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Why is the moon's shadow has a dark center surrounded by a region of increasing brightness? This is because the earth is also illuminated by

Why is the moon's shadow has a dark center surrounded by a region of increasing brightness? This is because the earth is also illuminated by the other, more distant, stars. The moon has greater angular size when observed from the center of the shadow since it is the place closest to the moon. That means in the center of the shadow the moon blocks not only the light emitted by the sun but also more light emitted by the other stars than in other regions. This is because the moon re-reflects some light reflected by the earth's lighted part. So some light finally reaches the surface of the earth in the shadowed region. The central part of the shadow is the darkest because closer we come to the center of the shadow less re-reflected light reaches the earth. This is because of the light diffraction. Central part of the shadow is the minimum of the light intensity, farther from the center the intensity rises. Other orders minima cannot be seen since they should be observed on the angles larger than the earth's angular size (observed from the moon). This is because the sun is an extended source. The darkest part

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