How odd is our solar system?

One of the most basic observations about the planets in our solar system is that there are two basic types. In the inner solar system, we have four rocky planets with radii less than 6500 km. In the outer solar system, there are four gaseous planets, with radii larger than 24,000 km. One long-held implication of this division is that there is some sort of significance in the lack of planets intermediate in diameter between Earth and Neptune.

One of the most striking observations from the list of planet candidates from the Kelper mission is just how unusual the terrestrial planetary size distribution is. The Kepler planetary radius distribution (figure 1) peaks in the middle of this gap; almost 70% of Kepler planet candidates are larger than Earth but smaller than Neptune.

Figure 1. probability distribution of Kepler planet candidate radii

So our solar system is unusual. But how unusual. A back of the envelope calculation will tell us. If we accept the Kepler figures, then only 30.8% of planets are, like ours, either smaller than 6500 km or larger than 24000 km. So the chances of an eight planet system having zero planets in this size range is 0.308^8. This works out as about one in twelve thousand. So for every 8 planet system like ours, there should be 11,999 with at least one intermediate-sized planet.

With a hundred billion stars in the galaxy, there are still bound to be quite a few solar systems like ours. But with only about 1800 known planets and planetary candidates discovered so far, it is unlikely that we will discover a solar system analog any time soon.

Time away

The lemming family has been on holidays. The geomorphologically curious are welcome to guess LLLL's location in the picture above, but the only hint I will give is that everything in the photo aside from the atmosphere is geologically young in the grand scheme of things, having formed in the last few percent of Earth's history. Scientifically meaningful content will return as time permits.

Mass–independent isotopic fractionation

The whole point of geology is to figure out what happened in the past based on the rocks from that time which are still around today. It isn’t actually about the rocks. It’s about the story. The rocks are just the publishing medium. And the craft of geology is learning to read the language of stones.

Similarly, the purpose of geochemistry is to determine the story told by a rock’s chemical composition. The way we do this is somewhat counter-intuitive. We generally search for chemical relationships- that are hard to change. The reason for this is that a ratio that is easy to change doesn’t tell us very much. The potassium/platinum ratio, for example can be changed by just about any process, so measuring it doesn’t tell us what process was occurring.

This is why geochemists like to study systems like noble gasses, rare earth elements, and isotopes. These things are generally changed by only a few processes, so if a change is seen in a rock, there are relatively few processes that could have made the change.

For example, isotopes are nuclei of the same element with different masses. They generally have similar chemical properties- all sulfur isotopes are still sulfur- so only a few processes can change them: evaporation, digestion by bacteria, and diffusion, are some examples. This is the basis of all stable isotope geochemistry; to use the limited number of possible processes to pin down a story by looking at isotopic changes.

In general, when isotopic ratios change, that change is mass dependent. That is, the change is a function of the difference in mass. For sulfur, for example, the change in the ³³S/³²S ratio should be about half of the change in the ³⁴S/³²S ratio. Mass-independent isotopic fractionation refers to a process that fractionates the different isotopes by a ratio that is not strictly mass-dependent. So instead of the ³³SS/³²S change being half the ³⁴SS/³²S change, it might be 0.6. Or 0.3.

The number of causes of mass independent fractionation is exceedingly small- way smaller than the number of effects that cause normal mass dependent fractionation. So if mass independent fractionation is observed, you pretty much know that a particular unique process must have happened.

Most mass independent isotopic work at present is done in sulfur. This is because mass-independent fractionation of sulfur is ubiquitous in rocks from the first half of the Earth’s history, but is rare to nonexistent since that time. So this is a powerful tool that tells us that the Earth’s surface was fundamentally different in Archean time; a process (photolysis of atmospheric SO₂) was occurring from 3800 to 2450 million years ago, and hasn’t happened since. SO₂ is not stable in the presence of oxygen, and photolysis requires UV light that is currently blocked by the ozone layer, so the sulfur isotopic record is the best tool we have for determining just how different the early atmosphere was from the one we breathe today.

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One unfortunate side effect of the wireless and handheld internet revolution of the past five years is that it has made internet cafes harder to find. So expect cratonic style inactivity to continue for a web epoch or two.