Eclipse
Umbra, penumbra and antumbra

For any two objects in space, a line can be extended from the first through the second. The latter object will block some amount of light being emitted by the former, creating a region of shadow around the axis of the line. Typically these objects are moving with respect to each other and their surroundings, so the resulting shadow will sweep through a region of space, only passing through any particular location in the region for a fixed interval of time. As viewed from such a location, this shadowing event is known as an eclipse.

Typically the cross-section of the objects involved in an astronomical eclipse is roughly disk-shaped. The region of an object's shadow during an eclipse is divided into three parts:

A total eclipse occurs when the observer is within the umbra, an annular eclipse when the observer is within the antumbra, and a partial eclipse when the observer is within the penumbra. During a lunar eclipse only the umbra and penumbra are applicable, because the antumbra of the Sun-Earth system lies far beyond the Moon. Analogously, Earth's apparent diameter from the viewpoint of the Moon is nearly four times that of the Sun and thus cannot produce an annular eclipse. The same terms may be used analogously in describing other eclipses, e.g., the antumbra of Deimos crossing Mars, or Phobos entering Mars's penumbra.

The first contact occurs when the eclipsing object's disc first starts to impinge on the light source; second contact is when the disc moves completely within the light source; third contact when it starts to move out of the light; and fourth or last contact when it finally leaves the light source's disc entirely.

For spherical bodies, when the occulting object is smaller than the star, the length (L) of the umbra's cone-shaped shadow is given by:

where R is the radius of the star, R is the occulting object's radius, and r is the distance from the star to the occulting object. For Earth, on average L is equal to 1.384 × 10 km, which is much larger than the Moon's semimajor axis of 3.844 × 10 km. Hence the umbral cone of the Earth can completely envelop the Moon during a lunar eclipse. If the occulting object has an atmosphere, however, some of the luminosity of the star can be refracted into the volume of the umbra. This occurs, for example, during an eclipse of the Moon by the Earth — producing a faint, ruddy illumination of the Moon even at totality.

On Earth, the shadow cast during an eclipse moves very approximately at 1 km per sec. This depends on the location of the shadow on the Earth and the angle in which it is moving.
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