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The three exoplanets of the TOI-1749 system are labelled b, c and d. A year ago, an article in the Astronomical Journal on this system by a group of scientists noted a near 2:1 orbital ratio of planets c and d, but made no reference to synodic periods.
Now, with newer data from exoplanet.eu, we analyse the synodics. The mean period between alignments of two planets with their star is as follows:
b-c = 5.0989527 days
c-d = 8.922796
b-d = 3.2447389
From that, the ratios can be obtained:
7 b-c = 35.692668 days
4 c-d = 35.691184
11 b-d = 35.692127
4:7:11 coincides with the Lucas number series which is closely related to the Fibonacci series and the golden ratio.
269 b = 642.477 days
143 c = 642.485
71 d = 642.529
126 b-c = 642.468 days
72 c-d = 642.441
198 b-d = 642.458
A simple comparison with the 4-7-11 calculations (above):
35.692 * 18 = 642.456
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