An Elliptical Puzzle

You know that the orbit of one body around another, such as the Earth around the Sun, is an ellipse.  In this example, you know that the Sun is at one focus of the ellipse.  You might well ask, "Which focus?  An ellipse has two foci -- which does the Sun occupy?"

People really do ask this question.

My Answer:

I think the problem is an unconscious inference that the location of the ellipse determines the location of the foci, and thus of the Sun.  Of course it is actually the other way around: the locations of the Sun and Earth determine the location of the ellipse and its foci.

This is in contrast to something like a teeter-totter, which has two positions that can be occupied.  The difference is that a teeter-totter already exists before anyone sits on it, while an elliptical orbit exists only because two bodies are there.

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Jeff Root
August 22, 2002