See also recent updates about offsets and visualizing "mars descending" and an analysis of the images on the Kronia home page.
A small point recently arose upon usenet, as small points are wont, thus
:: Wayne Throop <throopw%sheol.uucp@dg-rtp.dg.com> :: <49fg8t$70s@aurns1.aur.alcatel.com> :: [...] it is fairly easy to show that the image of the polar :: configuration on the Aeon home page could only be visible from within :: about 5 degrees of the north pole, hence looking within 5 degrees of :: straight up. In fact, at the portrayed distance ratio, mars' image :: would remain inside venus' only out to about 75 degrees north (within :: 15 degrees of directly-overhead) : wdmorris@iastate.edu (Walter D Morris) [Ev Cochrane] : <49ipe4$q9v@news.iastate.edu> : Wayne and I have been down this road several times before. Suffice it : to say here that he is quite wrong. What is *easy* to show is that : this very "tit" image (I prefer this name, although others call it the : celestial olive) results given a viewer at the 45th parallel or so and : any number of orbits of Mars/Venus/Saturn. I had one of the top : computer simulation firms in the world-- Engineering Animation Inc. : here in Ames--plug in the respective sizes of Mars, Venus, and Saturn, : place them at a certain distance from the Earth and on the same axis, : and presto: The celestial tit appears.
First of all, the characterization of the process of plonking down planets in a line along the Earth's spin axis at different distances "any number of orbits" is at best misleading. If Ev had called them "placements" instead of "orbits", I would not object. But "orbits" connotes a dynamic plausibility the model hasn't earned. In fact, Ev has never even come close to producing stable orbits that would yield this image (the Grubaugh distance ratios are all wrong, and the magnetic-supported versions are dynamically laughable).
But on the major issue of the plausibility of the image itself, even granting the fantasy of these so-called "orbits", nobody needs to take this on anybody's authority. You don't need to go out and hire "one of the top computer simulation firms in the world". You can do the arithmetic yourself; it's rather easy. First, a bit of projective geometry shows that the relationship of a foreground planet and a background planet in terms of image size, radius, and distance, is
d(fore)/d(back) = (r(fore)*i(back)) / (i(fore)*r(back))If we apply this formula to the Aeon home page (copied here for reference), we get this table.
planet pixels approx radius distance ratio
saturn 264 60000 km 1.000
venus 75 6000 km 0.352
mars 62 3400 km 0.241
cos(lat)*r(earth)*d(back)/d(fore)and one can draw the image. In the summary image below, we see the image currently on the Aeon home page, the image I reconstruct from the pole, and finally, on the right, the image as it would appear from latitude 50.
Note that the only case that comes out looking like the Aeon home page original is the view from 90 degrees, and it matches quite well. The methods used to generate these images were also checked against much more thorough 3D solids modeling and image rendering methods to which Andrew MacRae has access. They generated matching images for comparison cases, which confirms that the simplifying assumptions I used have not introduced problems.
Here are links to the full images.
I think it's quite clear beyond rational dispute. The Aeon home page image is wrong. It cannot possibly be seen within 60 degrees of the horizon for the relative image sizes and alignments it portrays. In fact I think it's clear that it was projected for an observer at the pole, and therefore would have been exactly overhead. The portrayal could be fixed in some degree by tinkering with the mars/venus distance ratio, but it will never look as symmetrical as it is portrayed on the Aeon home page from 45 degrees away from the pole.
