Apparent position of Venus corrected for phase
From: Frank Reed
Date: 2012 Sep 30, 11:30 -0700

Spinning off from another thread...

The position of the planet Venus in the "official" Nautical Almanac is not the true position of the planet's center. It's shifted by as much as 0.5 minutes of arc. The editors of the almanac years ago decided to list the position of the "center of light" for Venus. Venus goes through phases like the Moon, and when it is close to the Earth, it is a slim crescent with an apparent diameter of just about a minute of arc. If you're looking at Venus with an instrument, like a typical marine sextant, which can detect angular differences of a few tenths of a minute of arc, but can't quite visually resolve the disk of Venus at that same angular scale, then this procedure, perhaps, makes sense, though it's just barely useful. For lower resolution, e.g. eyeball observations without a telescope, it doesn't matter since the difference is below the ability of the eye to resolve (at best around 0.7 minutes of arc). For higher resolutions, like with a telescope equipped with a 7x scope or better, this choice is probably not a good idea since the disk of Venus can be visually resolved --you can see the little crescent. In that case, a navigator can use the actual center of the disk of Venus (or even its limb if a semi-diameter correction is added in). So overall, this idea of listing the position of the center of light has limited use and really leads to more confusion than value, as far as I can judge.

Apart from the "official" Nautical Almanac, nearly all other sources list the actual center for the position of Venus. For example, if you look at the position for 18h on December 15, 2013 from my online Nautical Almanac data here:
http://www.ReedNavigation.com/lunars/nadata_v5.html
and compare with the position from the USNO online calculator here:
http://aa.usno.navy.mil/data/docs/celnavtable.php
you'll find the exact same position. Lu Abel, you asked about Omar Reis's online Nautical Almanac (the "tecepe" site). I don't bother with that one myself anymore since I have found a number of small errors in it over the years.

We can still calculate the position of the center of light. One can work out various integrals for this and get quite formal about it, but we're talking here about a visual perception, not an exactly calculable astronomical quantity. Find yourself a nice montage of the phases of Venus. I'm attaching one to this message. I've increased the contrast to make the phases look more like their visual appearance in a small telescope. Now "squint" at each little Venus image and try to pick a spot that would correspond to the center of brightness of the crescent, imagining it just barely resolvable by your eye. On the attached image, I've indicated my best estimate with a little dot for each phase. Naturally the center of light falls somewhere on the line between the actual center, or "center of figure", and the leading edge of the illuminated limb. Its distance from the actual center is always less than the semi-diameter of Venus (and the SD of Venus is equal to the HP of Venus, which you can find in the almanac or elsewhere, since Venus is the same size as the Earth). When I was done placing all my dots on these phase images, I noticed that each estimated center of light was basically a constant distance from the leading edge of the illuminated limb. It's just about 0.1 minutes of arc. This yields a simple algorithm for finding the center of light from the center of figure (and vice versa if you're using the Nautical Almanac position). First get the SD (or HP) of Venus. From that subtract 0.1'. Call whatever's left the "offset". Now look at the relative positions of Venus and the Sun in the sky. The center of light is shifted towards the Sun, away from the actual position of Venus, by that "offset" amount. For most dates, this difference will be 0.1' or less. But when Venus is close to the Earth, it could be as large as 0.4'. Typically the position will change both the GHA/SHA and the Declination, too. You can work it out by drawing a little coordinate diagram remembering that the offset is always in the direction of the Sun in the sky. I don't think this offset correction for the center of light is ever necessary, as I said above, but it could be included as an option in software solutions.

-FER

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