Visibility of Venus during the march equinox

[kaleidoscope]

So this weekend I read a little about the Dresden Codex of the Maya (their astronomical log) and played a little bit with Stellarium trying to imagine the sky they saw. I noticed something that I think is interesting, Venus wasn't very visible during the equinox every four years because the sunlight would cover it (from Mesoamerica). I looked for some information about it and found some tables of the Venus-Sun Conjunctions for several centuries, and conjunctions appear to take place around march an repeat about the same date every 4 years. http://www.astropro.com/features/tables/geo/ve-su/ve000su/vesu27.html For instance, Stellarium predict it won't be visible in 2013, 2017, 2021, etc.

So, does Venus really "disappear" in the sky every 4 years during the march equinox?

 

[willem2]

Venus goes round the sun in 224.701 days and the Earth in 365.256 days, so in one earthyear venus, goes 356.256/224.701 = 1.62550 times round the sun.

In 4 years, venus will go 6.50208 times round the sun, so if venus is exactly in front of the sun at the start of the 4 years, it will be nearly exactly behind the sun at the end of four years (it will shift 0.75 degrees).
There will be a period of 80 years intervals, where venus is within 7.5 degrees of the sun, and very hard to see.

 

[kaleidoscope]

Venus goes round the sun in 224.701 days and the Earth in 365.256 days, so in one earthyear venus, goes 356.256/224.701 = 1.62550 times round the sun.

In 4 years, venus will go 6.50208 times round the sun, so if venus is exactly in front of the sun at the start of the 4 years, it will be nearly exactly behind the sun at the end of four years (it will shift 0.75 degrees).
There will be a period of 80 years intervals, where venus is within 7.5 degrees of the sun, and very hard to see.

Nice. How did you calculte the 0.75 degrees shift and the 80 year interval?

 

[willem2]

Nice. How did you calculte the 0.75 degrees shift and the 80 year interval?

The 0.75 degrees is from the 0.00208 extra rotations that venus makes in 4 years. This is however not the angle that venus moves as seen from the earth, and therefore the 80 years that I tought venus would remain too close to the sun to see isn't correct.

When the angle venus/sun/earth is 7.5 degrees and venus is close to its inferior conjunction, the angle venus/earth/sun is much larger than 7.5 degrees, so venus will be further away from the sun as seen from the earth.

When Venus is close to its superior conjunction, and the angle venus/earth/sun = 180-7.5 degrees, the angle venus/earth/sun will be smaller than 7.5 degrees.

If venus is above or below the ecliptic, because both orbits aren't exactly in the same plane, the angle between venus and the sun will look much larger when venus is closer to the Earth also.

Looking in stellarium, you can see that venus is much closer to the sun in the years 2013 +- 8n. Venus is almost exactly behind the sun in 2037, but is probably still invisible with the naked eye in in 1941 or 2133, while in 2017+- 8n years, venus never gets closer than about 5 degrees to the sun, and is probably only invisible 5 or 6 times.