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Fig. 11

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Elliptical Kepler orbit (a) and orbit squeezed into a circle (b) from scaling the x-axis by b/a. The travel time from r0 to r1 is equal to the ratio of the swept (cyan) area in (a) to πab times the period. In (b), this ratio is the (yellow) circle segment plus the (gray) triangle minus the image of the (gray) triangle in (a) over πb2. The circle segment has area ΔEb2/2, with ΔE = E1 − E0 being the difference in eccentric anomaly.

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