For a few days before and after a new moon, light from the Sun, reflecting off Earth and onto the Moon’s dark side, is just powerful enough to make the whole portion of the Moon facing Earth visible (see Figs. 1 and 2). This doubly reflected light (once from Earth’s surface, then from the lunar surface into our eyes) goes by the name earthshine. In the present note we discuss some features of earthshine and of the reciprocal phenomenon termed as moonshine.

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2.
The eccentricity of an elliptical orbit determines its closeness to a circle; it is the ratio of the distance between its two focal points to length of its major axis.
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4.
Reflectivity values of reflective surfaces
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5.
The Moon’s phase angle is simply that angle at the Moon that is subtended by Earth and the Sun.
6.
The expression for earthshine or moonshine luminous flux would be $122.7×103⋅κEarth⋅κMoon⋅REarth2l2⋅RMoon2l2.$ Here REarth = 6.37 × 106 m is the radius of the Earth, RMoon = 1.74 × 106 m is the radius of the Moon,  = 3.82 × 108 m is the mean distance between Earth and the Moon, κEarth (10%-90%) and κMoon (12%) are albedos of Earth and Moon, respectively; here moonlight flux is $122.7×103⋅κMoon⋅RMoon2l2=0.301x.$