Suppose, on the day of the vernal equinox, the planet Venus was at the point of greatest eastern elongation, while being near the ecliptic. At what latitudes of the Earth can Venus be seen in the sky when there is no Sun on it? Neglect atmospheric refraction.
During the greatest eastern elongation, Venus is 47 ° east of the Sun along the ecliptic, that is, given the date, in the constellation Aries. At this time, it is best seen in the evenings. At the moment of sunset, which has coordinates a = 0h, 5 = 0 °, sidereal time is 6 hours. The position of Venus in the sky at the time of sunset for different latitudes is shown in the figure. At this time, at the Antarctic Circle, the ecliptic coincides with the horizon, and Venus will go over the horizon simultaneously with the Sun, and will rise much later. With a further shift to the south, the visibility conditions for Venus, which has a northerly declination, will be even worse – it will be visible in the sky only during the day or not at all.
In the equatorial zone and the northern hemisphere of the Earth, Venus will be above the horizon after sunset, and it will not be possible to see it in the dark sky only near the North Pole, since the Sun will not set over the horizon there. Given the angular dimensions of the Sun, the final answer is that Venus will be visible in the sky when the Sun is not there, at latitudes from -66.2 ° to + 89.8 °.