Last edited 10may03 by Matt Townsend
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Analemmas and Orbits of Other Planets


Mars has a highly elliptical orbit, the most eccentric of all other planets, excluding Pluto. Because of the nature of its orbit, the pattern of its analemma is dominated by the ellipse aspect of the equation of time, and so the resulting figure has a single period rather than a double period, and the analemma does not cross itself. The analemma of Mars is shaped much like an avocado.


Although the eccentricity of Jupiter's orbit is not extremely high, its tilt is unusually low at only 3.5 degrees. Like Mars, therefore, its analemmic pattern is dominated by its elliptical orbit, and the pattern it forms has a single period. The tilt is so small that its role can't even be noticed, and the oval-shaped analemma is the simple product of the sine wave produced by the equation of time for the ellipse.


The analemma of Saturn is the most unique. Its orbit is quite elliptical, about three times more eccentric than that of the earth, and its tilt is 27 degrees, only slightly larger than the earth's. The pattern of the analemma is therefore dominated by Saturn's elliptical orbit, but a small trace of its tilt is still visible, leaving a small "bud" object on one side of the figure. The image is a graph of the equation of time reflected about the summer solstice on Saturn.


Uranus is a very unusual planet. Its axis is tilted 98 degrees, and so it spins almost perpindicular to its orbiting plane. The analemma it forms from this unusual motion is one that cannot be viewed simply in one portion of the sky. Part of the planet is dark for half of the year, and then light for half of the year. A sunrise must be a several week occurence, and the sun's motion is horizontal instead of vertical. This is a picture of the sun traced over the course of a year when standing on the equator, and the very large variation of the sun's position is apparent.


The eccentricity of Neptune is lower even than that of the Earth. Its tilt, however, is slightly larger, about 30 degrees. The resulting pattern is therefore strongly dominated by the tilt of its axis, and it therefore has a double period. Since the eccentricity is almost nonexistent, the analemma is almost a perfect figure eight, as is seen in the reflected diagram.


Pluto is hardly a planet so much as an extremely large asteroid. Its eccentricity is over twice as large as that of Mars, five times as large as most other planets in the solar sytem. A single day takes around 150 hours to pass, so Pluto rotates very slowly. Like Uranus, its tilt is unusually high at 118 degrees. The combined effects of these form an equation of time that cause the sun to be ahead or behind almost 100 minutes, giving a 200 minute variation throughout the course of the year. The graph is decieving, the scale is has been compressed from that used to graph the earth by a factor of ten.

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