Test this out - has a grand conjunction ever occurred?

fsgregs · Post #1by **fsgregs** » 09.11.2006, 02:23

Hi all. Here is an "extra credit" question I give to my high school seniors. See what you can do with it!!!

A Grand Conjunction of the sun and the eight planets on the solar system's plane of the ecliptic, all lined up in one straight line, is theoretically possible. It even served as the basis for a movie plot (The Dark Crystal) a long time ago. Of course, Pluto is not on the ecliptic plane and would, therefore, not technically ever be able to "line up" with the rest of the planets.

The question is ... just how probable is such an event? How often (if ever) has the Sun and its eight ecliptic planets ever lined up in a single straight line (positioned within 1 degree of each other)?

What do you think? You will be surprised at the answer.

Post your thoughts!!!

Frank

Malenfant · Post #2by **Malenfant** » 09.11.2006, 05:58

Didn't the Voyager spacecraft take advantage of that sort of alignment when they did their Grand Tour in the 70s-80s?

fsgregs · Post #3by **fsgregs** » 10.11.2006, 01:26

Nope!

Voyager took advantage of orbital movement of the four gas planets so that as it left one via a flyby, another one was on a distant trajectory that it could reach, provided it got a gravity assist from a close encounter with the first planet. At no time were the four gas giants actually lined up in a straight line. Had they been so, they would have moved far away by the time Voyager arrived at them.

Educational Activity 8 has the complete launch trajectory of both Voyager 1 and 2 built into it, accessed via cel"url. Check it out!

Frank

Hungry4info · Post #4by **Hungry4info** » 11.11.2006, 17:17

Okay... I'll give this a go. I think that the answer would probably result from finding the LCM of the orbital periods of the planets.

The orbital period of the planets (roughly) are about:
Mercury: 0.2
Venus: 0.6
Earth: 1.0
Mars: 1.8
Jupiter: 12
Saturn: 29
Uranus: 84
Neptune: 164

The LCM of all that is 299628 years. So... I'd say all 8 planets align every 299,628 years or so?

I probably went about that wrong, lol.

fsgregs · Post #5by **fsgregs** » 12.11.2006, 00:43

Hungryforinfo:

Remember that an alignment means that the planets occupy a particular position on an orbital circle, AT THE SAME TIME. While you could use orbital periods to align two planets, you cannot use them to align them all in a straight line.

Think about it geometrically.

Frank

Hungry4info · Post #6by **Hungry4info** » 12.11.2006, 03:58

Lol, I kind of figured that there was some geometry or trigonometry involved, but since I've never had those classes (sophmore... blah), I'm kind of lacking in knowledge.

Well, if nobody figures it out, could you let me know how you get the answer?

Another thing that's been annoying me, and maybe you can help with it:

1) If I have two orbits in a solar system, either one of them can be eccentric or inclined, how can I calculate their distance at closest approach?
2) How can I calculate WHEN they'll have their closest approach?

If you can help with this, it'd be enormousely appreciated.