User blog:Cerne/Density and internal differentiation

Hello Wikia, I looked into my density dilemma again earlier today and found that I can't really tweak my planet's density after all. The equations required to find Mass don't really allow you to do this without changing the gravity. On Elizabeth Anne Viau's site (which will come up later) the equation is 4 x Pi(3.14) x r3 / 3 while Geoff's site lists the equation simply as P(density) x r3. Which is, IMO, a lot more simple. Apparently the r3 in the latter equation is proportional to volume, which makes things a bit more flexible, but still no leeway in terms of internal differentiation is concerned.

Anyway.....

Density is defined as the amount of "stuff" you can fit into one unit of volume and Mass is defined by how much of it there actually is. Therefore, if I want a gravity that is close to Earth's gravity for a planet that is nearly half its size, I am going to need to take what Earth has and squeeze it into a tighter space. Obviously, while my planet will be more dense, the entire volume is still not going to be able to fit into a core that is proportionately smaller. The core will start to take up room in the rest of the planet's interior until it starts squeezing out the mantle and shutting down heat convection in the asthenosphere. This is my problem, and it is something I am going to have to fix if I want this damn thing to get underway.

I still don't know why I can't change the material in the core to get a different size with the same degree of mass, though. If I had an element that was less dense comprising the core, I could take the volume I have right now and squeeze it in until I have the density I want in a smaller core. It would need to be an element that would allow me to shrink the volume down to something that would make a more suitable size for a core but not something so small that heat couldn't escape to the surface and/or the planet's rotation would be inhibited. So it couldn't be something as light as Hydrogen or Helium. Likewise, I should be able to take enough of a particular element that is more dense than Iron to account for the mass and gravity that I want and then simply make that the new volume for my planet. Either way, having more "stuff" in my planet's core than Earth does that is less dense than Iron, or less "stuff" in it that is more dense than Iron - given that the element in question is proportionately more or less dense - should give me the same mass.

You would think my problem would be solved if I changed my planet's volume but all of the equations used for determining mass and gravity use "volume" to mean the entire planet, not just the mantle and/or core. This would be fine if the planet's interior density was proportionate to its size, but in instances where the density is proportionately larger than that of the overall radius, you may need to decide how much of the planet's interior is really that dense. Therefore, it makes more sense to differentiate the degrees of density in the interior and centralize it so that only a small portion of the planet is über-dense while the rest of it is significantly less so. Of course, then we are back to the issue of what exactly is in the core that makes it so dense. If you were to look at it as a matter of taking away from the outer parts of the interior and placing it in the centre of - say, a planet with a uniform density somewhere between rock and Iron - you should be able to come up with something dense enough to give the planet a suitable mass and gravity but small enough to allow convection to occur. With what I have now, I don't think I can shrink the core any more without either decreasing the mass or changing the composition. Which is odd, because as long as the mass of the planet fits its radius, it shouldn't matter how that mass is concentrated.

Take the examples given on this page of Elizabeth Viau's Worldbuilders site: density of rock relative to water is 3; density of Iron relative to water is 8. Apparently the relative density of Earth is 5.5 on that page, yet if it was only made up of rock, it would have a relative density of only 3. Meaning that if it was made entirely of Iron, density would be at 8. What I want to know is why Earth's relative density is at 5.5, which is somewhere between the two, when the density used to determine mass requires you to pick a single relative number. Obviously, only a portion of that number represents the Iron part. But how much? I don't know. On the one hand, I need to think about the amount of space within the interior that the core takes up. On the other hand, I need to think about the percent of the total density that the core alone takes up. I have been told in the thread I provided a link to in my last entry that right now my planet's core and mantle take up 75% of its total radius, which is even bigger than Mercury's core at 70% of its total radius.

One thing is for certain: I am definitely going to try to keep my planet's density where it is as much as I can. I have got all of my other stats just fine where they are at the moment. Decreasing density could mess everything up again and I don't want that.

Speaking of stats, I was checking Geoff's site again and for a while I thought that r3 meant the square root of the radius rather than the radius squared... Good thing I didn't follow through with that. Looking through the rest of my stats, I see that I might have been negligent with squaring and cubing a few of my other numbers. At the time, I was following Wikipedia's Earth article and I tended to ignore the square and cube aspect of the numbers that were provided. Actually, I am not sure whether I accounted for them or not. And I would rather not find out. Luckily, I had received assistance with my calculations from another member. They may have caught my mistakes and corrected them when they gave me their calculations. In light of this, I think I am only going to use the numbers I received and not the ones I came up with myself, just in case I did screw up a few times. I will be sure to list the member(s) in question as contributors in the article's Contributions section.

This is all I can think of to type at the moment. Yep, this entry is shorter than the others I have posted recently. Not a whole lot shorter, but short in a relative sense. I am glad I am keeping up with the entries so far...there may be a lot of these before I type my first article. Not sure if it will keep up once I get it and other articles up and running. Guess we will have to wait and see. Thanks for reading.