# Phases of Venus

A well-known mathematician Gauss recounted that one day he invited his mother to look into the astronomical pipe on the phases of Venus, brightly shining in the evening sky. The mathematician thought to amaze the mother by surprise, since the pipe phase of Venus is visible in the shape of a sickle. He was surprised, however: he put his eye to the eyepiece, the woman did not express any amazement at the sight of the planet, and asked only why the sickle is turned in the tube in the opposite direction... Gauss did not suspect until that time that his mother distinguishes between phases Venus even with the unaided eye. Such acute sight is very rare. The first records of observations of the phases of Venus were made by Galileo Galilei in 1610. Venus was observed many times with the naked eye, but before the invention of the telescope. There was no indisputable historical evidence of the observation of the phases of Venus. Using a telescope, Galileo was able to observe Venus, passing successively through all phases, which, at that time, was excluded by the Ptolemaic system. The observations obtained corresponded to the Copernican system and to some other systems.

The phases of Venus are special in that the diameter of the planet in different phases is not the same: a narrow sickle with a diameter is much larger than the total disk. The reason is different distance from us of this planet in different phases. The average distance of Venus from the Sun is 108 million km, the Earth is 150 million km. It is easy to understand that the nearest distance of both planets is equal to a difference of 150-108, i.e. 42 million km, and the furthest is 150 + 108, i.e., 258 million km. Consequently, the removal of Venus from us varies within these limits. In the immediate vicinity of the Earth, Venus is facing us with an unlit side, and therefore its largest phase is completely invisible. Moving away from this position of "noveneeria", Venus takes the form of a sickle, the diameter of which is less than the sickle wider. Venus reaches its maximum brightness not when it is visible by a full disk, and not when its diameter is the largest, but in some intermediate phase. The full disk of Venus is seen at a 10 "angle of view, the largest sickle is at an angle of 64". The highest brightness of the Venus phase reaches three decades after the "noveneeria", when its angular diameter is 40 "and the angular width of the sickle is 10". Then Venus shines 13 times brighter than Sirius, the brightest star of the whole sky.

In Nineveh, in the library of King Ashurbanipal, two text that plunged into the astonishment of the modern astronomers. This is a table of phases of Venus, compiled from observations in Babylon during the 21 years of the reign of the Babylonian king Ammizadugi (1646-1626 BC). The data turned out to be so accurate (errors in the measurement of angular values did not exceed fractions of a second), that with their help it was possible to establish an absolute chronology of the Old Babylon era. The only thing that remains unclear is how, without modern optics, the Babylonian astrologers have achieved such high accuracy.