Many attempts have been made to estimate the brightness of the moon in comparison with the sun and the stars. The results obtained by Sir John Herschel, Bond, Miner, Pickering and others show a range of over 20% but the mean result indicates that the sun is about 465,000 times brighter than the average full moon. On account of the varying distance of the moon from the sun and the earth there must be a real variation of over 2o%. The variation of the brightness of the moon with its phase is complicated by the nature of the surface and the varying angle of incidence of the sun's light. Although at first quarter half of the hemisphere turned towards the earth is illuminated, it appears only to as bright as
full moon and at third quarter it is only i as bright. This is only partly due to the fact that near the terminator the sun's rays strike the surface very obliquely. The greatest cause of the relative faintness of the half moon must be the unevenness of the moon's surface so that an important fraction of the surface is in the shadow. The amount of sunlight reflected by the moon is only about one-fourteenth of the total sunlight falling on it. This is a small fraction compared with that for cloud-bound planets, but it is of the order to be expected from a body with no atmos phere and with a rocky surface. Of course, this is only an average value and different areas of the moon differ widely in reflecting power. E. C. Pickering in America was the first to determine the relative brightness of different parts of the moon, and his work has been continued by European observers. They find that the
darkest parts of oceanus procellarum and mare crisium reflect only as much as the very bright crater Aristarchus.
The total brightness of the moon is reckoned as equal to about one-quarter of a meter-candle, equal, that is, to a ioo candle power lamp at a distance of 22 yards.
Constants of the Moon's Size and Motion. Synodic month (relative to sun) . . . . 29.53059 days Sidereal month (relative to stars) . . . . 27.32166 Tropical month (relative to equinox) . . . 27.32156 Anomalistic month (relative to perigee) .
Nodal or draconic month (relative to node) . . 27.21 2 2 2 Mean eccentricity ......
Revolution of perigee (direct) . . . 3232.9 days node (retrograde) . . . 6793.5Mean inclination of orbit to ecliptic . .
43" Maximum 5°
. Minimum
57' Inclination of axis of rotation to ecliptic 0 , le 3i'
(FrallZ) 1I 32 6 ' (Hayn) Lunar parallax 57'
Mean apparent diameter
7" Mean distance from earth . . . . 238,86o miles Maximum distance 252,710 " Minimum distance . . . .
/y Diameter ...... . . . 2159.9 " in terms of earth's diameter . . .27227 Mass in terms of that of earth . . . :81 56 Density in terms of water . . . . 3'33 that of earth . . . . 0.6043Ratio of gravity to gravity at the earth's surface 0-165 Maximum geocentric libration in longitude . .
54' latitude . . 9° so'Fraction of moon's surface always invisible . 0.450