Beer and elliptical orbits
Published on Jul 3, 2006 at 4:36 pm.
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Filed under astronomers, planets.
The last couple of posts have related to planetary orbits. I will continue that for this one. In both previous posts, I mentioned the elliptical nature of orbits. As it turns out, perfectly circular orbits are very rare. Most orbits are at least a little, and sometimes a lot, elliptical. The degree to which an orbit is elliptical can be characterized by a term called eccentricity. The eccentricity of an orbit ranges form 0 (for perfectly circular orbits) to 1 (for parabolic orbits). Technically, you can have an eccentricity greater than 1 for a hyperbolic orbit, but those are not bound, so we’re not going to consider them. The closest point of an orbit to the Sun is its perihelion, and the farthest point from the Sun is the aphelion. Actually, everything that I say here could also hold for pretty much any orbit. In that case, you change terms a bit. For orbits around Jupiter, the closest point is perijove, and the farthest is apajove.   In general, the closest point in the orbit is generically peripasis and the farthest is apapsis. If we use the symbol A for the farthest distance, and P for the nearest distance, then the eccentricity of an orbit can be given by the equation     e = (A-P) / (A+P).
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Earth’s eccentricity is 0.0167. Among the major planets, Venus’ orbit is most circular, with an eccentricity of 0.0068. Mercury’s eccentricity is 0.206, meaning that at aphelion, it is just over 50% farther from the Sun than it is at perihelion. That makes it the most elliptical of the major planets. That statement excludes Pluto, though, which has an eccentricity even greater, at 0.254, but readers of my blog will recall that I don’t really think of Pluto as a real planet, as this post explains, even thought it is on the list. Even larger than Pluto is the Kuiper belt object 2003 UB313, which has an eccentricity of 0.442. Most asteroids have orbits that are only slightly more eccentric than those of the planets, but now and then one gets kicked into a very eccentric orbit. Ceres, Pallas, and Vesta, three of the largest asteroids have orbital eccentricities of 0.080, 0.231, 0.089, respectively.   Many of those that cross Earth’s orbit are very eccentric. Comets typically have the most eccentric orbits, ranging from near the Sun to very far out in the Solar System. Comet 71P (Comet Clark), which is not too far from the Sun at the moment, has an eccentricity of 0.500, and Comet P/1999 X1 (Comet Hug-Bell) which makes an appearance this month has an eccentricity of 0.471. Halley’s Comet has an orbital eccentricity of 0.967 (more typical for comets). As, I said earlier, all the talk about orbits around the Sun can be used with minor modification to orbits around planets, or anything else for that matter. So, we can talk about the eccentricity of the Moon’s orbit about Earth. Our Moon’s orbital eccentricity is 0.055. The Martian moon Phobos has an eccentricity of 0.0151, but the Martian moon Deimos orbits in an almost perfectly circular orbit, having an eccentricity of only 0.0002. This is one of the most circular orbits in the Solar System.Â
Though we take for granted that orbits are typically elliptical, this is a notion only four centuries old. Since the times of the ancient Greeks, the heavens have been thought of as a place of perfection. The Greeks thought of a circle as a perfect shape. An ellipse was a sort of warped circle, to their way of thinking. So, there was a philosophical hurdle to overcome to imagine planetary orbits as being anything but perfect circles. Even Copernicus, when he worked out his heliocentric model for the Solar System used circular orbits in his work. This introduced periodic errors, which he corrected using epicycles — the very problem that he was trying to get away from! Johannes Kepler, though, finally introduced the idea of elliptical orbits. According to one legend, he was drinking beer one day thinking about the problems that he was having matching orbital calculations to observations of the positions of the planets. The circular orbits simply were not working. So, he was trying to think of what shape they might actually be. As he tilted his beer glass to his lips, he looked at the surface of the beer. Even though the glass was cylindrical, with a circular cross section, the surface of the beer made an elliptical shape when the glass was tilted. This, according to legend, gave him the idea of elliptical orbits. I don’t know if the legend is really true or not, but it sure makes an interesting story!
-Astroprof
