## Knowledge of celestial mechanics pays off! Helps Win a "Math Chat" Challenge Question.

My friend on Planet X reports that the sun stayed at the same spot on the horizon for a whole 24-hour day. How can this be? (From the Christian Science Monitor, 16 July 1996, p.15.)

My answer (e-mailed 19 July 1996): The rotational axis of Planet X happens to be pointing directly at the sun that day, and the friend happens to be on the equator of the planet.

Further implications of this scenario are the following curiosities:

A. Half of the sun's disk will be above the horizon all day, but the visible part of the sun will change as the planet rotates (unless the sun's rotational axis is also aligned with the planet's axis, and the sun rotates at exactly the same rate as the planet).

B. The sun will not be *exactly* at the same spot on the horizon all day because the the planet's rotational axis will remain oriented in the same direction in space (except for presumably slow precession) as the planet revolves around its sun. The faster the planet revolves around its sun, i.e., the shorter its year, the more noticeable this shift will be.

C. Seasons on Planet X will be especially severe. That is, the difference between winter and summer will be extreme, compared to a planet in the same orbit with a rotational axis that is perpendicular to the orbital plane.

D. The friend on Planet X's equator will have two days a year when the sun is stationary; once when the "north" pole points at the sun and once half a year later when the "south" pole points at the sun.

E. For another friend on Planet X who lives at either of the poles, there will be one day a year when the sun stays at the zenith all day long, and another day half a year later when the sun stays (unseen) at the nadir all day long.

As a prize, they sent me a copy of the book Flatland, and published my name on p.15 of the 16 August 1996 edition. Were any other winners SSP graduates?

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