cc: michael.waterman@gecm.com
Hi all -
Mike Waterman showed a neat bit of science when he posted his
note concerning his measurements of the brightness of the moon
(and therefore, of the sky and the limiting magnitude). The
"ball bearing photometer" he described was used quite a bit over
the past two centuries to visually measure the brightness of
objects (such as total lunar eclipses) for which there were no
comparison objects of similar magnitude.
Mike's comments on not finding any references to the moon's
brightness variation with phase sent me scurrying to my all-
purpose astronomical reference book, "Astrophysical Quantities",
by C.W. Allen, University of London - Athlone Press; 2nd ed.,
1963. I was not surprised to find a whole page on the brightness
of the moon.
Following is a table of the "Moon's phase law", which, for given
phase angles (sun-moon-earth angle; full moon = 0 degrees, new
moon = 180), lists the magnitude difference (mag. at phase angle
- mag. at phase angle 0):
0 0.00
5 0.08
10 0.23
20 0.51
30 0.79
40 1.06
50 1.35
60 1.62
70 1.91
80 2.24
90 2.63
100 3.04
110 3.48
120 3.93
130 4.44
140 5.07
150 5.9
160 7.5
Since the sun is 400 times farther away than the moon, the
moon's elongation will be very close to (180 - phase angle). So,
the last entry in the table says that a crescent moon at an
elongation of 20 degrees from the sun will be 7.5 magnitudes
fainter than the full moon, or about magnitude 12.7 - 7.5 = -5.2.
I'll let Mike try to fit a curve to this.
The book also lists phase laws for the moons of Jupiter, for
those concerned about the sky brightness on that planet.
cheers, Rich Keen
Coal Creek Canyon, Colorado, USA (39.877N, 105.391W, elev 2728m)
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