Constellations & Asterisms Redefined - Joseph Schreiner

How I Created the New Asterisms

Though I took one step backwards for every two steps forward, I created the asterisms through the stages below. Even the word “step” implies a linear progression toward a final goal, which was not the case. All work was done with Visual Basic and C on a Windows machine.

First, on the WWW, I obtained positions and magnitudes of the 9000+ brightest sky objects (at http://cdsweb.u-strasbg.fr/cgi-bin/Cat?V/50 ). I converted the file to text format and extracted the data that I needed. I converted right ascension and declination to 3-dimensional coordinates. I used only stars (some galaxies and extinct novae were listed among the brightest objects).

Second, I had to decide on the number of stars and asterisms. I used multiples of 8 to maintain symmetry with the 8 octants of the celestial sphere. I needed a number of stars that would be clearly visible, given light pollution prevalent in many areas. Too many stars in an asterism become a confusing jumble of dots, rather than a coherent pattern. I tried the brightest 480, 500, 512, 576, 600, 640, and 664 stars. I tried creating 48, 56, 60, 64, 72, 80, and 88 asterisms. After examining these combinations, I decided that 80 asterisms for 576 stars was best.

This next step was the iterative partner to the previous step. When running the cluster analyses, I gave slightly extra emphasis to the brightest stars. The lesser number of asterisms (48 – 64) usually did not stop iterating, or converge, to a stable solution. The lesser number of stars (480 – 512) tended to generate many trivial clusters (only 3 to 5 stars in a cluster) and few interesting (8 or more stars) clusters. The greater number of stars (600 or greater) produced more interesting clusters, but no more so than 576 stars. The addition clusters were usually trivial. So 576 stars produced the best ratio of interesting clusters to trivial clusters. The 576 brightest stars had magnitudes of 3.98 or less.

I ran 1000 randomly-chosen K-Means cluster analyses, and chose the best solution from those 1000. I assigned numbers to the final asterisms, in order of their average declinations. Thus, the northernmost cluster was Asterism 01, and the southernmost cluster Asterism 80.

I had to separate the interesting from trivial clusters. I chose a threshold of eight or more stars to a cluster. A minimum of eight stars in an asterism usually guaranteed an interesting pattern. I also included three clusters (having distinctive patterns) of seven stars each. It is nearly impossible to generate an interesting pattern with 6 or fewer stars. In the end, I had 29 interesting (primary) clusters with which to work.

Assigning pictorial archetypes to the asterisms was difficult and subjective. I created a list of approximately 120 archetypes from which to choose. I assigned scores to archetype-asterism combinations, and ran combinatorial programs to find the “best” solution. This process was so fraught with problems (quadrillions of combinations, good total scores at the expense of a few mismatches …) that I abandoned this mechanistic procedure. I had to visually compare each asterism to the list of archetypes, and make assignments personally. In doing so, I made certain that the archetypes were evenly divided among:

1) Living beings (plants and animals)
2) Human beings, their relationships, and their activities
3) Human creations (machines and artifacts)

Where possible, I assigned dual names to an asterism – one for a concrete physical object, the other for an abstraction it represented.

Next, I printed the asterisms, and manually traced a picture of the archetype on the asterism. In depicting the asterisms, I redressed the imbalance between the northern and southern hemispheres. If the center of the asterism was north of the celestial equator, then it is depicted the traditional way (North = Up, East = Left). If the asterism’s center was south of the celestial equator, then South = Up and West = Left. The asterisms are displayed as they would be seen crossing the meridian from east to west, from their respective northern or southern hemispheres

I made no attempt to map the entire sky. Much of the celestial sphere has dim stars that can barely be seen. Too many dim stars in an asterism make it difficult to discern a meaningful pattern. If an asterism has too few stars, we have a mere polygon (either too little or too much material for the imagination). Even now, many of the current 88 constellations contain just a few bright stars, with unimaginative names (Triangulum Australe, Pictor …). I refer to my results as asterisms, not constellations, because I defined clusters of stars, not regions in the sky.

Show Me the Asterisms! The ET's Are on the Line!

Did Any Constellations Survive?

Where Are the Lost Stars?

How Does Cluster Analysis Work?

Defining the Heavens

A Brief History of the Constellations

References & Links

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