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Principia Prop. I.15

Figure for Newton Principia Prop. I.15 The periodic times in ellipses are in the sesquiplicate ratio of the major axes.
Periodic time is proportional to the area of the ellipse divided by the square root of the latus rectum. The sesquiplicate ratio of the major axis is . You can drag the point C to enlarge or shrink the ellipse, and see how the values for the periodic time and compare - they should stay in proportion. Click the play button at bottom left to make body orbit.