# Objects hotter at their poles than their equators?

Do we know of any astronomical objects--planets, dwarf planets, moons, etc.--that have a higher average temperature at their poles than on their equator?

If we haven't observed this, is it still a possible phenomenon?

That is completely possible, consider for example a planet tilted 90°. There, a pole gets maximal sunlight insolation comparable to $\frac{1}{\pi}$ of the time, compared to $\frac{1}{4}$ for the planet overall (the ratio between the area of a circle and a sphere). For bodies without an atmosphere, that therefore conducts heat poorly, this difference should result in a higher average temperature at the poles.

The 1 to $\pi$ ratio can be intuitively understood by the fact that the pole rotates around the planet by one rotation a year relative to the Sun, because it is fixed in a inertial frame of reference. The Sun only fully illuminates $\frac{1}{\pi}$ of this path:

Also, at the poles of a tilted planet, the Sun can be in zenith in long periods of time, something that is not possible at equator as it rotates away. Note that such a planet have seasons where the equator may be warmer, when the rotational axis is parallel with the orbital motion. Then, the general trend of Earth-like planets holds briefly.

• How does the math work out for Uranus with its 98-degree inclination? – Russell Borogove Feb 27 '16 at 21:32
• Voyager 2 showed it's equator is hotter than the pole facing the sun. The mechanism behind this is still unknown. – GdD Feb 27 '16 at 21:33
• It has a turbulent atmosphere. When introducing complex heat flow dynamics, all bets are off. – SE - stop firing the good guys Feb 27 '16 at 21:50
• @GdD What about Uranus's moons? – Gwen Feb 28 '16 at 0:25
• Insufficient data on the moons really @Gwenn, we only have the Voyager 2 flyby to go on, plus telescope work. The moons orbit on Uranus' equatorial plane, so they likely rotate on the same axis as Uranus. None have any atmosphere, so the point facing the sun would almost certainly be hottest. – GdD Feb 28 '16 at 9:55

For what duration? Uranus, with its axis tilted 98 degrees, faces the Sun nearly head-on with one of the poles for a considerable part of its orbital period, while the other remains in the darkness - nearly all of the planet is subjected to lengthy polar day/polar night, and the vicinity of the pole facing the sun at given time will be the hottest area.