Can Venus be both an evening and a morning star on the same day?
My knee-jerk answer is yes, but it is a matter of defining the term 'morning' and 'evening' very exactly.
Clearly an object is in the evening sky if it is on the EASTERN side of the Sun, with the Sun's eastern limb exactly below the western horizon. The object is in the morning sky if it is on the WESTERN side of the Sun, with the Sun's western limb just below the eastern horizon. Confused? Just draw the picture and you will see what I mean.
Now, the Sun is 1/2 a degree in diameter, and it travels across the sky at a speed of 360 degrees per 365 days or just under 1 degree per day .This means that, for example, near the equinoxes, day and night are about 12 hours long and the Sun travels 1/2 a degree to the EAST during each part of the day. For an object that is stationary in the sky during this time, I can easily imagine that at sunrise, the object would be exactly on the Sun's east limb in the evening sky, and then by sunrise, the Sun has occulted the object by exactly its own diameter so that the object is now on the Sun's west limb as a morning sky object. For Venus, Venus has its own daily motion that depends on its orbital location relative to the Earth, so its location after 12 hours could enhance this effect.
In any event, Venus would have to be in very close conjunction with the Sun, called its Inferior Conjunction. At the start of the conjunction, Venus will be an Evening Star, and at its end it will be a Morning Star.
Copyright 1997 Dr. Sten Odenwald
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