Tuesday, November 29, 2011

The synodic cycle of Venus, and why it is currently the evening star

The planet Venus is currently in position on its orbit to function as the beautiful evening star. No doubt you have noticed it in the sky at sunset, along with the waxing crescent moon. The moon is currently further and further behind the sun each evening, ever since the sun "overtook" the moon to cause a new moon on the 25th of this month (see explanation of the mechanics of this process here). Above is a picture of the first sliver of the moon after the new moon, following the sun towards the sunset on the 26th.

Venus spends part of its time as the evening star and part as the morning star. Because the orbit of Venus is interior to the orbit of the earth (closer to the sun than the orbit of the earth), Venus is always seen relatively near to the sun, either in the morning or the evening (the same holds true for Mercury). It will never be seen traversing the entire sky during the middle of the night the way the planets whose orbits are exterior to the orbit of the earth can be seen to do (Mars, Jupiter and Saturn in particular, with the naked eye).

The mechanics of this process are well explained in this webpage by astronomer John P. Pratt. That page contains a helpful diagram of the orbits of the earth and Venus which can assist in understanding these mechanics, and which is reproduced in simplified form below.

In this diagram, the sun is obviously in the center, and the orbits of the earth (outermost) and Venus inner ring) are shown around the sun. The earth is indicated as a blue disc on the outer ring, and various positions of Venus are shown as numbered grey circles on the inner ring.

This diagram shows the "synodic" cycle of Venus. A "synod" is a gathering or meeting, and the term "synodic" denotes the period of time that it takes for a heavenly body to reappear at the same point relative to another heavenly body -- in this case, the synodic cycle of Venus relative to the sun as seen from earth. The synodic period of Venus is 584 days, as explained very clearly and helpfully on the webpage linked above.

The points of the synodic cycle marked on the diagram above are as follows:
  • 1. Venus appears after being invisible due to passing behind the sun, from the perspective of the earth. Venus is invisible for about fifty days between point 6 and point 1. At point 1 and until it reaches point 3, Venus will be "east of the sun" and therefore will be trailing the sun, and thus it will be the evening star. You can easily verify that Venus is the evening star in the positions from point 1 to point 3 by looking at the blue disc of the earth and thinking of it turning on its axis, which you are looking down on from a point over the north pole (thus the disc is turning counter-clockwise). As a point on the edge of the disc turns around towards the sun, it is daytime to an observer at that point, and as the disc keeps turning counter-clockwise, the sun will eventually disappear from view to that observer, and Venus will still be visible to that observer.
  • 2. Venus reaches its point of "maximum eastern elongation" -- the greatest angle of separation from the sun on this side of its orbit, as viewed from the earth (it will reach the same maximum angle again on the other side of its orbit, at point 5). This maximum angle of separation from the sun (or "elongation") is about 47o for Venus.
  • 3. Venus begins to be "swallowed up" by the sun and hence invisible. This is somewhat analogous to the new moon, except that the moon goes from being ahead of the sun to trailing the sun at the new moon, and Venus goes from being an evening star that trails the sun to being a morning star that leads the sun during this time. Venus will be invisible for approximately eight days between point 3 and point 4.
  • 4. Venus emerges onto the western side of the sun, and will now be the morning star (it may be somewhat confusing to learn that Venus is termed "west" of the sun when it is a morning star, since morning stars are seen in the east, but the way to reconcile this terminology is to think about the fact that when Venus is the morning star, it will be closer to the western horizon than the sun at daybreak: it will be ahead of the sun when the sun comes up in the morning over the eastern horizon -- Venus will already be a bit ahead of the sun and on its way towards the west). Venus will be the morning star from point 4 through point 6.
  • 5. Venus reaches its point of maximum western elongation, which is analogous to the situation described in point 2 above.
  • 6. Venus disappears behind the sun for another fifty-day period, enroute to starting the synodic cycle over again.
There are various tables on the internet which show the dates at which Venus passes through various points on its synodic cycle over the years. Here is one from Wikipedia. It shows that Venus passed its point of maximum western elongation (point 5 in our discussion) on January 8 of this year 2011, and that it will get all the way around to its point of maximum eastern elongation (point 2 in our discussion) on March 27 of 2012.

The terms "superior conjunction" and "inferior conjunction" are used in reference to the two planets with orbits interior to earth, Venus and Mercury, to designate the points at which they pass the sun on the far side (superior) and near side (inferior) from the point of view of an observer on earth. Thus, superior conjunction is the point midway between point 6 and point 1 of our discussion and diagram, and inferior conjunction is the point midway between point 3 and point 4 of our discussion and diagram. As can be seen from the table linked above from Wikipedia, Venus passed the point of superior conjunction on August 16 of this year 2011, and thus we are seeing Venus currently between points 1 and 2, and closer to 1 than 2 right now.

Here is a link to another table which shows similar data for Venus going out to the year 2050 and back to the year 1900. To find 2011 and 2012, you can move up to page 10 in that online document.

There is a lot more celestial mechanics related to the motions of Venus, including the fascinating pentagram-shaped circuit of Venus over five such synodic cycles, which equates to very close to eight earth years, and the pattern of Venus transits across the sun (which do not occur every time there is an inferior conjunction, due to the slight difference in orbital plane between earth and Venus, just as the difference in orbital plane between the earth and the moon mean that we do not get lunar eclipses and solar eclipses every month at the full moon and new moon). Many more amazing aspects of the celestial mechanics of Venus can be seen with excellent diagrams and illustrations at this website by Nick Anthony Fiorenza.

Be sure to look to the west each evening this week and in the coming months for the beautiful planet Venus as the evening star.