Being in the northern hemisphere, on December 22, we observe a paradoxical phenomenon: the planet Venus

Being in the northern hemisphere, on December 22, we observe a paradoxical phenomenon: the planet Venus, being at the point of greatest elongation, rises exactly in the south. What latitudes are we in, and what is the elongation of Venus – east or west? Where was the Sun at this time?

The rise of Venus in the south in the northern hemisphere can occur only if its declination at this moment is
δ = ϕ – 90 °,
and at the same time it increases due to the motion of Venus among the stars (ϕ is the latitude of the place). Prior to this sunrise, Venus was non-ascending at this latitude. Being at the point of greatest elongation, Venus moves near the ecliptic in direct motion with an angular velocity equal to the angular velocity of the Sun. In this case, the Sun itself is at the point of the winter solstice, and the declination of Venus will increase if its elongation is east, and it overtakes the Sun in motion along the ecliptic (Venus will be in the constellation Capricorn). The declination of Venus at this time will be about –17 °, therefore, it happened at a latitude of 73 ° N. The sun on December 22 at this latitude does not rise above the horizon, and during the rise of Venus in the south it was 47 ° to the west, that is, not very deep under the southwestern horizon.

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