During the greatest elongation of Venus at some point on the Earth, the Sun is visible in the south, and Venus is at the same height in the north. Could this be, if so, in what latitudinal regions of the Earth and at what height above the horizon were the Sun and Venus? Solve the same problem for the case when the Sun is in the west and Venus is at the same height in the east.
During the greatest elongation of Venus, this planet and the Sun are on the ecliptic 47 ° apart. Recall that exactly one large circle of the sphere can be drawn through two different points on the sphere that are not opposite. In the case of the Sun and Venus, this large circle will be the ecliptic (during the greatest elongation, Venus moves away from the ecliptic by a small angle, which is insignificant for this task). If the Sun and Venus are at equal heights in the south and north, then a large circle drawn through them will also pass through the zenith and points of the south and north, that is, the ecliptic will coincide with the celestial meridian and thus will pass through the North and South poles of the world, which should not be can.
If the Sun is in the west, and Venus is at the same height in the east, then a large circle drawn through them will pass through the zenith and points of the west and east. The ecliptic can be so located in the sky in the northern tropic at 6 o’clock in sidereal time and in the southern tropic at 18 o’clock in sidereal time. Zenith is midway between the Sun and Venus, 23.5 ° degrees from both stars. Consequently, their height was 66.5 °. It can also be added that this was the greatest eastern elongation of Venus, and it happened around May 30, if the observations took place in the northern tropics (the Sun did not reach 23.5 ° to the summer solstice point) or around November 30, if the observations were made in the southern tropics.