User blog:Cerne/A dense revelation

On June 23, 2011, at 8:39:54 PM, I typed:

''"So it has been three weeks now since I typed my last entry. That means I owe three entries this week instead of one… Bah, I will make this entry worth it. To be honest, I don’t actually know what I am going to type. I am no closer to figuring out how to reconcile planet core radius with planet core mass. The more I think about it, the more sure I am that it must have something to do with the planet’s internal density. Shrinking Earth’s core radius would lead to less total density because there would be less iron in the interior to contribute to it. You wouldn’t be able to compress an iron core beyond what it already was by natural means so for an Earth-like mass and gravity there is an absolute value when you are using iron. Or any other metal, for that matter. On the other hand, a heavier and/or denser metal should theoretically be able to re-create the same mass if there was less of it. How much less? I don’t know. It would depend on the metal, and that I don’t know either. What I am looking for is a smaller core radius with the same total mass."''

That was 22 days ago. It has been 41 days now and I really need to type something. Fortunately, I have some good news that will finalize all of this density business and allow me to continue my progress on my first article (why do I feel so edgy about typing that, I wonder?). As it turns out, I was right when I assumed an astrobody would need to be more dense in order to decrease its volume and retain the same mass. I say "volume" instead of "radius," "diameter" or circumference because these latter three words refer to distance whereas "volume" refers to the amount of stuff you can fit into a three-dimensional space. Which we need, because we are referring to the entire amount of stuff within a planet's core, not just its width.

To reiterate what I was typing about in previous entries, I was having a problem figuring out how a planet with a mass the same as that of Earth but with a radius of only 2/3rds that of Earth could remain geologically active in the long term. I.e. beyond the first billion years or so. The problem came up when I asked what the metallicity of my planet would be in a ZBB thread of mine under a slightly unrelated OP title. As it initially turned out, if I kept my original density of 7452 KG/m3, my planet's core would be so large that it would shut down heat convection in the mantle and eventially make my planet geologically dead. Probably before complex macroscopic life had evolved on it. That was when I started reconsidering what my planet was going to be made of and typing about it in the last few entries I have been making in this blog. The ZBB member who pointed this problem out to me gave me some equations to work with, and I eventually ended up asking about them later in a PM when the thread had finally gotten pruned. Around that time I was thinking about actually changing my planet's density, rather than merely changing the type of metal it was made of. I was aiming for a heavier planet at first because I thought that if I could make my core more dense then it wouldn't need to be as big to hold the same mass. I was mostly right, too; when looking back now, though, I realize that my options then were much too dense for my purposes.

Then I got around to looking through my Photographic Card Deck Of The Elements again and I found out that the density of the elements featured in it were listed as grams per cubic centimetre (g/cc or g/cm3 - whichever way you want to put that) rather than kilograms per cubic metre. I also learned that iron has a density of 7.874 g/cm3, which is actually heavier than the density I had listed for my planet, so I started looking for elements that were closer to what I had chosen.

This next thread OP on the ZBB explains more, so I won't need to here.

This was asked in another thread of mine under a different topic but was not concluded. As was pointed out in that other thread, with its current density my planet will have issues with heat convection. However, I believe this may have had to do with its composition: I think I remember typing somewhere that it was made of iron...

I took another look at the number I have for my planet's density, which right now is set at 7452 kg/m3, and tried to see what I could do with it. Element densities are given in a certain number of grams per cubic centimetre (cc or cm3) so I converted 7,452 kilograms into 7,452,000 grams and then divided it by 1,000,000 cubic centimetres. I am not sure if I did that right, though...is 1,000 grams per m3 equivalent to 1 gram per cm3? If I am wrong, please correct me.

Anyway, what I got was 7.452 g/cc - which, surprisingly, was lighter than iron at 7.874 g/cc - so it turns out my planet will not be nearly as metallic as I thought it would be. Unfortunately, no known element in its pure form amounts to 7.452 g/cc. Which means, if I want to use this number, I will need to come up with something else that equates to it.

This leaves me with three options, each with their own question(s) that I hope to answer if I want to proceed further:
 * 1) I could attribute the density per cm3 to an alloy rather than an element, but then I would need to add two or three existing element densities together somehow to come up with the exact number; or
 * 2) I could change the density I have right now to that of an existing element, albeit something lighter since I don't want a heavier gravity for my planet; or
 * 3) I could come up with my own fictional element, but the scope of this option seems quite daunting; not only would I need to come up with an atomic radius and weight, I would also need to think about electron shell configuration, melting and boiling points, radioactive isotopes, their decay rates and decay chains, and so on.

So what do you think? Does anyone know of any alloys that would approximate to 7.452 g/cc, or do you think I should use the pre-set density in grams per cubic centimetre of an existing element? It would mean changing some other existing stats but that wouldn't matter too much. The list I currently have - in order of molecular density - is neodymium, chromium, zinc, indium, tin, and samarium. Promethium would also be included but it is radioactive and has a half-life of only 17 years or so. So would any of these other elements be good to use, or do you think I should use an element that hasn't been listed? If anyone has any suggestions, I would like to read them. Creating a new element is also worth considering but I am hoping to use this option only as a last resort in case the other two options don't work out.

Any advice and/or assistance would be greatly appreciated. Thanks for reading.

I did get a response to my question, and at first it still didn't make any sense, which was why I decided to ignore it for the time being. This was not long after I had begun looking for lighter metals instead of heavier ones. Thank the gods I didn't actually change anything.

Anyway, within minutes of posting that OP on the ZBB, I looked through Wikipedia's Earth article and I found out that the density listed for it was 5.515 g/cm3. When I had typed about Earth's density in previous entries, I was referring to its relative density. Not its actual weight-per-cubic-area density. It was actually considerably lower than what was listed for iron. More importantly, I noticed that it was listed as mean density. Meaning (no homonym intended) that what I had listed for my planet was also its mean density.

A mean in arithmetic is sort of like a median, or center number, in the middle of a collection of numbers represented as a scale. But whereas the median needs to be exactly in between the range you give it, a mean can waver a bit depending on certain factors. Factors like core differentiation.

Assuming the following equations: Then the rocky crust of Earth must have a density of around 3.156 g/cm3. Therefore: In other words, I can have my planet's core density anywhere around 11.748 g/cm3 as long as it is reasonably close to that number. Even better, I can have my planet's core number match an element that is more dense than that - if I want a more centralized interior - or less dense if I want a more uniform interior.
 * 7.874 - 5.515 = 2.359
 * 5.515 - 2.359 = 3.156
 * 7.452 - 3.156 = 4.296
 * 7.452 + 4.296 = 11.748

Suddenly the equations I had been looking at for all that time made sense. Having a mean density that was so close to what the core density was would mean a significantly larger core in relation to the rest of the planet. The person who had given me the equations must have assumed that I was giving them a mean density, and that I wanted my core to be made of iron. If I wanted a smaller core, I would have had to provide a core density that was farther away from the mean density. And if I want the same mass, I need a denser element.

I ended up picking a denser element because I liked the idea of a thicker crust and less constant but more explosive (for lack of a better word) volcanic activity, and I settled on palladium because it has a melting point very close to iron and because it is a transitional metal. Ruthenium is a similar metal, but its melting point is much higher. This metal seems to be one of iron's counterparts on column 8 of the periodic table of the elements. On column 10, nickle's counterpart happens to be palladium. Earth's core is made up of a mixture of iron and nickle which come together to form an alloy, so I may be able to have an alloy of ruthenium and palladium in my planet's core. Ruthenium and palladium can apparently form alloys together, though they seem to be most recognized in a three-element alloy of those two together with platinum. I haven't done as much research on platinum so I don't know whether I want a lot of it in my planet or not.

Interestingly, copper's counterpart on column 11 happens to be silver. Earth has a lot of copper in it so I may be able to get away with having a lot of silver in my planet's interior and its crust. For now, I am going to stick with a combination of ruthenium and palladium and worry about other metals later. I think I will have the ruthenium-palladium alloy make up the inner core, with a smaller ratio of ruthenium, and have an outer core made up mostly of palladium.

This is where I am now. So that is the good news. I don't need to change anything. All I needed to do was a little extra research.

And this will be it for my blog entry. I just wanted to provide an update of my progress and what I have learned thus far. Maybe, when I type my next entry, I will have started on my article. Until then, thanks for reading.