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Lunar cycles and illumination

> Thank you for the lunar information!  In school they taught me the moon cycle 
> was 28 (+ decimal) days between full periods, but that was grade school and 
> not astronomy courses in college.  This is most interesting!  My Celestron's 
> The Sky program lists moon phases.  It seems 6 months have a 30 day cycle and 
> 6 have a 29 day cycle.  This ran true for 2002-2003 and averages 29.5 days.  
> The pattern appears to be random but is also ordered in the fact each year 
> has 6 months with 29 and 6 with 30.  Also, the new moon and full moon did not 
> seem to be evenly divided in each month which is very interesting.  Is there 
> a physical reason for this or could it just be a coincidence?

Hi Cliff,

This is due to the fact, that the lunar orbit is no circle -- when the
Moon is close to the Earth (in perigee), it runs more quickly than when in
apogee. This results in visible change of its face, as the lunar rotation
is almost constant. When the Moon runs close to the Earth, her revolution
(orbital motion) is quicker than rotation (in angular terms) and then the
Mare Crisium on the right side of the Moon becomes more circular, getting
farther from the lunar limb. After apogee, it is closer to the limb (not
so easily visible without binoculars) and appears more elongated. The
extreme apogee/perigee distances of the centres of Earth and Moon differ
some 14 per cent of the mean distance (resulting in more than 1.25 ratio
of possible brightnesses due to the variable distance, the less extreme
ratio is just 1.14 however).

In fact, the orbit is even no ellipse, it's a complicated non-periodic
process due to disturbances by the Sun. The mean length of the synodic
cycle (synodic: with respect to the Earth-Sun line) is 29.53 days. The
true lengths of intervals between full moons are within 29.2--29.9 days.
One reason for the variability is, that in one cycle, two perigea can
happen (then it is shorter) or two apogea instead (meaning a longer

> For the past year I have been measuring horizontal illuminance cast by the 
> Moon and have never seen a reading rise above 0.1 lux or 0.01 footcandles.  
> This leads me to believe that *for my latitude* the Moon may never get high 
> enough in the sky to travel through only one atmosphere.  It is probably 
> traveling through more like 1.4 atmospheres instead because I live at 
> slightly above +41 latitude.  This is most interesting stuff that makes me 
> wonder.
> Resolution of my meter is 0.01 fc / 0.1 lux +/-3% (cosign corrected 
> selenium).  I get the feeling it may be rounding up to that number most of 
> the time because anything beyond 0.051 lux will naturally round up to 0.1 -- 
> the lowest reading available.  I do not know this to be fact, it is a logical 
> assumption.
> One fellow I know has seen readings as high as 0.24 lux which is 
> substantially higher than any readings I have seen.  He also claims this has 
> been published by other astronomers but I do not know if they were amateurs 
> or pros.

He is true. 

In winter the full Moon can be high in the sky and its light goes through
just 1.1 atmosphere thickness. For a perfectly clear air (zenith
extinction of just 0.20 mag) the direct moonlight could be, as my
programme says for Rocky Hill, when called as
     planet i c10 t0:24 d29.1 mjd ne f41.665 l-72.640 ut-5

2002- 1-29  at  5:24: 0, expressed in UTC, or
2002- 1-29  at  0:24: 0  (Tuesday)
 expressed in the used time, which is -5.00 h ahead of the UTC:

Julian date :  2452303.7250   Local sidereal time :  9: 6:37

Just planet number 10 (Moon) is displayed

 MJD     from S  ang.height far L-LS  illumin.  b   PA  long. PhA
         -------- -------  ---- ----  ------- ----- ----- ---
         degrees  degrees   AU  degr.   lux        d e g r e e
                        Ea.R.                            col.
52303.225    0.37  68.49  55.7  -176  2.5E-1   -4.5  17.8 -2.5  96.4


The Moon was a bit after full on your (approx. midnight) culmination, at
lambda=30 it would illuminate the ground by 0.27 lux (as got with
  planet c10 i t0:15 d29.1 mjd ne f41.665 l30 ut2  

For a bit dusty air with extinction of 0.30 mag in zenith the direct
horizontal illumination for your site would be just 0.23 lux. However, the
stray light goes mostly downward as well, so the total illumination should
definitely be over 0.25 lux.

Perhaps you missed the brightest and highest full moons during winter
(they were also almost perigee ones last two years, they will become
apogee ones, i.e. fainter after next two years, again perigee ones after
next four years... in a 9 years cycle).

In fact, the lunar values are still uncertain, as the project ROLO 
(as mentioned in my
   Linkname: [Astro]Re: Moon Light
        URL: http://amper.ped.muni.cz/astro/a/msg00024.html )
 is somehow sleeping -- I wrote to its chief recently, with no result.

I attach the programme planet as planet.exe (there has been still a
mistake, when the illumination computation has been overriden by air mass
computation, now it's OK, e.g. 
  planet  c10:5 t22:24 d28.1.2002 f41.665 l-72.640 ut-5 zm
 would give air masses for Moon and Jupiter two hours before lunar

clear skies for seeing the Comet (it's really beautiful),

Attachment: planet.exe
Description: DOS executable, from command line