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geocentric - ‘Earth centered’ Until four hundred years ago or so, the common conception was that the Earth was in the center of all things. Nicolaus
Copernicus changed all that.
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greatest elongation - ‘When either Mercury or Venus reach that part of their orbits where they are seen farthest away from the Sun in our sky, they are
said to be at greatest elongation. To the east of the Sun is in the evening sky, and to the west is a morning elongation. Yes, those directions are
correct. As you look up into the southern sky, east is to your left!