# Periodic behavior of Venus

After a couple months of watching a very bright Venus appear at dusk and set soon after the Sun, I've noticed that it seems to have temporarily disappeared to the naked eye. I used a virtual sky simulator (Stellarium) to confirm that the Evening Star has indeed transitioned to being the Morning Star (though due to obstacles blocking my view of the horizon in my backyard, Venus is still too close to the Sun for me to witness it at dawn before sunrise renders it invisible).

What is the period of Venus's alternation between morning and evening visibility? I gather this isn't a simple seasonal period as its visibility should depend on the Sun-Earth-Venus angle rather than just Earth's yearly orbit.

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Assumed a Venus year is 0.615 198 Earth years.

0.615 198 yr / (1 - 0.615 198) = 1.598739 yr = 583 days 11 hours 24 minutes for one period in mean, or roughly 19.5 months.

That's 1.598739 periods for Earth and 2.598739 periods for Venus: 1.598739 * 365.256 days = 583.95 days = 2.598739 * 224.705 days

The relative accuracy should be somewhere near 1e-5.

Since both orbits are elliptical the actual period oscillates around that mean value.

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Explained here en.wikipedia.org/wiki/Elongation_(astronomy) – Envite Jan 16 '14 at 20:30
@Envite Thank you for the link. I knew there had to be a wiki for it, but I didn't know what to call the effect. – David H Jan 17 '14 at 18:29