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Problem of the Week 879

The Pluto Paradox

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.

9 February 1999