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Venus's Eight Halos

In Which Eight touching circles define Earth's Orbit from Venus's








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  In the same way that three touching circles emanating from Mercury's mean orbit produce Venus's mean orbit, if eight touching circles are drawn from Venus's mean orbit then the circumcircle enclosing these eight circles defines Earth's mean orbit with over 99.9% accuracy. Try building the shapes out of coins using three modern ten pence pieces to show the Mercury-Venus proportion, and eight one pence pieces for the Venus-Earth proportion; the centres of the eight one penny coins should lie on a circle around the three ten penny coins. The Royal Mint sadly does not quite produce two coins in the 6120:5040 ratio required but these are near enough for the human eye.