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Problem of the Week 879

The Pluto Paradox

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Which of the other planets is, on average, closest to Pluto?

The word "other" is used advisedly, as there are many who do not think Pluto is a planet. Indeed, the International Astronomical Union decided last week that Pluto does deserves to retain its status as a planet. Pluto is the only planet discovered by an American. Moreover, on Thursday, Feb. 11, the Pluto-Neptune anomaly will end and Pluto will return to its place outside Neptune's orbit.

All this makes the problem a timely one. Some assumptions:

  1. Planetary orbits are in the same plane and circular (with radius equal to the long-term average distance from the sun: thus the planetary order is Mercury, Venus, Earth, Mars, Jupiter, Uranus, Neptune, Pluto).

  2. Planets are found in random positions along their orbits.

For advanced space travelers:

Which planet is most likely to be closest to Pluto?

For this you will need the radii of the circles, which I do not have handy I am afraid, though they are easy to find. Michael Schweitzer, who spotted the error in #878, has worked out the probabilities. Hmmm....looking at his results I see that a much better way to phrase this auxiliary problem is:

Which planet is least likely to be closest to Pluto?

And something I have not thought about:

Which planet is most likely to be farthest from Pluto? Which planet is least likely to be farthest from Pluto?

Source: A problem book by Friedland

© Copyright 1999 Stan Wagon. Reproduced with permission.

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9 February 1999