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The Dagobah System

Tonight: Rudolph the Red Planet

Special to the BPP from Summer Ash:

Last Monday, we had our closest approach to Mars. However, orbital mechanics gives us something else to celebrate this holiday season as Earth, Mars, and the sun will all align on Christmas Eve. If the holiday weather is in your favor for a clear night, you should be able to see it fairly high in the sky, somewhat near the just past full moon, glowing reddish-orange. And you shouldn't have to look to hard, because it will easily outshine the stars.

This alignment is called "opposition," as Mars will be directly opposite in the sky from the sun with respect to Earth, or more simply Earth is directly between the sun and Mars, and it happens roughly once every two years. Tonight's date between Mars and Earth happens because both planets take a different amount of time to orbit the sun. Earth takes 365+ days and Mars takes approximately 687 days. Therefore, Earth moves faster in it's orbit and gradually "laps" Mars in the race around the sun. The approach and subsequent passing of Mars is what occurs every two years.

Earth laps Mars. Got that? Summer Ash/Newtonianism for the Ladies hide caption

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Summer Ash/Newtonianism for the Ladies

It's not easy to see in the diagram, but the elliptical orbits of the planets actually allow for their closest encounter and their opposition to occur separately. If all orbits were perfectly circular, the two events would be simultaneous and inseparable.

Let's step back a second, and discuss the geometry of the solar system.

Each planet in the solar system orbits the sun in an elliptical orbit, as discovered by Johannes Kepler back in the day. As opposed to a circle, and ellipse has two "centers" — termed foci - instead of one. For our solar system, the elliptical orbits of the planets all have the sun at one focus. But the orbit of each planet is elliptical in a different way; ellipses come in varying degrees of eccentricity, or distortion from circular. A circle is defined by an eccentricity of 0, while ellipses can have a range of eccentricities greater than 0 and less than 1. The more eccentric the orbit, the farther apart the two foci are. At an eccentricity of 1, the closed path of an ellipse breaks and becomes a parabola instead with the second focus at a distance of infinity. But that's a lesson for another day, back to Earth and Mars.

Earth's orbit is less eccentric than Mars' orbit, so the second focus of our elliptical path is closer to the sun than the second focus for Mars. In the diagram this is exaggerated to the point where Earth's orbit looks almost circular by comparison. This, combined with the oppositions plotted on the diagram, make it harder to see how the Earth can really be closer to Mars when the two aren't directly in line with the sun, but this can be the case. Only once in much less than a blue moon will the two events occur at the same time. More often they will happen in succession as they do this year, with the closest encounter on Monday, Dec. 18, and opposition on Monday, Dec. 24.

If you feel you are sinking into a geometrical quagmire, just take my work for it.

Whew, all that academic mumbo-jumbo for what is hopefully still a worthwhile payoff...

The reason for this point being that in honor of this Christmas Eve spectacular, the New York Times has proposed a cover version of "Rudolph the Red-Nosed Reindeer," with Mars as Santa's new best friend. Yes, it's totally cheesy and geeky, but you know you love it. Check out some of the lyrics in below and the full article. Feel free to sing along!

But this very Christmas Eve
Santa came to say:
"Rudolph, now with Mars so bright,
You can stay at home tonight."

Then all the reindeer teased him.
And they shouted out with glee:
"Rudolph, the red-nosed reindeer
Outsourced to astronomy."

—Special to the BPP from Summer Ash.