# How unusual is the solar system?

In Isaac Asimov's Foundation series, the main characters are looking for the long-lost Earth. There are two major features of the solar system that seem to make it unusual among the millions of inhabited systems: the rings of Saturn and the size of the Moon.

The conversations below are mostly between Golan Trevize, ex-military, well-versed in astronomy, and Janov Pelorat, a naïve and recluse history teacher.

## The rings of Saturn

"That's what the poem was speaking of. Three wide rings, concentric, wider than the planet itself."

Trevize said, "I never heard of such a thing. I don't think rings can be that wide. Compared to the planet they circle, they are always very narrow."

"Is that sort of thing common?" asked Bliss, awed.

"No," said Trevize. "Almost every gas giant has rings of debris, but they tend to be faint and narrow. I once saw one in which the rings were narrow, but quite bright. But I never saw anything like this; or heard of it, either."

Pelorat said, "That's clearly the ringed giant the legends speak of. If this is really unique-"

"Really unique, as far as I know, or as far as the computer knows," said Trevize.

## The Moon

"A giant satellite is more difficult to accept. No other inhabited world in the Galaxy has such a satellite. Large satellites are invariably associated with the uninhabited and uninhabitable gas-giants. As a Skeptic, then, I prefer not to accept the existence of the moon."

"Yes. It's rather farther from the planet than one might expect but it's definitely revolving about it. It's only the size of a small planet; in fact, it's smaller than any of the four inner planets circling the sun. Still, it's large for a satellite. It's at least two thousand kilometers in diameter, which makes it in the size range of the large satellites that revolve about gas giants."

"No larger?" Pelorat seemed disappointed. "Then it's not a giant satellite?"

"Yes, it is. A satellite with a diameter of two to three thousand kilometers that is circling an enormous gas giant is one thing. That same satellite circling a small, rocky habitable planet is quite another. That satellite has a diameter over a quarter that of Earth. Where have you heard of such near-parity involving a habitable planet?"

Pelorat said timidly, "I know very little of such things."

Trevize said, "Then take my word for it, Janov. It's unique. We're looking at something that is practically a double planet, and there are few habitable planets that have anything more than pebbles orbiting them. Janov, if you consider that gas giant with its enormous ring system in sixth place, and this planet with its enormous satellite in third—both of which your legends told you about, against all credibility, before you ever saw them-then that world you're looking at must be Earth. It cannot conceivably be anything else. We've found it, Janov; we've found it."

Quotes are from Foundation's Edge (1982) and Foundation and Earth (1986).

My question is in two parts:

1. Are the various descriptions and facts given above generally correct?
2. How unusual are Saturn's rings and the Moon compared to other systems we've observed?

First, Azimov was writing (Edge 1982, and Earth 1986) before the first extra solar planets were tentatively detected (1989), or definitely detected 1991 or 1992. So what he wrote could not be based on any real data on extra solar planets, and must have been an educated guess.

However both books were written after the discovery of Charon, so he may have been ill advised to claim that large moons were unlikely around non-gas giants.

Personally I think both the large moon and broad planetary ring guesses are unlikely to pan out. Uncommon maybe but not uncommon enough for Azimov's purpose.

If you believe it, we have already discovered an exoplanet with a more impressive ring system than Saturn's

• It's no guess. I have tables upon tables. The characteristic Moon of Earth is way out of range. For all it's small size Pluto has a larger SOI than Earth and its the SOI that makes the moon mass. – Joshua Oct 29 '18 at 21:58

• What Conrad said about ring systems is true, we have a possible first detection, but nowhere near detections to make any claim about such phenomena being normal. Also our knowledge on that won't change much in the coming years. With the upcoming photometric missions on transits like NASA's TESS or ESA's PLATO we'll probably be only able to detect this type of bigger-than-Saturn ring systems. This is simply due to the fact that small ring systems won't give a strong enough transit signal to be detected.
So in total, we won't know about the normality of Saturns rings for quite some time.
• Terrestrial Moons: There are ideas out there how to detect exomoons, but those are usually also dependent on photometric measurments. Transit-timing variations may lead to clues of exomoons. Also very big moons could lead to detectable signals in the photometry, but radial velocity detection of exomoons is out of the question at the moment.
So in total: Exomoon distributions are totally unknown at the moment and will, for the same reasons as planetary ring distributions remain unknown for some time.

As much as this sounds a bit depressive concerning the search for rings and moons around exoplanets, we have to understand that this is due to the fact that at the moment those questions are not one of the main science drivers behind currently upcoming exoplanet missions.
We're still trying to understand exoplanet populations themselves thoroughly, before moving on to the much tougher challenges of detecting the much fainter signals of moons and rings.

That said, I'm convinced that the moon/ring question will some time in the future move much more into scientific focus. This is simply because, at least for gas giants, moons and rings should be 'fine-probing' theories of planet formation. This happens in the sense that when gas giants are growing, at some point they will have a subdisc of gas and dust forming inside their own Hill-sphere that will eventually do something interesting. Comparing what those subdiscs do to theories of moon and ring formation will teach us how those processes work in detail.

Also +1 for Asimov because of non-professional personal bias.

• For Azimov's thesis that the Solar system could be unambiguouly identified by the presence of a gas giant with a spectacular broad ring system and a terrestrial planet with a large moon requires that these features occur in a vanishingly small proportion of planetary systems. You do not need these features to be common or normal to invalidate the thesis, a one in a million chance would be sufficient given the number of systems out there. – Conrad Turner Jan 14 '16 at 17:23
• @ConradTurner: Well if you want to go there: With the specifics given, even your number of $10^-{6}$ might be a very high estimate. In particular the quote "and there are few habitable planets that have anything more than pebbles orbiting them." that might another very high factor to this number, is simply unknown at this moment. The probability of all combinations together might be $10^{-12}$ (making it unique in the galaxy) or $10^{-4}$ (making it normal), we just don't know, and thus can't refute the hypothesis. It's a numbers game with unknown numbers. – AtmosphericPrisonEscape Jan 14 '16 at 17:31