User blog:Cerne/A place in the solar system

Another blog entry about density. Yes, I know, I was going to type about atmospheric gases again. The idea for this entry just happened to precede it, that's all.

If you have read my earlier blog entries (not the way earlier ones - about three or four entries back I think), you will have remembered reading that there was something I wanted to bring up regarding density and what it has to do with a planet's place in the solar system. This goes all the way back to when I was pondering what my planet was going to be made of. At that time I had found out a few things about the process by which the planets are formed in the primordial solar system, and which ones form first and closest to their star, and which ones form later. It turns out there was a theory extrapolated from the formation of our own solar system, and the types of planets in it. The theory stated that the first planets to form in our solar system - and any other solar system - were the rocky terrestrial planets. Then came the gas giants, and then came the dwarf planets from leftover rocky debris (...or they could have been there since the beginning of the solar system's formation and never completely developed into full planets...but anyhoo).

When the first exoplanets were discovered, starting with 51 Pegasi b, this theory was said to have been proven wrong. Its star, 51 Pegasi, which lies well within the parameters of the constellation of Pegasus, is a G2 star much like our own sun. One might think, then, that the theory (I forget its name) had indeed been proven wrong. It may be a complete lack of knowledge responsible for me saying this, but I don't think it was proven wrong at all. As far as I know - and I do expect to be corrected if only by my own research after typing this entry - no solar system has yet been discovered with a gas giant being closer to its star than a terrestrial planet within the same solar system. I know 51 Pegasi b is a lot closer than any discovered terrestrial planet in a comparative sense, but I am talking about a terrestrial planet and a gas giant in the same solar system. No gas giant has ever been found to be closer to its star than a terrestrial neighbor in the same solar system.

Going back to planet creation, this may have to do not only with what order the planetesimals - and later, proto-planets - were formed and the amount of "stuff" they were formed with, but also what kind of "stuff" they were formed out of. Of course when we say "stuff" we are talking about lots of hydrogen gas and rocky debris. Terrestrial planets form first because the heavier elements - like iron - are closer to the newly-formed sun than the lighter elements like helium, hydrogen, water ice, and silicate rock. This leaves one to assume that maybe the "Hot Jupiters," like 51 Pegasi b, were created so close to their sun - and were among the only planets to form in their solar systems - because their solar systems were formed only out of the lighter elements. And less of them. Or maybe not, because TrES-4b trumps Jupiter in size by 70% (albeit being lower in mass) which may mean that the majority of the leftover hydrogen went into forming a single planet instead of multiple smaller ones. And then there is CT Chamaeleontis b, which is now known to be a brown dwarf. This leads to another hypothesis: if we can assume that the amount of material left in a protoplanetary disk after the star forms makes nearly no difference at all, then perhaps the type of material will make a difference.

I will explain.

So far, from what I have seen, the "Lonely Hot Jupiter" occurrence seems to be rather common. Yet we have Jupiter amongst seven other planets, four of them being terrestrial. Saturn may not be an indicator of anything, but the two other planets are dubbed "Ice Giants," meaning the distance from our sun may have had a role in the kinds of gases they contain. Place Neptune where Mercury is now and prevent it from becoming terrestrial by taking away all of the denser material that formed the four terrestrial planet we know of now - or assume it was never there to begin with - and it (Neptune) might have become a very different planet. Not rocky, but it might have turned out more like 51 Pegasi b (we will call it by its unofficial title "Bellerophon" from here on in). It makes sense, then, to assume that in order to get multiple gas giants - and maybe an ice giant or two - we need terrestrial planets to form between them and their star so that the hydrogen and helium these planets are composed of will be far enough away from their star as to invoke different kinds of reactions and therefore create different kinds of planets. Otherwise all of that hydrogen will probably accumulate into a "Hot Jupiter."

To get terrestrial planets, a protoplanetary disk must contain elements that are dense enough to give a developing planetesimal a metallic core. This depends largely on the material left over from the star-forming nebula once the star itself has finished (or nearly finished) forming. There doesn't seem to be a correlation between the type of star and the type of planets it will have as long as the right material is available. It should be obvious that any elements that are dense enough will form a terrestrial planet, but OGLE-2005-BLG-390Lb has no other planets sharing its solar system so not a whole lot of gaseous material is needed to form a terrestrial planet as long as it is sufficiently dense enough to do so. We can still assume, however, from the examples of extrasolar planets we have discovered thus far, that the formation of terrestrial planets - and how many of them there are - plays a big role in what the rest of the solar system will be like.

So what does this mean for me? Well, it gives me a rough idea of what kinds of other planets my solar system will have. I have already decided that I want two terrestrial planets, one closer to their star than my main planet is. This makes sense because my star is (I think - I may need to re-check my records) a K-type reddish-orange dwarf. It will be smaller and therefore have less of a gravitational pull on the surrounding planets, so if I want a cold(er) planet, I should choose the terrestrial planet further from the star. Next up, I will probably have a gas giant. Given the amount of planet-forming material there will be left and the type of the star, I will probably only have enough lighter gases for one gas giant. This gas giant may or may not be cool enough to qualify as an ice giant but I do not know yet. Throwing in a dwarf planet or two is still optional for me so I may decide later whether I still want them or not.

Now that I have decided how much "stuff" I will have and how dense the elements will be in my protoplanetary disk, I should decide what type of "stuff" (the elements themselves) I will have in it. I have already decided a few entries back that I want palladium and ruthenium in my planet's core, as well as a silicate rock mantle and crust which will probably more likely have originated from colliding chunks of rocky debris like asteroids from farther out rather than from the same material making up the core. Ruthenium and palladium are already rare enough as it is so I shouldn't push my luck - two terrestrial planets will probably have to be my limit.

An interesting tidbit of info: when Earth's solar system was formed, the first 26 elements - all the way up to iron with atomic number 26 - were already present. Or at least most of them were. This means any elements with an atomic number of 26 or lower are actually relatively common inside our planet. In contrast, elements that have an atomic number higher than 26 will be quite rare. I already mentioned in an earlier entry that ruthenium could be a heavier counterpart of iron and palladium could be a heavier counterpart of nickel. In my case, therefore, the rule will be that any element with an atomic number of 44 or lower will be considered common while any element with an atomic number higher than that will be rare. I would like to extend this boundary to 46, which is palladium, but Earth's core already has a lot of nickel in it so I figure using element 44 (ruthenium) as my limit will be fine.

This leaves a lot more possibilities open to me as to what the other planets in my solar system can be made of. Particularly my gas giant, which might be an ice giant after all. More attention should be focused on the other terrestrial planet in my solar system, though. It will be larger but it may not necessarily need to be heavier.

I would like to point out what I think is a common misconception regarding planet size and planet mass. Planets that are larger than Earth are often assumed to be more massive in proportion to Earth because it is assumed they have the same material - iron and rock - that Earth has, just more of it. And to a certain degree, it would be true if the planet were substantially big enough. I call this a misconception precisely because of the idea of terrestrial planets being larger and consequently more massive. If we assume that - in order to have terrestrial planets in the first place - a certain amount of denser elements need to go into making them, and that - depending on what kinds of elements go into forming a new star and the surrounding protoplanetary disk - these elements are not all that common, then we need to ask where all of this dense material came from to make a planet so big. In a solar system with multiple terrestrial planets, I would expect to find a more massive terrestrial planet closer to its star unless the planet was mostly a large ball of rock, in which case the gravity on such a planet would be much lower than what we have on Earth. That being said, a larger terrestrial planet found closer to its star would make more sense because denser material in a protoplanetary disk does stay closer to the center of the disk than the lighter elements do and hence does have a greater chance of building a larger planet because there is more of it. In adherence to the amount of protoplanetary material available, however, it would also probably be the only terrestrial planet in the solar system because there would be no rocky material left to build other planets with. Most of that extra rocky material would have been snatched up by the other terrestrial planets, had there been any. This goes well with the discovery of OGLE-2005-BLG-390Lb (this planet needs a better name) because the planet is several times bigger than Earth and is also the only planet in its solar system. I predict a much higher gravity on that planet. Or it might be mostly composed of rock. I don't believe anyone has made any educated guesses as to what the gravity might actually be like yet. Whatever the case, placement seems to be the key in determining whether a large terrestrial planet will be more or less massive.

Interestingly, our own solar system seems to contradict this "larger planets first" model completely. Take Mercury, for instance: with a diameter of only 4,875 kilometers wide and a mass of only 0.055% that of Earth, its core comprises as much as 75% of the entire planet. Venus' diameter is 12,104 kilometers wide and it has a mass of 0.82% that of Earth; while it may be proportionately smaller than Earth is on the outside, its core takes up roughly 25% of the planet. Earth's core only takes up 20% in comparison. Mars' 6,780 kilometer-wide diameter and a mass that is 0.11% that of Earth's mass gives it a core somewhere between 1/3 and 1/2 its total size; however, because its density is lower than that of the other three terrestrial planets, its core does not contribute as much to its total mass. Meaning that Mars probably has more rock per cubic centimetre than the other three terrestrial planets. Because of this, I feel it safe to assume that the composition of terrestrial planets - either by the overall size of the core (indicating how much material the planet received while forming) or by the core size relative to the rest of the planet (indicating how much rocky material it obtained during formation) - will decrease with the more planets there are and the further they are from their star while the actual size of the planet matters very little.

The key in determining whether a terrestrial planet will be larger and smaller as a planet, then, seems to depend on how many terrestrial planets there are. This in turn depends on how much denser material - iron in most cases but ruthenium in my case - there is in the solar system while it is still forming. A lot of denser material leads to multiple terrestrial planets of moderate sizes while a small quantity of this denser material seems to lead to one very big terrestrial planet. Iron doesn't seem to have the same conglomerating effect that the gases hydrogen and helium do, and this seems to be due to a certain limit in size that an iron core can reach before it stops accepting more iron during formation but I cannot say this for sure because I haven't learned about all of the other exoplanets out there. That, and we just haven't found enough exoplanets to come to any useful deductions on how solar systems typically form. Nor do I think we can determine whether the number of terrestrial planets will have any effect on how many gas giants there will be. Gas giant are common enough to say that most solar systems will have at least one. Then again, there is that OGLE-2005-BLG-390Lb exception...

All in all, we (see: myself) can say with a fair amount of certainty that a protoplanetary disk made up entirely - or at least mostly - of hydrogen and helium will have one (or two if there is enough of the gas and it is widely distributed) very large gas giant. Or a brown sub-dwarf star. If the protoplanetary disk has some iron in it, then you will get one very large terrestrial planet and maybe a few dwarf planets farther out. A lot of iron, and you may get several terrestrial planets. Add hydrogen and helium gas, and you may get multiple gas giants, too. The more terrestrial planets you add, the more likely you may get an ice giant due to colder temperatures and wider gas dispersal. The amount of planets you have may depend somewhat on the mass of the star so a red or orange dwarf star may not yield as much planet-making material. Our sun is a G2 spectral class yellow dwarf and it has eight planets so G-type stars may exact the largest limit on solar system size...but (again) this is mere speculation and is only intended to provide an educated guess on what one could aim for when designing a solar system.

Where this has to do with my own solar system, I don't think there is any reason why that second terrestrial planet can't be a lot larger than my main planet is. More metallic elements closer to the center of the solar system means my second terrestrial planet can be more massive to begin with, then all I need to do is throw on a lot of rock and I am good to go. So why isn't my main planet not as large? With less metallic elements in its core, perhaps it didn't attract as much rock while forming. Because of the limit I have, there is not much else where it could go. I may end up with a larger version of my main planet, or I may not. I am still not certain as to the metal-to-rock ratio and therefore what the gravity will be like, though if it as more metal and a lot more rock, the gravity will probably be a lot higher than that of Earth.

All of this speculation on planet type and planet surface conditions reminded me of an illustration I found in a book I had bought more than a decade ago. The book itself was about extraterrestrial life but it included a review of possible sizes that a planet could take. For those who are interested, the book may be found here.

As for the illustration, it is on the right:

Here you can see a total of twenty different kinds of astrobodies. Starting at the top, there are the gas giants; the biggest are those like Jupiter, then there are the smaller and much lighter gas giants like Saturn, and then we have the ice giants like Uranus and Neptune. Next in line we have a "Super Earth" - a very large terrestrial planet that is probably (but not definately) mostly made up of rock. Then we have three Earth-like planets, with an Earth-sized planet as the left-most planet in the illustration and in-between two other very similar Earth-like planets. Immediately in front of them is what is thought to be the minimum in size a planet can be to support life. After that are six astrobodies that could be dwarf planets or asteroids. And the last six are comets, which - because they hold a very simple atmosphere - are also included.

Please note: that picture was scanned directly from my book. I scoured Google's collection of images and could not find the illustration anywhere. If, in the chance that someone does manage to find this illustration online, I would very much appreciate it if they could tell me where they found it. Not only would the image itself probably be clearer, I would also have an easier time referencing it.

Well, that is about it. I need to be somewhere in a little more than an hour and a half from now and I very much think this entry has gotten exceedingly long as it is right now. Of course there is always more to say on constructing solar systems but that will need to wait another day if I am ever to publish this entry. I could go on, so be lucky I am not going to go on right now.

If anyone is still awake or hasn't run off yet, thanks very much for reading.