NavList:

John Howard: 
I feel that maybe you had a sort of "sign error" since you've gone in the wrong direction but by roughly the correct distance.

Ed Popko:
Thanks for suggesting this puzzle. I had a passing thought to propose this same problem for the group when I first saw the image, but did not get around to it. The photo, by the way, was taken by a spacecraft known in some quarters as the AlGorSat, which of course refers to its algorithmic origins. Of course... :)

The center of the image is in the Gulf of Campeche, the southern arc of the Gulf of Mexico. That's the sub-satellite point, dead center in the nearly circular outline of the Earth. The Earth is not quite at "full" phase, with the terminator (sunset line) clearly visible on the right side. That implies that the sub-Sun point is off to the left/west from there in the image. Given the date, July 6 of this year, and given that the western hemisphere is nearly fully illuminated, we can look up the Sun's declination for a time around 2000 UT. It's about 22° 39'. The globe is oriented in a way that strongly suggests that the photograph is aligned with the ecliptic. Since we're still close to the solstice, that means all we have to do to find the Sun's GHA is go directly left in the image from that sub-satellite spot in the Gulf of Campeche until we cross latitude 22° 39'. Given that there is some uncertainty in the location of the center of the image, this translates into a corresponding uncertainty in the longitude. I estimate that the longitude of the sub-Sun point, equivalent to the Sun's GHA, falls between 106° and 107° W, from the western coast of mainland Mexico heading towards the southern tip of Baja California. The geometry is reasonable, but how can I add evidence to the case?

In images of the Earth, there are three clues you can look for to determine where the Sun was when the photograph was taken. We can look for the terminator and of course a line drawn through the ends (or poles or horns) of the terminator will run perpendicular to the direction to the Sun. That's not much help here since the phase is so close to full. Next, the fraction of the Earth illuminated will roughly determine the phase angle to the Sun. In this photo, the Sun is to the left and behind the camera's point of view. Since the Earth is nearly full, it's roughly 10° away from the direction directly behind the camera, or in other words the Sun is about 170° away from the direction towards the Earth. If I imagine myself as the photographer, the Sun is "over my left shoulder". Also, we can look for the region of specular reflection off the ocean. This is a bright spot in the ocean, usually rather vague, where sunlight is reflecting off the ocean like a mirror. In this photo we can see that bright area to the left of the sub-satellite point. It is most prominent to the south and west of mainland Mexico  but also visible in the western Gulf of Mexico. The center of that region of specular reflection of sunlight falls just about halfway between the sub-satellite point and the estimated sub-Sun point which is consistent for small angles.

Next we can ask what the time would have been. On this date, the Sun's GHA would have been 106° - 107° from 1909 to 1913 UT. We can compare the full earth image with archived weather satellite imagery taken around this time, and the clouds should match, within some margin of error given that clouds don't change much in less than ten minutes at the scale of this photograph. But it's worth checking. GOES images are archived with easy access for at least a month. Comparing the thunderstorms bubbling up over Mexico, Florida, Georgia, and even Ohio, the time of the image is most consistent with the GOES East image from 1915 UT --close enough. Also note that this nails the date. The date might have been reported in error (maybe a Greenwich date listed instead of a local date for example, or even a simple typo), but the clouds could not match even in general features unless the date is correct.

In the attached image, I've outlined the Earth with a circle that clearly shows the "defect" on the right where the phase isn't quite full. At the center of that circle, I've marked another small circle representing the sub-satellite point. The satellite was directly above that spot in the Gulf of Campeche when the image was made. The yellow line to the left of there marks the possible sub-Sun positions running along latitutde 22° 39.4' N (more exact since we know the time now) and ranging in longitude from 106° to 107° W, roughly. The larger light-yellow circle around the sub-satellite and sub-Sun points shows the region of specular reflection where we can see sunlight reflecting off the ocean in the original image. It is consistent that it is centered on the spot halfway between the two other locations, but it's a very rough estimate so no better than "consistent". I've also included a couple of GOES weather satellite images with time tags which help to confirm the time based on the clouds, as described above.

Incidentally, we can also think of this as a genuine navigation problem. We now have a rather good idea where the satellite was relative to the Sun-Earth line when the image was made. 

Frank Reed
 

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