Chris Peterson wrote:... But maybe I'm making a logic error connecting the compass direction of the lasers to the orientation of the lasers on the sky.
Yes, that logical correlation to horizontal coordinates does fall apart. Actually, the heading (azimuth) is close to 311° & 63° altitude.
Using graphical and
necessary trigonometric analysis, I'm quite sure of the local circumstances comprising the APOD image including the 50-cm observatory location, time and consequently AZ/ALT of M42. See the APOD overlaid on a Stellarium field below (M42 coordinates and time are on the image):
The green arrow in the overlay represents the telescope optical axis; the white arrow points to North. Empirically matching M42 orientation in the sky does not yield a unique solution - the laser beam angles in horizontal coordinates are confusing and totally confound a certifiable solution. However, I discovered a 2016 SPIE slide-deck presentation
stating the 4LGS asterism is adjustable only radially, and it is a square locked to AZ/ALT horizontal coordinate axes. The presented APOD image shows a diamond shape, so clearly the image was rotated for aesthetic reasons; beams heading upward appear more normal than beams heading downward. But, I wasn't happy with relying on a constant square asterism so I did the trigonometry to solve for the projected angles in the APOD given the specific launch distance and reasonable height difference
from the 50-cm telescope. Surprisingly, the calculated and actual slopes of beams agree within a few percent.
Next, the image time stamp says the creation date was 3/13. The solution does allow for this 3/13 date as the overlay image shows, but as I said isn't required - first light for the 4LGS was in April 2016. Lastly, I looked at two possible observatory locations: the one due north and the one almost due east. The eastward location does not agree at all where the calculate slopes differ by 50%.
There is a second possible solution with the square asterism rotated another 90° but this also makes no sense. The northern location does agree with vendetta's statement that the 50-cm telescope is north of UT4. In Google image of the VLT site, I show the azimuth range for all possible M42 images on March 13. The azimuth limits are bounded by sunset
, with the laser heading also shown.
The solution holds together in all regards of consideration and calculation I could muster. I think I got it