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As the eccentricity reaches zero the two foci merge together and the ellipse becomes a circle.

If a is half the major axis of the ellipse, and e is the eccentricity, the distance between the foci is 2ae. For a planet the Sun occupies one focus and the other is vacant, so the Sun is a distance of ae from the centre of the ellipse.

The minor axis is sqrt(1-e^2) times the minor axis, so for all the planets except Mercury the minor axis is more than 99½% of the major axis. The best way to draw an orbit is to ignore this small difference and draw a circle, and then place the Sun at the right distance off-centre.

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10y ago

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