Closest-Stars Model

The universe of stars above and below us is relatively fixed in position from our vantage point, not oscillating above and below the equator every year as the sun appears to do, but only appearing to slowly rotate around once each day due to the rotation of the earth in the opposite direction.

Stars have been photographed and studied by astronomers for a long time and their directions from our solar system are well known, but determining their sizes, absolute brightnesses and distances is not easy, so different reference books may not give the same data.

To make a model of the nearest stars in their relative distances and directions to the earth, at least two different 3-dimensional systems may be used:

Polar Coordinates

The latitude and longitude measurements of a point on the earth's surface are given in polar coordinates. As I write this, I am almost 90 degrees west of Greenwich England (the Prime Meridian) and 41 degrees north of the Equator. Those two dimensions specify a point on the earth quite precisely.

Celestial positions are specified in "right ascension" (RA) and "declination". Right ascension is measured clockwise around the north pole when looking up (which would be counterclockwise looking down on the northern hemisphere of the earth). The handle of the big dipper joins the bowl at almost exactly 12 hours RA (180 degrees). The official starting point of RA is where the ecliptic (apparent path of the sun) crosses the celestial equator on the vernal equinox (first day of spring). My position on the earth at noon Greenwich (or zulu) time that day would be under the stars of 18 hours RA (looking down on the northern hemisphere, I'm 270 degrees counterclockwise from the prime meridian divided by 15 degrees per hour).

Declinations of stars are given in positive or negative degrees, which correspond exactly to latitudes on the earth, positive being above the equator, and negative, below. The north star, Polaris, has a declination of almost 90 degrees. If there were a "south star" it would be -90 degrees declination.

To construct a model of the nearest stars in this system you might begin with a ball to represent the position of the earth and rods or sticks of some sort inserted into it having lengths corresponding to the distances to the stars. A small simple model might use a styrofoam ball and bamboo sticks. A larger one could be made from a croquet ball and steel wires (clothes hanger wires, or steel welding rods). For a large model a bowling ball might be suspended by a chain with dowel rods cut to lengths to indicate the distances to the stars. The stars might even be made of small light bulbs and wired to make an illuminated model. The brightest by far (other than the sun) is Sirius Alpha. Those which are visible with the naked eye are marked with an asterisk - Greek for "little star."

	Star		Distance (ly)	   RA (hr:min)	Declination (deg:min)
Proxima Centauri        4.2             14:30           -62:41
Alpha Centauri (binary) 4.3    *        14:38           -60:45
Barnard's Star          5.96            17:58           + 4:34
Wolf 359 (CN Leo)       7.7             10:56           + 7:01
Lalande 21185           8.11            11:03           +35:58
Alpha Sirius            8.7    *         6:45           -16:43
Beta Sirius             8.7              6:45           -16:00
Luyten 726-8 (binary)   8.93             1:39           -17:57
Ross 154                9.45            18:50           -23:50
Ross 248               10.3             23:42           +44:10
Epsilon Eridani        10.69   *         3:33           - 9:28
Luyten 789-6           10.87            22:37           -15:27
Ross 128               10.9             11:48           + 0:48
61 Cygni (binary)      11.1    *        21:07           +38:45
Epsilon Indi           11.3    *        22:01           -56:53
Procyon (binary)       11.4    *         7:39           + 5:13
Sigma 2398             11.6             18:43           +59:38

Sticks, wires, rods should be cut so that their lengths from the center of the mounting sphere correspond to the distances to the stars. Although the stars vary greatly in size, their sizes to this scale are insignificant when compared to their distances.

Cartesian (x,y,z) Coordinates

The name comes from Rene Descartes, a 17th century French mathematician. Facing a plane, the X coordinate specifies a distance to the left of center if negative, and to the right if positive. The Y coordinate is toward the top of the plane if positive, and toward the bottom of the plane if negative. The third coordinate, Z, is upward if positive (away from the plane), and downward if negative. Using this system the location of the earth (x,y,z) would be 0,0,0. The north star (Polaris) at a distance of 680 light years would be: 0,0,680.
There are a large number of stars which are closer to the earth than the pole star, so it will not be included in the data.

	Star		X	  	Y		Z
Proxima Centauri        -1.56           -1.20           -3.73
Alpha Centauri (binary) -1.66           -1.37           -3.75
Barnard's Star          -0.05           -5.97           +0.47
Wolf 359 (CN Leo)       -7.35           +2.11           +0.94
Lalande 21185           -6.44           +1.64           +4.76
Alpha Sirius            -1.63           +8.20           -2.50
Beta Sirius             -1.63           +8.20           -2.40
Luyten 726-8 (binary)   +7.76           +3.58           -2.75
Ross 154                +1.88           -8.49           -3.82
Ross 248                +7.39           -0.58           +7.18
Epsilon Eridani         +6.32           +8.46           -1.76
Luyten 789-6            +9.82           -3.72           -2.90
Ross 128               -10.89           +0.57           +0.15
61 Cygni (binary)       +6.37           -5.99           +6.95
Epsilon Indi            +5.49           -3.14           -9.46
Procyon (binary)        -4.75          +10.31           +1.04
Sigma 2398              +1.11           -5.87          +10.01

If I were building up the model from a piece of plywood, I would notice first that the values of x and y are all less than 12, so you might do the dimensions in inches and a 24x24 inch piece of plywood would contain all of them. I would then use a 10-inch post to support the location of the earth (since no value of z is more negative than -10) and I would add 10 to each value of z to raise the entire model above the plywood plane.

If you build a model, send me a photograph and I'll put it on this page.

(David Hunter sent THIS LINK to his.)

Here is a photo of a model done in polar coordinates by David Hunter.

HOW TO CALCULATE x,y,z from the polar data: The horizontal (along the plywood plane) distance to the star support rod is the stellar distance times the cosine of the declination angle. I call this "R". The east longitude angle around the earth is the RA times 15deg/hr. I call this "E". The "X" coordinate is R times cos(E). The "Y" coordinate is R times sin(E). The "Z" coordinate is the stellar distance times the sine of the declination angle.

Proposed model for New York City
Table of the Nearest Stars
The Gordon Speer Home Page
Updated July 15, 2009

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