don steward
mathematics teaching 10 ~ 16

Tuesday, 14 April 2009


There are several tricky Mensa problems involving highly idealised, concentric circle orbits.
Here is a selection:
Two planets and the sun are initially in line. The planets circle the sun, clockwise, at different rates.

When are they next in line if they circle the sun:
1] A: every 2 years. B: every 6 years?
2] A: every 5 years. B: every 15 years?
3] A: every 20 years. B: every 100 years?

For a given ratio, it can be helpful to think about the angle turned by the faster planet when the slower planet goes through a particular angle.

In general?

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