I'm attempting to build a MMSN, I've been trying for about... a week to get an intuition on the scaling factors for calculating the mass of the disks, I'm not entirely sure how to think about it. I feel as if the concept is extremely simple but that I'm thinking of it incorrectly. Can someone explain what exactly these scaling factors account for and how one would calculate them? I'm not looking for a solution, I'm looking for intuition on how these scaling factors are found.

My understand is that you pick an element, (Fe), and compare that to the solar abundance (does this mean the abundance of Fe in the sun? From there I would look at the abundance of Fe in the cores of the planet and compare them somehow to get some sort of scaling factor. From what I understand Fe makes .14% of the suns mass, so if I know lets say that neptune has a mass of 17m(earth) how would I start finding the scaling factor.


  • $\begingroup$ I can't understand this question, though it sounds of interest. $\endgroup$
    – ProfRob
    Feb 15 '16 at 8:32

Attempt to do an intuitive explanation:

The Sun was formed from a cloud of matter. A small amount of that matter remained around the Sun, and had a similar composition. This was the solar nebulae.

But the composition of the planets are now not the same as the Sun. This is explained by that some of the matter was collected by the Sun, and some of it was blown out of the system.

That was only the light stuff! like hydrogen and helium. Most iron and other metals are conjectured to have remained in orbit, forming the planets.

As the Sun is representative for the original composition (partly at least, stellar fusion has skewed the hydrogen/helium ratio). So if iron is 0.14% of the Sun, that is also the original abundance in the nebulae. So all the iron in the planetary bodies is 0.14% of the original nebulae mass.

From that you can calculate the original mass. It is a 'minimum' because some of the iron may have escaped as well.

  • $\begingroup$ Thanks for your reply! So to calculate the MMSN, I'd say that (for the rocky planets inside the snow line), if I know their masses and I know metals are 2% of the solar abundance, I can say that the sum of the masses of the rocky planets is x, and that the nebulae must have had 50 times as much material? $\endgroup$ Feb 15 '16 at 15:56
  • $\begingroup$ @Stacksofoverflow That is correct! 50 times is a minimum though, as some of the metals may have been lost too. $\endgroup$ Feb 15 '16 at 16:12
  • $\begingroup$ Awesome, thanks so much. But now what if I'm looking at the planets outside of the snow line, would I assume that they are gas giants and so assume that their masses are only off by 2%? (Based on those assumptions?) Or would I have to try and find data on their cores? $\endgroup$ Feb 15 '16 at 16:16
  • $\begingroup$ @Stacksofoverflow You have found one of the basic limitations of the MMSN. We do not actually now a lot of the size nor the composition of the gas giant cores, so that gives a lot of uncertainty. $\endgroup$ Feb 15 '16 at 16:19
  • $\begingroup$ Interesting, so in that case, when constructing the MMSN, how do astronomers scale for the masses of these planets? $\endgroup$ Feb 15 '16 at 16:22

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