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George Huxtable wrote:
> Wolfgang Köberer is right to question that example of an intended lunar 
> distance measurement by camera, in Navigator's Newsletter 99. Andres Ruiz 
> has provided the relevant link in-
> http://www.starpath.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=31;t=000040

That's a conventional altitude shot for a LOP. Also, the location is at 
opposite corner of the U.S. from Florida.

This page seems to be the right one:
http://www.starpath.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=31;t=000017


> Now look at the spacing between the Moon and Jupiter, that's being measured 
> in the photo in an attempt to determine the Moon's position along its track. 
> You can see that it's nowhere near that optimum direction; in fact, it's not 
> far short of being at right-angles to it. The Moon isn't travelling towards 
> or away from Jupiter, it's simply going past it.

My lunar program confirms the bad geometry. As the output (below) shows,
the lunar distance rate of change at the observer is only about 1" per
minute! However, the geocentric rate is 14" per minute due to the
different point of view.

I came up with the idea of "velocity efficiency" as a figure of merit
for the geometry between the bodies. It's the rate of change of lunar
distance, divided by the total angular velocity of the bodies. If
they're moving directly toward or away from each other, velocity
efficiency is 100%. But it's only 4% in the photo.

Checking the computed position angles vs. the image shows that it seems
to preserve the original orientation you would have seen that night.
That is, it hasn't been rotated so it could be cropped for display.

The observed lunar distance reported by the program is a little
different from the value on the web page. That's because I repeated the
pixel computations but rounded the result to a higher precision, and
added Jupiter's refracted semidiameter to simulate an observation from
the Moon's near limb to Jupiter's far limb.

That latter correction is necessary the program has no provision for a
center to (Moon) limb observation, unless the other body has zero
semidiameter. From the relative orientations of the bodies and the
direction of the Sun, the correct limbs to observe are determined. If
the actual observation was different, the measured angle has to be
adjusted. In this case, I believe the center of Jupiter was measured
rather than its limb. The difference is only a couple pixels, though.

It's interesting that if the web page computation is repeated, but with
the refracted Moon diameter from my program instead of the USNO value,
the measured lunar distance is only 22" different from the prediction!
This shows the difficulty of determining image scale from such a small
object. In fact, I think they have the cart before the horse. It would
be better to first use lunar distance photos to determine the scale and
distortion of the camera. Then see how well you can measure an unknown 
angle.


Program Lunar1.

2006-03-19T05:38:23.00  UTC (Gregorian)
              + 0:00.28  delta UT (UT1-UTC)
2453813.735743  JD (TT)
2006-03-19T05:39:28.19  TT (Gregorian)
           +00:01:04.90  delta T (TT-UT1)
2006-03-19T05:38:23.28  UT1 (Gregorian)
           -05:20:53.60  LMT-UT1
2006-03-19T00:17:29.68  LMT (Gregorian)
              -07:52.71  equation of time
2006-03-19T05:30:30.57  GAT (Gregorian)
2006-03-19T00:09:36.97  LAT (Gregorian)

Moon, apparent geocentric (true equinox)
14h48m52.97s  -19°54'57.2"  RA, dec
55'33.9"  15'08.1"  HP, SD

Jupiter, apparent geocentric (true equinox)
15h05m47.63s  -16°05'53.1"  RA, dec
  0'01.9"   0'20.8"  HP, SD

geocentric separation angle:
    5°32'37.3"  (center to center)

geocentric angular rate, velocity efficiency:
-13.7" per minute
44% of total angular velocity is utilized

observer position:
+27°12'12.0" - 80°13'24.0"  north lat, east lon
- 80°29'40.2"  ephemeris east lon
0 meters above ellipsoid

atmosphere at observer:
20°C  68°F  temperature
1010.0 mb  29.83" Hg  altimeter setting
1010.0 mb  29.83" Hg  station pressure

Moon illumination:
48°  phase angle (0 = full Moon)
152°  position angle to Sun (0 = 12 o'clock)
5°  -63°  Sun az, alt

Jupiter illumination:
8°  phase angle (0 = full)
151°  Sun position angle (0 = 12 o'clock from Jupiter)

position angles:
80°  Moon to Jupiter
263°  Jupiter to Moon

topocentric unrefracted angles:
    5°37'05.9"  center to center
    5°22'11.7"  Moon near limb to target far limb

topocentric angular rate, velocity efficiency:
-1.1" per minute
4% of total angular velocity is utilized

topocentric refracted angles:
15'14.8"  moon SD (refracted)
  0'20.8"  target SD (refracted)
    5°37'00.0"  center to center
    5°22'06.0"  Moon near limb to target far limb

    5°23'55.7"  observed lunar distance
    0°01'49.7"  error (observed - predicted)

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