simplistic in nature, introduces some novel and thought provoking ideas. I would be most grateful of any comments you could offer.

Thanks very much for your time and effort, and I look forward to hearing from you soon.

Sincerely,

[Signature: William H. Clark II]

William H. Clark II, P.E.

O’Connell Robertson & Associates
811 Barton Springs Rd #900
Austin, TX 78704

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[Handwritten note at the bottom:]

Apr 30 ’93

Thank you very much for sending your very interesting paper. I recommend that you send this paper for evaluation and publication to the Journal of Celestial Mechanics.

Congratulations and best regards,
V. Szebehely

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Page 2

[Logo: Red square with a white star]

April 8, 1994

Dr. Victor Szebehely
Department of Aerospace Engineering
University of Texas
Austin, Texas

Dear Professor Szebehely,

Several months ago I received some help from you in trying to get a computer analysis on celestial mechanics published. Although I have been unable to find a receptive forum, I appreciate your help and support. Perhaps I need to target a less technical journal than Celestial Mechanics.

Enclosed are two more reports that are less sophisticated than my earlier computer based study. In fact they form part of the basis for that analysis. I would appreciate your input and suggestions on these papers.

Thanks for your time and effort, and I look forward to hearing from you soon.

Sincerely,

[Signature: William H. Clark II]

William H. Clark II, P.E.

Enclosures (2)

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[Handwritten note on the right/bottom:]

Apr 15 ’94

Dear Bill: Thank you for your two papers which are very interesting. Unfortunately, it is difficult to publish these kinds of papers in a scientific journal, so I suggest you try a more popular publication.

Regards,
Victor Szebehely

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O’CONNELL ROBERTSON AND ASSOCIATES
ARCHITECTS                                                                                                ENGINEERS
811 BARTON SPRINGS ROAD SUITE 900 AUSTIN, TEXAS 78704 512/478-7286 FAX 512/478-7441

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Page 3

[Header Graphic:]
AUSTIN TEXAS

SIDEREAL TIMES

Austin Astronomical Society

[24-hour clock face graphic]

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Program for May 13th

Dr. Beverly Smith

"Infrared Extra Galactic Observations
using the
Keiper Airborne Observatory

Club News

Nomination of officers for next year will be held this month. Please think of someone you would like to serve as an officer. Contact them for their approval and nominate them at the May meeting. Elections will be held next month.

The Star Party at the LBJ State Park was a rousing success. We had a beautiful sky and a good time was enjoyed by about 110 visitors. Thanks to all.

Continued on page 2

Star Party
8:00 pm
Bee Cave Site
Saturday, May 14th

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Of Interest

Chaos in the Solar System

by William H. Clark II

Chaos – the latest scientific fad. It is an elegant philosophy and one with parallels throughout the natural world. It is the idea that common patterns are repeated at many different scales, sometimes in widely divergent realms. And yet, patterns may be pretty, and forms and shapes can be functional – where are the numbers to substantiate and explain them? This paper proposes one such pattern, subjects it to numerical analysis, and proposes a few hypothetical thoughts on how or why it may be so. The topic is the solar system, and how as a system of objects orbiting around the solar nucleus, it can be thought of as a two-dimensional or planar equivalent to the orbital electron clouds and therefore reflect what happens about the nuclear core of every atom.

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Mr. Clark is an honors graduate of the University of Texas, and is presently employed as a design engineer for a consulting firm in Austin, O’Connell Robertson & Associates. He has attended several meetings of the Austin Astronomical Society. This is his first article for the Sidereal Times.

Continued on page 2

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Page 4

[Top left, partially cut off:]
…ks…
…olunteers, who helped with another
…nt. Kids of all ages appreciated our

[Top right:]
Jim Walker; Kelley Knight; Ed Popp; Mike M…
Earl Carls; Ruben Gamboa; Mike Robichaux;
Sands; Brian Cuthbertson

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…os in the Solar System, Continued from page 1

Introduction:

The idea of other stars having planetary systems has been in the news lately, sparked by a possible sighting of a planet attached to a nearby star. It would seem to be a logical premise, for a thinking man to figure that other stars have planets. Yet the lack of any theoretical basis for this proposition precludes a scientist from taking one side or the other on the issue.

This brief report is a cautious exploration of the idea of planetary existences, a tentative proposition suggesting that solar systems are the rule rather than the exception.

This singular premise derives from the recent philosophy of chaos, and the idea that patterns are not only common in the natural world, but repeat themselves at any number of different scales or levels. The pattern suggested herein is the most fundamental of all: That the solar system, as a collection of objects orbiting a massive central core, is a planar representation of the atom itself.

Is it wise, to entertain the thought that an astronomical entity, though it is comprised admittedly of naught but atoms; can you credibly conceive that a celestial parallel exists such that the most fundamental patterns of all are reflected in the most complex? Is the “galactic atom” a grandiose idea, or a genuine insight which – though inexact and sketchy – might lead toward more insightful and accurate hypotheses?

Orbital Energies

The engineer, where the scientist may theorize and conjure, will seek a definitive analysis thereof. He would require numbers and data, to supplant a novel hypothesis. A most basic place to start, then, is to consider the relative energies of the planets. This can be done by using an equation found in any engineering mechanics text, for orbital energies of celestial objects:

$$\text{Total Energy} = 1/2 \times m \times v^2 \qquad (1)$$

where: $m=\text{mass}$      $v=\text{velocity}$      $I=\text{moment of inertia}$      $w=\text{angular velocity}$

This rule of orbital dynamics can be further customized to our situation by substituting the value of “$I$” for a spherical object:

$$I = 1/5 \times m \times r^2 \qquad (2)$$

where: $m\text{-mass}$      $r\text{-radius of the body}$

An equation which assumes that the object is of a uniform density throughout its cross section. Which, in the case of planets, we know is far from the truth, the density of the core being always greater than that of the outer layers of a planet. If this divergence is kept in mind, however, and if you do not expect a completely exact answer at this stage, then a reasonable hypothesis can be devised – at least one worthy of further examination, e.g…, pursuing the exact calculation of a planet’s inertia assuming a certain variance in density.

One final function and the analysis will be ready for the test of truth. The angular velocity is a function of other entities:

$$w = v/r \qquad (3)$$

where: $v=\text{tangential velocity}$      $r=\text{radius of the body}$

Keep in mind that the velocity of Equation 3 is the tangential acceleration of the body, e.g…, at the equator; while the velocity in Equation 1 is of the planet through space, e.g…, in its orbit around the sun.

Obtaining the data from the CRC Handbook of Chemistry and Physics, the data on the planets can be substituted into these equations to produce the results tabulated in Table 1 for the total orbital energy of the planets.

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Table 1

Planet	mass (kg)	$1/2\text{ mv}^2$	$1/5\text{ Iw}^2$	total	rank
Mercury	3.18 E23	3.64 E26		3.64 E26	3
Venus	4.88 E24	3.00 E27		3.00 E27	7
Earth	5.98 E24	2.65 E27		2.65 E27	6
Mars	6.42 E23	1.87 E26		1.87 E26	2
Jupiter	1.90 E27	1.62 E29	6.09 E28	4.26 E28	9
Saturn	5.68 E26	2.64 E28	1.21 E28	3.85 E28	8
Uranus	8.68 E25	2.00 E27	2.63 E26	2.26 E27	5
Neptune	1.03 E26	1.52 E27	1.31 E26	1.63 E27	4
Pluto	1.08 E24	1.21 E25		1.21 E25	1

Where the inertial energies are not included for several of the planets, because they are negligible relative to the orbital energy. Also, the units are consistent, but not included, because it is the relative values for the planets that are important in this analysis.

QUANTUM ANALOGIES

Now, to see if any corollaries exist on the atomic level. Here we endeavor to rank the electrons by increasing energy level; again, a common ladder to be found in any basic reference manual, in this case a textbook in college chemistry (See Table 2 for this information).

Table 2

Planet	Orbital	#Moons	Planet	Orbital	#Moons
Pluto	1s	–	Earth	4s	1
Mars	2s	2	Saturn	3d	6
Mercury	2p	2	Venus	4p	–
Neptune	3s	5	Asteroids	5s	–
Uranus	3p	5	Jupiter	4d	6

The number of moons is above a nominal size; for comparison only.

Now the conjuring begins in earnest. Of the many possible ways to correlate the two hierarchies, an intriguing one is to match them as illustrated above, which follows the orbital energies of electrons exactly; the planets ranked alongside according to their orbital energy.

The only leeway happened with Saturn and Venus whose energies were close enough to reverse their order to fit the pattern; and, of course, the hypothetical spotting of the asteroids.

A couple of analogies: The two planets with noticeable rings, Saturn and Jupiter (which has very faint ones) are both in d-orbitals; which have a unique donut shape in atomic orbital probability distributions. The two planets with retrograde (reverse) rotation are both slotted in p-type orbitals, Venus and Uranus. Also, the planets with moons are located in the more complicated orbitals; i.e., the s-type orbits are simple spherical ones, the p-type barbell-shaped.

CONCLUSION

The solar system is a mysterious, and extremely complex place. Small patterns are evident, and readily explained – elliptical orbits, periods of revolution – but what of the overall scheme? It is a giant leap to accept the proposal suggested herein that a star cannot exist without planets, no less than an atom can be found sans electrons. And yet, such a philosophy may be a requisite mind-set, if the unexplained patterns of the planetary motions are to be comprehended – such questions as what causes retrograde rotation, what force makes the axes of rotation incline as they do, etc… and developed into a useful scientific theorum.

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EQUIPMENT DONATION:

Thanks to serendipitous timing, Earl Carls arranged the donation of two precision lead-screws to the club. These are about 30 and 40 inches long, 8 tpi, with recirculating-ball travelers. Anybody with a good idea for their use?

FOR SALE
Novak Mirror Cell
for 12.5" primary
Research-grade, 9-point
Brand new, still in wrapper
$50
459-5137

Deadline for the Sidereal Times is the second Tuesday prior to the monthly meeting. All articles/notices must be at 2518 Guadalupe by that time.

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Welcome New Members and Guests

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Larry Kemp, President
411 Central Drive
Georgetown, TX 78628
930-4710 (home)

Rick Kirchhof, Vice President
454-4306 (home)

Membership in the Austin Astronomical Society is open to anyone interested in astronomy or the space sciences. Dues are $26.00 for regular membership, and $16.50 for junior membership (18 years or younger). <u>Sky and Telescope</u> magazine is included as a privilege of membership. Annual dues are collected during the September and October meetings, the magazine subscription running from December through the following November. The Society operates a 12.5" Newtonian telescope for the use of members following a brief period of instruction and payment of $1.00 annually. Society observing sessions are held monthly, weather permitting (guests and visitors are welcome).

Monthly meetings of the Society are held on the second Friday of each month at the Austin Community College, 12th and Rio Grande, room 320, at 7:30PM.

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[Mailing Section:]

Return Address:
Austin Astronomical Society
P.O. Box 12831
Austin, TX 78711

Postmark / Stamp:
(Circular Postmark): AUSTIN TX / AM / MAY 7 / 1994 / 787
(Stamp): 29 USA / 500th Anniversary Columbus Landing in Puerto Rico

Recipient Address:
Jo M. Burley
2009 Oakglen Drive
Austin, Texas 78745

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Page 7

ASTRONOMY®

September 30, 1991

William H. Clark
O’Connell Robertson & Associates
811 Barton Springs Road, Ste 900
Austin, TX 78704

Dear Mr. Clark:

Enclosed is your manuscript:

“Chaos of the Solar System.”

Thank you for taking the time to prepare this manuscript for us. Unfortunately, it doesn’t meet our present needs and so I am returning it to you.

Since you may be interested in submitting again, I have enclosed a copy of our Guidelines for Writers. They will give you a good understanding of the kinds of materials we are looking for.

Thank you for giving us the opportunity to consider your article, and please don’t hesitate to consider ASTRONOMY for any other submissions you think may be of interest to our readers.

Sincerely,

[Signature: Robert Burnham]

Robert Burnham
Senior Editor

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KALMBACH PUBLISHING CO., 21027 CROSSROADS CIRCLE, P. O. BOX 1612, WAUKESHA, WI 53187, (414) 796-8776, FAX (414) 796-0126