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On 2019-12-12 12:02, Fred Hebard wrote:
> The fullest of the full moon was meant to occur last night on December 12 at 
12:12 am, eastern standard time.  It was billed as the 12-12-12-12 moon!
According to JPL Horizons the Moon phase angle reached a minimum of
1.6621° at Dec 12 05:31 UTC. That's the Sun - Moon - Earth angle. My
result doesn't necessarily contradict the above time, which is possibly
for an observer at the surface, not the geocenter. I haven't looked into
the sensitivity of this phenomenon to the observer location (geocentric
vs. topocentric).

Phase angle changes slowly even at .0001° precision, so its minimum
isn't as sharply defined as, for example, an equinox or solstice.

As for the last two columns in the table (phase angle bisector), I
confess they are beyond my comprehension. But I include the Horizons
explanation.


  Date__(UT)__HR:MN:SC.fff        S-T-O      phi  PAB-LON  PAB-LAT

  2019-Dec-12 05:28:00.000       1.6628   1.6624  79.6640  -0.8356
  2019-Dec-12 05:28:30.000       1.6628   1.6623  79.6665  -0.8354
  2019-Dec-12 05:29:00.000       1.6627   1.6622  79.6690  -0.8352
  2019-Dec-12 05:29:30.000       1.6627   1.6622  79.6715  -0.8350
  2019-Dec-12 05:30:00.000       1.6627   1.6622  79.6740  -0.8348
  2019-Dec-12 05:30:30.000       1.6627   1.6621  79.6765  -0.8346
  2019-Dec-12 05:31:00.000       1.6627   1.6621  79.6790  -0.8344
  2019-Dec-12 05:31:30.000       1.6627   1.6621  79.6815  -0.8342
  2019-Dec-12 05:32:00.000       1.6627   1.6621  79.6840  -0.8340
  2019-Dec-12 05:32:30.000       1.6628   1.6622  79.6864  -0.8338
  2019-Dec-12 05:33:00.000       1.6628   1.6622  79.6889  -0.8336


Column meaning:

TIME

   Times PRIOR to 1962 are UT1, a mean-solar time closely related to the
prior but now-deprecated GMT. Times AFTER 1962 are in UTC, the current
civil or "wall-clock" time-scale. UTC is kept within 0.9 seconds of UT1
by introduction of integer leap-seconds for 1972 and later.


  S-T-O =
    "S-T-O" is the Sun->Target->Observer angle; the interior vertex angle at
target center formed by a vector to the apparent center of the Sun at
reflection time on the target and the apparent vector to the observer at
print-time. Slightly different from true PHASE ANGLE (requestable
separately)
at the few arcsecond level in that it includes stellar aberration on the
down-leg from target to observer.  Units: DEGREES


    phi  PAB-LON  PAB-LAT =
    "phi" is the true PHASE ANGLE at the observer's location at print time.
"PAB-LON" and "PAB-LAT" are the J2000 ecliptic longitude and latitude of the
phase angle bisector direction; the outward directed angle bisecting the arc
created by the apparent vector from Sun to target center and the astrometric
vector from observer to target center. For an otherwise uniform
ellipsoid, the
time when its long-axis is perpendicular to the PAB direction approximately
corresponds to lightcurve maximum (or maximum brightness) of the body.
PAB is
discussed in Harris et al., Icarus 57, 251-258 (1984).

    Units: DEGREES, DEGREES, DEGREES, DEGREES

   

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