Charle's star charts for projection

Posted by: Ken Miller Apr 2 2008, 06:23 PM
QUOTE(charle @ Apr 1 2008, 08:17 AM) *
Great. Now I can finally
ask my questions re: compared to
the original Spitz star maps.

QUOTE
1. Are these even close?I am amazed and impressed. Those are very close!
QUOTE
2. I assumed from the pictures of the Spitz A1
the the NCP and SCP are centered on the face
of the top and bottom faces. Is this correct?That is correct
QUOTE
3. Where is RA=0 located? In the maps I am generating
at present, I put RA= 0 at the edge of two faces. It
turns out that with this selection, there are no magnitude
3 or brighter stars near the vertical edges on the faces
in the Northern hemisphere. But there are several
important stars near the edges of the top face.Without checking any further, the accuracy of the charts that I have determined so far suggests that you must have RA=0 in the same place as on the Spitz
QUOTE
4. I am currently using a star base of about 3100 stars.
Should I have versions with 10,000 stars?The answer to this is definitely not 10,000 stars. You wouldn't be able to have sufficient range in brightness, and still differentiate the constellations. Spitz played tricks with hole sizes to make the constellations "pop out". Much more stars than 1000 would be nice, but it wouldn't be faithful to the original Spitz, and it would give you diminishing returns (in my opinion).

QUOTE
Thanks for the help.

Charle'

Posted by: charle Apr 2 2008, 07:28 PM
That's great news for me. I am now working on a version
of the program that others can use directly. The program
files when compressed require less than 200 Kbytes. This
will make the charts available to people with standard
telephone access while allowing higher quality output.
In addition, I am including the ability
to subset the star set based on min to max magnitude.

So thanks to your work I feel comfortable charging
ahead but everyone should be aware that I program
at a snails pace.

Thanks again Ken.

Charle'

Posted by: charle Apr 4 2008, 11:32 AM
QUOTE(Ken Miller @ Apr 3 2008, 11:43 PM) *
Charle'

I had to do this quickly, but I will try to do it better later on. Here is a photo for comparison with your chart for your plate "zero".


Thanks for the photo. A rough graphical
analysis of the image shows about a +2.5 degree
shift in right ascension. I would conjecture that
Spitz did indeed place RA=0 on the vertical edge
and the difference is due to precession.

Thanks Again.

Charle'Posted by: charle Apr 4 2008, 11:32 AM
QUOTE(Ken Miller @ Apr 3 2008, 11:43 PM) *
Charle'

I had to do this quickly, but I will try to do it better later on. Here is a photo for comparison with your chart for your plate "zero".


Thanks for the photo. A rough graphical
analysis of the image shows about a +2.5 degree
shift in right ascension. I would conjecture that
Spitz did indeed place RA=0 on the vertical edge
and the difference is due to precession.

Thanks Again.

Charle'

Posted by: charle Apr 4 2008, 10:39 PM
QUOTE(Ken Miller @ Apr 4 2008, 07:03 PM) *
Charle'

I'm looking at this and thinking I see the vertical edge that is in Ursa Major at RA = 12 HR. But as you go around the starball, there probably are other vertical edges that do line up with RA = 0/24. Am I confused? You don't have to answer that, because I undoubtedly am.

There are 5 vertical edges in the northern hemisphere, on every 72 degrees. Thus there is only one opportunity for
a vertical edge to fall exactly on an hour angle. I realize now that I have previously stated the reference incorrectly.
My model place RA=0 at the CENTER of one of the faces (not the edge), because this would be
the center of a gnomic projection. The center of each face has no distortion, while the edges have
significant distortion and the greatest distortion occurs at the vertices. So as you point out, this
leaves RA=12 to be close to an edge at about the position of Phad in Ursa Major.

I thought precession was about 1 degree every 80 years. If that is the case, a 50 year old starglobe shouldn't be off by 2.5 degrees because of precession. Am I correct?

Yes. My analysis is rather crude with a number of errors. Since precession has both RA and DEC
components, its not accurate to speak of only an RA change although RA is the larger of the
two. On the other hand, the closeness of Polaris to the north pole is always a topic of misunderstanding
to be dealt with so the DEC component can not be ignored. To get a more accurate value, we need
to use a photograph which is as perpendicular as possible to the face using a camera with very
little distortion (usually a longer focal length). In spite of the errors
in the graphical analysis, it is clear that there is SOME difference. Down the road, I will
put proper precession into the program. This will make it easier to get a closer match.

If anything, I would think that Spitz lined up the edges to minimize the number of bright stars that
ended up in inconvenient places. Other than aesthetics, I'm not sure there is a compelling reason why he would precisely line up RA = 0 on a vertical edge.

I have a personal interest in how Spitz approached the problem of creating his templates
from a computational perspective. He obviously didn't have a PC available. It's possible of course
the he got the templates from some one else. But, if he did created them himself (which would
require only a knowledge of trigonometry which was fairly common in his time frame) he would
have had to make a choice ... I prefer to believe that he was a pretty good architect
(as demonstrated by the successful production of a number of machines) so that he would
have made a studied choice for the RA=0 assignment. On the other hand, he may have
noted as I did that the assignment of RA=0 to the center of a face has the desirable property
that there are no major stars on the vertical edges. Also, I would think that such a choice would
make it easier to synchronize the star ball with the other projectors.

Does anyone know of a set of star charts which are based on the 12 gnomic projections
of a dodecahedron? Usually, star charts chose a pattern so that each band of faces maps
evenly to major RA values. For example, the popular 8 chart simple starmap that uses
gnomic projections for the poles and 6 projections spanning the equator.

Sorry for the misunderstanding.

Charle'


I am eager to hear you take on all this. This is a good learning experience for me.

Ken