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JPL '2 body' simulation seems to show SO16 trailing earth by between 5 and 20 degrees which cycles over a period of a year. Even relative to earth it doesn't look like a horseshoe. Relative to earth it seems to orbit a point behind earth about 10 to 15 degrees and this point itself trails further behind earth over many decades. (Simulation only seems to run to 2200.) Rod57 (talk) 11:47, 10 April 2011 (UTC)
In order to get the "horseshoe" comparison in there you have to pull some rather non-intuitive relative logic stunts. Image at http://i.dailymail.co.uk/i/pix/2011/04/06/article-1374054-0B8198BB00000578-54_468x472.jpg and comparing that to the NASA orbital simulation might help. Speaking as a moderately educated layperson with jack all expertise in the field, I'd say the orbit is more of a deformed elliptic. The horseshoe pattern comes if you somehow plot its position relative to the earth's orbit as stationary (?) which is a bit public-attention-seeking behaviour if you ask me, as it's actually orbiting the sun, natch. Not that NASA and geeky space stuff couldn't use some public attention.Pär Larsson (talk) 15:42, 24 April 2011 (UTC)
The accepted MNRAS paper here, Fig 1b (and described in Sec. 4), shows the semi-major axis alternates between about 1.004 and 0.996 AU, with a period of about 350 years. Fig 1a shows the horseshoe shape, as seen in the rotating coordinate system. (Note however that according to the caption for Fig 1a only, "The radial extent of the horseshoe oscillations has been exaggerated by a factor of 20 for clarity".) This libration pattern is stable for over 200,000 yr, which is >500 repetitions of the horseshoe. Wwheaton (talk) 01:11, 11 May 2011 (UTC)