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.