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Tuesday, February 19, 2008

 

Why do Venus Elongations Skip Years?

Correspondent and fellow Science Natterer Cynthia Ma has noticed that there were two greatest elongations of Venus in 2007, but none in 2008, and she wondered why that was the case, when Mercury had multiple greatest elongations in each year.

A greatest elongation is when an inner planet, either Mercury of Venus, is at its furthest distance from the Sun as seen by us from our vantage point on the Earth. Have a look at the image to your left, diagrammatically showing the orbits of Venus and Earth (not to scale) to see where a greatest elongation occurs with respect to the alignment of Venus and Earth. If you look at the tables below showing the greatest elongations of Venus and Mercury, you will notice something interesting.

Elongations of Venus (and whether it is above the eastern or western horizon)

2004 Mar 29 16:39

East

2004 Aug 17 18:31

West

2005 Nov 03 19:33

East

2006 Mar 25 06:44

West

2007 Jun 09 02:44

East

2007 Oct 28 15:05

West

2009 Jan 14 21:23

East

2009 Jun 05 20:50

West

Elongations of Mercury

17 Oct 2006 04:07

East

25 Nov 2006 12:56

West

07 Feb 2007 17:39

East

22 Mar 2007 01:47

West

02 Jun 2007 09:56

East

20 Jul 2007 14:59

West

29 Sep 2007 16:08

East

08 Nov 2007 20:31

West

22 Jan 2008 05:25

East


You will notice that there is a consistent pattern. For Venus, a western elongation occurs approximately 5 months after an eastern elongation, while an eastern elongation occurs approximately 15 months after a western elongation. For Mercury, a western elongation occurs approximately 1.5 months after an eastern elongation, while an eastern elongation occurs approximately 3 months after a western elongation.

A quick look at the diagram will show why, the distance a planet has to travel in its orbit from eastern to western elongation is shorter than the distance it takes from western to eastern. Hence you will get a pattern of two elongations close together, then a big gap before the next elongation.

But hang on, you astute readers will say, Mercury’s year is only about 3 months long (87.97 Earth days), and Venus’s year is just about 7.4 months long. Why does it take as long as or longer than a year to get from western to eastern elongations? Well, what this diagram can’t show is that Earth is also orbiting the Sun. By the time Venus or Mercury get back to the same position they were at the previous eastern elongation, Earth has moved on a bit, and Venus or Mercury have to catch up. There is an actual mathematical formula that you can use to work this out, and it turns out that Venus takes around 15 months, nearly two Venusian years, to catch up with Earth so that we can see a western elongation (for more details see this Wikipedia site).

Try this java applet to see for yourself, it’s actually designed to show asteroidal orbits. However, if you use the sliders to zoom in on Earth and Venus, then use the change time button to type in the time of the 2007 western elongation and press the animate button, you can see how Venus has to catch-up to Earth. If you have access to Celestia, select Sol, and set the system to follow Sol, turn on planetary orbits, orbit the Sun until all the planets are visible and use the time set tool to type in the elongation dates, then run forward.

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