Tropical timings – the solar barycentric orbit

Solar barycentric motion [credit: Wikipedia]

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With the emphasis on timings, analysis of the solar barycentric orbit (SBO) can be summarised as follows:

Due to the motions of the four giant planets, Arnholm’s solar simulator shows us that the Sun’s motion around the barycentre of the solar system consists of alternate loops and arcs (image, right).

Broadly speaking, a Jupiter-Saturn conjunction occurs halfway round every arc of solar motion, and a J-S opposition halfway round every loop.

After three J-S cycles (each of conjunction + opposition) on average nearly every 20 years, three loops and three arcs of solar barycentric motion have been completed. We observe:
3 loops of 360° = 1080°
3 arcs of 240° = 720°
Sum of those = 1800° = 5*360°
Therefore the mean period of 3 J-S = 5 SBO (as a mean value).

In practice the SBO can be quite variable in length but the mean value is very close to, but slightly greater than, the Jupiter orbit period as we show below.

From our recent post on Jupiter-Saturn timings:
67 Jupiter orbits = 40 J-S conjunctions
3 J-S = 5 SBO (see above)
67*3 (201) J = 40*3 (120) J-S = 40*5 (200) SBO.

The difference of 1 (201-200) between the Jupiter orbits and the solar barycentric ones defines the cycle of 2383~ tropical years shown in that post (including screenshots from the simulator). A mean solar barycentric orbit should therefore take:
201/200 * J orbit (83/7 TY) = 11.916428 tropical years.

NB due mainly to the combined influence of Uranus and Neptune orbits, or sometimes the absence of it, the period of any one SBO can vary by as much as 20% (+/-) from the mean value, or occasionally a bit more. However the long-term average shouldn’t be affected.

A better idea is to use the Jose cycle (9 J-S), a period of nearly 179 years when there should be 15 SBO per cycle as a mean value, with little variation from that figure.

This can be checked simply by counting the orbits, i.e. one per every 360° of solar barycentric motion, on the solar simulator over the period of 9 J-S conjunctions or ~179 years. This follows from our earlier calculation: 3 J-S = 5 SBO (as a mean value), so 3*3 J-S = 5*3 = 15 SBO.

The 15 SBO figure was known in science papers and articles at least as far back as the 1980s, as this article extract (above, right) by former NASA researcher Dr. Jane Blizard shows.

(NB what the author calls ‘three small loops’ are in fact three arcs, on the simulator and in reality.)
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Image: Solar barycentric motion [credit: Wikipedia]