Soft and Multiple Climax

Tomorrow evening, Venus will be at the peak of her  nearly eight-month-long performance in the evening sky.

Or, sort of. To define the climax is not quite simple.

The event that happens now is the “greatest eastward elongation.” Venus appears farthest out from the Sun, in the eastward direction (leftward, as seen from Earth’s northern hemisphere).

This angular distance is 45.4 degrees. Venus’s orbit being nearly circular, the maximum elongation doesn’t vary much; 45.4 degrees is about the least it can be, and it can reach 47.15 (as it will on 2017 Jan. 12).

The instant of greatest elongation is June 6, 18 UT, which is 2 PM by eastern American clocks. This is when Venus starts to move more slowly across the map of the sky than the Sun does.

But the exact time hardly matters for an observer.  When a quantity such as elongation is reaching a maximum, it is changing most slowly, so it is very little different for many hours either side of the peak. The peak is more like a rounded hill: where is the exact top? After all, what is happening in space is that Venus in its path around the Sun is swinging toward us, and this is the moment when we see its orbit at a tangent.

This is why I call it a “soft” event.

And why is it “multiple”?

Well, elongation is not the only climax Venus reaches. There is also the time when it stands highest above your horizon around the time of sunset, and this is affected by the angle of Venus’s path to your horizon; in other words, by your latitude. So for an American latitude of 40 north, that date was back on May 8. For an Australian at 35 degrees south, it won’t come till July 4.

And does Venus, when out at this conveniently great distance from the Sun, appear at its brightest or largest? No, because these are affected by the size and shape of the planet’s sunlit side as it whirls toward us: it is growing longer, but slenderer.

Venus’s apparent shape and position at sunset for latitude 40 north. It is shown 480 times too large; the dots at one-day intervals are nearer to its real size. Part of an illustration in Astronomical Calendar 2015.

These two factors fight with each other, and there will come – on July 10 – a moment of “greatest illuminated extent.” That means: the angular area of the part of the sunlit surface that we can see is greatest. Mark Gingrich in 2000 suggested this as a good event to calculate, rivaling “greatest elongation” in importance, because it is of obvious interest to anyone observing Venus through a telescope. It’s when you see the most Venus.

Then, there’s the moment when Venus – brightest of all planets – comes to its peak of brightness. This is affected by another factor: the nearness of that sunlit surface to us; so the moment of maximum brightness comes two days later, on July 12. Venus then reaches magnitude -4.5. This too is a soft hill of an event: Venus is seldom below magnitude -4.

And there’s one more phenomenon, called by the perhaps intimidating Greek-derived name “dichotomy.” The tomy part means “cutting,” as in lobotomy, vasectomy, and anatomy. The dicho part is from the same root as Greek and Latin duo, “two.” Dichotomy is simply the moment when the disk of Venus is divided into white and black halves by a straight line down the middle. So the only picture we need is:

D

Dichotomy has to be near the moment of greatest elongation, because the angle Earth-Venus-Sun is a right angle. But not exactly, because of the slight departure of Venus’s orbit from a circle. So the moment of geometrical dichotomy, this time, is 9 hours earlier: June 6, 9 UT.

The curious thing about the dichotomy of Venus is that it doesn’t appear to happen at the time when it geometrically should, but earlier. Venus’s visible surface is soft, the top of the blanket of cloud that wraps it. The brilliant white of the sunlit side must grade through a narrow transitional gray zone into the black of night, and apparently our eyes draw the boundary slightly on the whiteward side. It has already happened: when you study Venus in your telescope tomorrow, can you see that the line down the middle already looks slightly concave?