Planetary Models

These images are 3D models of planetary arrangements as proposed by Velikovsky supporters like Dave Talbott and Ev Cochrane (ecochrane@delphi.com), who have participated in talk.origins in recent years. Their model is based on the similarities of ancient art and myth. The implementation of these 3D images was attempted in order to test their claims.

Implementation

These images were rendered using Pixar's RenderMan (TM). Technically, this is not a raytracer, and therefore shadows are not implemented for most of the images. The initial images were 24-bit TIFF files, most of which I have converted to JPEG. The "thumbnail" versions on this page are GIF, so that people without access to JPEG viewers can at least see the half-size versions.

Planetary radii were obtained from Glass (1982). All units were converted to 10^3 kilometres (i.e. the Earth's radius is 6.378*10^3km) for convenience. Viewpoints are normally located on the surface of the Earth, and are expressed in terms of a paleolatitude from the pole of the Earth, which was apparently aligned with the axis of the other planets. The camera direction is normally set to look directly at Saturn. This means high paleolatitudes (e.g., 90 degrees) near the pole look almost straight up, while lower paleolatitudes look closer to the horizon.

I gave Mars a reddish-brown colour, Venus a white colour. For Saturn I used the "wood" shader to give the (crude) appearance of banded clouds with an off-yellow-brown colour (it needs work). The bodies are illuminated either from a lightsource approximately "behind" the Earth (i.e. the opposite side from the other planets) in order to clearly show the shape of the bodies, or from a position off to one side of the arrangement, in a crude attempt to duplicate the "crescent" appearance as depicted by the image at Ted Holden's WWW page. Again, shadows are *not* implemented, so beware of the assumption the illumination is accurate! Someday, if there is interest, this might be fixed. Initial experimentation with shadows (Using BMRT) suggests the variations in illumination orientation (as predicted by Talbott's model) would regularly produce obvious shadows and eclipses on one or more of the planets:

45 degree viewpoint, slight offset of lightsource

The experimental images do not implement umbra-penumbral effects, so they still need some work before they can be used to really test this effect.

Input and Results

Ev's original description of the model

Some time ago, Ev provided distances from Earth to Mars, Venus, and Saturn, representing their position away from Earth along a linear axis centred on the rotational pole of the respective planets. The basics of this arrangement are shown in profile in the following image:

"lateral view"

"oblique view"

This shows Saturn on the left, followed by Venus, Mars, and Earth on the right. At this scale the latter three are very small in the "lateral view" image (only two or three pixels!). These images also have rings around Saturn thanks to my initial confusion about the model. According to Ev, these were not present at the time the arrangement existed, and they are removed from subsequent images.

Ev provided the following distances, all measured from Earth, in article

<pM4Y-E0.ecochrane@delphi.com>

on March 27, 1995:

       Saturn    807000 km
       Venus     500000 km
       Mars      400000 km

These images also have the Moon at its current distances from Earth, displaced a bit to the "up" side of these images, and in the upper left of all the "from Earth" views. This provides a relative angular scale to judge the visual size of the views from Earth. Basically, this planetary arrangement would be *HUGE* from Earth:

Original model, 90 degrees viewpoint.

Try to imagine this next time you are out looking at the Moon :-)

The Aeon home page image

More recently (Nov. 1995), people have noticed the image at the Aeon home page, and have pointed out that it does not correspond to the previous distances Ev has provided (For that matter, the same thing was said of the image on Ted's page). Venus and Mars are proportionally much bigger, implying they are closer. Wayne Throop (throop@aur.alcatel.com) has anaylzed the image using simple geometrical calculations, and determined the relative position of the planets. His results, including images, are presented at: Wayne's analysis. Basically, the geometrical calculations result in a ratio of distances between the planets, which can be scaled to the furthest distance, Saturn, using Ev's previous distance:

          Ev's original    Ratio    Revised to fit Aeon page
  Saturn    807000 km      1.000           807000 km
  Venus     500000 km      0.352   807000km*0.352 = 284064 km
  Mars      400000 km      0.241   807000km*0.241 = 194487 km

Subsequent to Wayne' work, and Ev's claim there was no problem, I decided to revise my 3D models to double-check Wayne's results:

Aeon model, 90 degrees viewpoint.

There is a close correspondance.

Effect of Earth viewpoint

The Aeon image has two interesting features: 1) the outline of Venus and Mars are perfectly centred on each other and on Saturn, and 2) the depiction seems to imply the image was capable of hovering over the pyramids of Egypt. These features appear to be mutually exclusive. The near-perfect alignment only occurs within a few degrees of the pole before becoming obviously out of alignment, and at this position, the planets would be almost directly overhead. For example, here is the appearance at 70, 50, 45, and 30 degrees:

Aeon model, 70 deg. viewpoint

Aeon model, 50 degrees viewpoint

Aeon model, 45 degrees viewpoint

Aeon model, 30 degrees viewpoint

Approaching the "paleoequator"

As 0 degrees is approached (i.e. the "paleoequator"), the image of the planets begin to sink below the horizon:

Aeon model, 0 degrees viewpoint

[NOTE: The Moon appears larger in this image because the relative positions of the planets was changed for this model. This does not change the qualitative appearance of the planets. See the next image for justification.]

Effect of distance

Changing the absolute distance of the planetary bodies while keeping the relative distance the same does not change the appearance of the geometry of the bodies, only their relative size. This next image was rendered with the planetary positions at twice the distance in the model above (i.e. 1614000 km for Saturn with the others suitably scaled). In order to make it approximately the same rendered image size as before, the field of view of the camera was reduced by about half (from 15 to 8 degrees). This is reflected in the much larger relative appearance of the Moon. In reality, the Moon would be the same size, but the planets would appear smaller because they are more distant (think of the effect of using a zoom lens: smaller field of view == greater magnification).

Aeon model -- 2x distance, 70 degrees

Other than the size difference, the "off centre" position is the same as in the 70 degree image above.

Interpretation and Conclusions

In conclusion, the image presented on the Aeon home page is A) not consistent with the model Ev previously described, B) its low position in the sky and close alignment of the planets are mutually exclusive, C) this close visual alignment (i.e. close enough to not be noticeable) only occurs within < 20 degrees of the "paleopole". On the rest of the Earth, clearly off-centre images would be observed, not to mention intersection with the horizon.

The only way to "fix" this would be to make the spin axis of the Earth out of alignment with the linear arrangment of the planets (which would produce other interesting variations), or to change the *relative* planetary distances. Absolute changes with the same planetary distance ratio make *NO* significant difference in the visual appearance other than size.

Note

Subsequent to preparation of this document, Ev has stated in talk.origins that the image on the Aeon home page was meant only as an artistic rendition. The original numbers he presented are therefore the correct ones. This does not significantly change the distance and "paleolatitude" trends observed above. I also find the implication the image is only "artistic" to be rather interesting if ancient art is what is being used to construct the model in the first place. Couldn't they have been "artistic" renditions too? How much can they be trusted?

New hacks

For fun, I put together an animation which uses a crude geometrical model analogous to the one proposed by Bob Grubaugh. It shows the changes in illumination expected as a "stack" of planets rotates around the Sun. The animation is an MPEG file, and is currently rather crude (the MPEG input parameters need to be better tuned):

MPEG animation (30Kb)

As before, the viewpoint is from Earth, this time at "90 degrees".

Understanding the model requires familiarity with discussions in the newsgroup talk.origins about a year ago. I do not have time to put the details in here. If you have questions, please send e-mail.

References

Glass, B.P., 1982. Introduction to Planetary Geology. Cambridge University Press: Cambridge, 469pp.

Andrew MacRae macrae@geo.ucalgary.ca