A Pattern And A Puzzle

In my previous post, I talked about the strong evidence for the presence of water ice in permanently shaded crater floors around the north pole of Mercury. Part of the evidence for this was the thermal modeling of surface and near-surface temperatures to predict polar temperatures. We’re all familiar with the fact that polar regions of the earth are colder than equatorial regions, and the same is true for Mercury. But things are a lot simpler on Mercury. There is no atmosphere to carry heat from one part of the globe to another, and there are no oceans to act as heat traps. The only things much affecting these temperatures are

• The angle of the sun, which is related to latitude and the time of solar day (morning, noon, etc.)
• The topography of the surface (an area might be shaded from the sun most of the time)

But while these are certainly the most important, are they really the only influences? Take a look at the figure below, showing the average temperature just below the surface over a two-Mercury-year period.

(From Paige, D.A., Siegler, M.A., Harmon, J.K., Neumann, G.A., Mazarico, E.M., Smith, D.E., Zuber, M.T., Harju, E., Delitsky, M.L., and Solomon, S.C., 2013, Thermal Stability of Volatiles in the North Polar Region of Mercury, Science, vol. 339, p. 300-303. Reprinted with permission from AAAS.)

See anything odd about this? The topographical variations that you would expect are there, and indeed they are the reason that ice can survive on this scorched planet. See if you can find something unexpected, though. (Explanation after the jump.)

See how those cooler temperatures (the green colors that indicate average temperatures around 250 K [-10° F]) extend to lower latitudes around longitudes 90° and -90°? Or conversely, how it gets hotter even at high latitudes around longitudes 0° and 180°? To quote from the paper:

The latitudinal and longitudinal symmetries in…near-surface temperatures result from Mercury’s near-zero obliquity, eccentric orbit, and 3:2 spin-orbit resonance.

Let’s break this down into each of the three influences cited.

Obliquity—This refers to the planet’s axial tilt, how much its spin axis is tilted relative to the plane of its orbit. If the axis is normal (tilted at 90°) to the orbital plane, the obliquity is said to be zero. Mercury’s obliquity is essentially zero.

That doesn’t explain the pattern, however, because with zero obliquity you would expect the temperature distribution to be completely symmetrical around the pole. In other words, the color bands should be in concentric circles.

Eccentric Orbit—Now we’re beginning to get somewhere. Eccentricity is an astronomical term that has nothing to do with the uncle you don’t let out of the house; it refers to the non-circularity of an orbit. An eccentric orbit is an ellipse, and an eccentric solar orbit has a point of closest approach to the sun (perihelion) and one of greatest distance from it (aphelion).

The perihelion distance for Mercury is 46 million km (29 million miles); aphelion is 70 million km (43 million miles). Quite a difference, and quite a difference in the intensity of sunlight hitting the surface. Solar heating would be more than twice as strong at perihelion as at aphelion! But this still raises the question of why heating would be more intense at some longitudes than at others.

3:2 spin-orbit resonance—Here is the answer to the puzzle. What this term means is that Mercury spins on its axis three times in every two trips around the sun. Let’s walk through the diagram below.

mercury rotation

Mercury is not oblong of course, nor does it have a big dot on the surface. The diagram uses these artifacts to make it clear how the surface is oriented in space at each of the numbered locations. Notice that one of two exactly opposite sides of the planet will be always be directly facing the sun when Mercury is at perihelion. And the two sides that are at a 90° angle to those two will always be directly facing the sun when Mercury is at aphelion.  The big red dot is at 0° longitude, exactly opposite it is 180° longitude. When it’s high noon at one or the other of these latitudes, Mercury is at perihelion. When it is high noon at either 90° longitude or -90° longitude (this is designated as 270° longitude by some), Mercury is at aphelion. It gets hotter at higher latitudes around 0° and 180° because when it hits high noon at these latitudes, Mercury is as close to the sun as it ever gets.

Here is a good web site to further illustrate the point. Cool (OK, let’s say interesting) stuff!

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