Phobos Update: 2/15/2000

  1. Second Monolith Image
  2. Other Interesting Objects in SP255103
  3. More Information On Interpreting the Sun Elevation
  4. Estimate of Sun Elevation at Position of Monolith (2/19/00)

 

1. Second Monolith Image

SP255103 was not the only image of Phobos taken by the MGS. There were five other high-resolution images acquired. And one of them, SP252603, also shows the "monolith," but at 5.3 time lower resolution. While the lower-resolution image provides less detail of the object, it provides something equally useful: context. Figure 1 shows the two images for comparison. It can be seen from the longer shadows in craters that the sun angle of SPS252603 is noticeably lower than in SP255103. But yet the Monolith, (labeled 1 on both images) is still a large distance away from the day/night terminator. This is important because the shadows of small objects become progressively longer as the sun sets and the terminator approaches, until eventually common boulders can cast long shadows that look like they are being cast by enormous towers This second image indicates that is not the case for the monolith.

 

Figure 1. Comparison of SP252603 and SP255103. Only the part of SP252603 that contains Phobos is shown. The SPS255103 is shown in its entirety. The position of the monolith is indicated by the red dot labeled "1" in each image. The dot labeled "2" is the position of another group of objects described below.

An enlargement of the section of SPS252603 containing the monolith is shown together with the section of SP255103. The former has been enlarged by a factor of 2 while the latter has been reduced in size so that they are roughly comparable. The shadow cast by the monolith in SPS252603 is noticeably longer - about 50% - than it is in SP255103, consistent with the lower sun angle in SPS252603 .

 

Figure 2. Left: Monolith in SPS252603 enlarged by factor of 2. Right - Monolith (same object) in SPS25103 reduced in size for comparison of shadow lengths.

 

2. Other Interesting Objects in SP255103

As noted by several people, there are other objects in this image casting interesting shadows. Some of them are so close to the terminator that it seems probable that they are just boulders or rock fragments with elongated shadows. However, there is a group of objects with elongated shadows at a position much farther from the terminator than the monolith, as can be seen in Figure 1 where their position is marked by a dot labeled "2". Their sunlit position makes at least the tallest of them even less likely to be just boulders or rock outcroppings of the sort that would be expected on an airless moon. Several objects of this group are shown in Figure 3 below, including the tallest.

 

Figure 3. Westernmost (highest sun elevation) group of objects in SPS255103 with elongated shadows.

Notice that there is no shadow in the adjacent crater, another indication of a high sun angle. It seems quite possible that these objects are actually much taller than the lengths of their shadows might suggest, given the apparently high sun elevation. These objects are much smaller than the monolith, so the above image has been enlarged. It was also "orthorectified" by stretching the image until the nearby craters were round. The craters in the western (upper) part of the raw image are extremely elliptical in shape. That could be explained by a difference in resolution in the vertical and horizontal directions of the image plane that is in turn related to the scanning rate of the camera as the spacecraft rotated to sweep the 1-pixel wide array of CCD elements across the moon. Alternatively, it might be explained by an extreme off-nadir viewing angle of the region in that part of the image. The latter cause is familiar to anyone who has seen a few spacecraft images of planets or moons. As shown in Figure 4, the MSSS processed version that most people would see when browsing the USGS archive, further distortions were introduced by the stretching of the already distorted raw image, making these features virtually unnoticeable. There are other "orthorectified" images in the MGS archive that were stretched to make the craters look round. In this case, however, the rectification worked only for a few craters at the bottom of the image near the shadow terminator. The stretching operation distorted the rest of the image, particularly toward the top.

Figure 4. Left: Raw image with a contrast adjustment showing western objects. Right: JPL/MSSS enhancement. Both are full scale.

The complete processed image is available at:

http://ida.wr.usgs.gov/fullres/complete/orb_0551/55103.jpg

 

3. More Information On Interpreting the Sun Elevation

Each set of images in the USGS archive is accompanied by an "errata" file that describes known errors in the image data listings. To see if the extraordinarily high sun elevations cited for the Phobos images containing the monolith might be in error, I looked at the errata file for the set that included all the Phobos images.

This text file is at:

ftp://ida.wr.usgs.gov/cdroms/MGSC_0010/errata.txt

Rather than finding any error correction, I found a statement that reinforces the likelihood that the monolith and other objects have long shadows because they are extraordinarily tall objects:

All images from the Phobos orbits (476, 501, 526, and 551) were processed with Phobos position information from the NAIF SP kernel file mar033-5.bsp. Owing to limitations in our processing software, coordinate information is relative to the IAU triaxial ellipsoid model of Phobos in some instances, and relative to a spheroid with equatorial radius 13.4 km and polar radius 9.2 km in other instances, and should be treated with some caution. C-kernel information was not available for Phobos images 526/01, 526/02, and 526/03, and in these cases the ancillary values are grossly in error.

The "C-kernel" software computes positions of the spacecraft relative to the target and does not appear to have any bearing on the sun elevation data.

The primary reservation I expressed in the previous article about taking the surprisingly high sun elevation too literally was the irregular shape of the moon. But if either the "triaxial ellipsoid" model or the spheroid model was used to compute the sun elevation, there seems to be little reason to believe it was more than a few degrees different from the stated angle. Either of these models should be more accurate than the simple spherical model that I had conjectured might explain an overly high sun elevation - and an overly great height-to-width ratio of these objects.

Caution, of course, is still needed as this file says. It may be that the shadows of these objects are very long because they are being cast down slope. There is no obvious indication of this in the images, however. A slope of approximately 30 degrees from the horizontal would be needed for an object whose height-to-width ratio was only 1:1 to cast a shadow as elongated as that of the monolith for a sun elevation of 45 degrees. It seems such a steep slope would be more noticeable.

 

4. Estimate of Sun Elevation at Position of Monolith

There is a quantitative estimate that can support this seeming lack of a steep slope. As noted previously, the sun elevation stated in the image data listing applies only to the central point in the image and only for a surface that is in the horizontal plane of the model of the moon being used. The sun may be much higher or lower at points other than the center of the image. But given the sun elevation at the central point, there are methods to determine the slope angles at other points.

In The Martian Enigmas, Mark Carlotto describes the basis for a shape-from-shading technique based on a simple relationship between brightness and slope that is applicable under the following conditions:

The first image satisfies all three conditions, and the second image satisfies all but the last - the stated sun elevation of over 45 degrees may be too high. But for the purposes of a rough estimate, it may suffice, particularly when the results can be checked against the first photograph.

This relationship between digital image brightness, B, and the sun incidence angle, A, relative to the surface normal (perpendicular relative to the surface) of a slope is:

B = K cos(A) + D,

where K is some constant, D is the digital brightness for the points in the image where there was a complete absence of light. For the first image, the blackness of space around Phobos can be used for D and in the second, there is total shadow toward the bottom.

The value of K for an image can be computed from the measure brightness at the center, Bc and the stated sun incidence angle, Ac.

K = (Bc - D) / cos( Ac )

To compute the value of the constant K, I measured the average brightness for a square consisting of a hundred pixels near the center of both images. After determining K, I measured the brightness for a small strip of pixels running along the length of the Monolith's shadow and then computed the estimate of the sun incidence angle at the position of the Monolith as:

Ax = acos( (Bx - D) / K)

The sun's elevation, Ex, is 90 degrees minus the incidence angle, Ax. After running through the measurements several times, selecting slightly different sets of pixels for both the center points and the monolith's position, the best estimate seemed to be a sun elevation at the position of the monolith of 28.1 degrees for the first image and 38.5 degrees for the second.

The height, H, of an object can be computed from the length, L, of the shadow it casts at a sun elevation angle, E, simply as:

H = L tan(E).

Assuming the sun elevations I estimated for the two images are accurate, the ratio of the lengths of the shadows cast by the Monolith in the images should be:

L1/L2 = tan(38.5) / tan(28.1) = 1.5

The results varied from 1.4 to 1.6, depending on which blocks of pixels I used for the brightness measurements. The interesting thing about this ratio is that it is almost exactly the ratio of the shadow lengths of the monolith that I measured on the two images. (Recall I stated previously that the shadow in SP252603 was about 50% longer than in SP255103). The shadow length measurements are completely independent of the computation of sun angles. The direct shadow length measurements are consistent with the estimated sun elevations, and so provide verification that the computed sun elevations are accurate, at least within a few degrees. The sun elevation estimates could still be wildly off, but it seems unlikely they would both be off in the right way to produce the correct ratio of shadow lengths.

These sun elevation estimates imply a height-to-width ratio for the Monolith of 2.5 to 1. That would mean the Monolith is "only" 28 stories high rather than the possible 40 stories that would be the case if the stated sun elevation at the center point in the image was applied directly to the Monolith's position. This still makes Efrain Palermo's mock-up, with a height-to-width ratio of about 2 to 1, a conservative speculation about the true proportions of the Monolith.

This new information gives sound reason, in my opinion, to believe that these objects deserve serious investigation by NASA, even if they ultimately prove to be less unusual than they now appear to be.

-- Lan Fleming

VGL

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