Solar System Density Distribution

This page last updated on 01/26/2019.

For years, I had noticed that the inner planets of the solar system were dense, rocky planets while the outer planets were either gas giants or basically balls of frozen gas. I harbored an idea that the density of the planets decreased the further you moved from the sun. I decided to test this impression by plotting a graph of planetary density against orbital distance.

Plotting the Data

I plotted planetary density in grams per cubic centimeter against distance from the sun in astronomical units using data from here. Here's what I got:

In a very gross way, it did confirm my thoughts that planetary density decreased with distance from the sun. However, I did not expect the density to increase for the planets further out than Saturn.

After looking at the graph for a while, I thought it looked a lot like a drag graph for an airplane. Just for reference, here's what one looks like:

The "U" shaped curve is commonly referred to as the "drag bucket." It is actually the summation of two different sources of drag on an airplane. One source is just the plain ol' speed of the airplane through the air and the drag that creates. This is known as "parasitic drag" and increases non-linearly as the speed of the airplane increases. The other source of drag is "induced drag." This is the drag caused by the airplane wing as it generates lift. This drag decreases non-linearly as the speed of the airplane increases. Here are those two components revealed:

Anyway, the density distribution graph struck me as sort of looking like the drag bucket of an airplane. It leads me to think there are two different factors at work contributing to the net density of planets as their distance from the sun increases.

Trying to Explain It All

There does seem to be a fairly clear pattern of density distribution with increase of orbital distance. I think there are two different factors at work.

Factor 1 - The Left Side of the Graph

The curve of the line out through Saturn is really prominent. I think there are a couple of possible explanations for it:

Gravity Gradient - This is the action of the solar gravity gradient on the primordial cloud of dust and gas from which the planets coalesced. Basically, the heavier elements sank towards the sun and the lighter elements stayed further out. Heavy stuff sinks, light stuff floats.
Momentum Distribution - Orbital position is based on speed, not mass. A hydrogen atom can be in the very same orbit as an anvil if they have the same speed. The particles of the primordial cloud were all imparted with the same general amount of momentum. Heavier elements have more mass, so the momentum they received caused them to travel more slowly than the lighter elements. As the primordial cloud coalesced, this speed difference caused the elements to stratify into layers. The higher speed particles (dominated by light elements) orbited further out because their higher speeds allowed them to. The lower speed particles moved to appropriately lower orbits. This theory could be checked by modeling the primordial cloud on a computer. If correct, the distribution of elements in the solar system is mostly dependant on exactly how the particles in the primordial cloud received their initial kinetic energy. There could be very wide variations on element distribution in other solar systems, but they would all place dense rocky planets closer to the sun than light gas planets.
Solar Wind - Perhaps when the planets were first formed, they all contained pretty much the same mixture of materials. Then fusion reactions began in the Sun and it started shining. The sun heated the gaseous envelops surrounding the inner planets and the solar wind blew the lighter elements away. All that was left were heavier gases and the rocky interiors. Further out, like at Jupiter and Saturn, the heating was less and the solar wind weaker, so those planets retained more of their original gaseous atmospheres and light elements. I favor this theory. It just seems to make more sense to me.

Factor 2 - The Right Side of the Graph

Ah yes, this is the part of the graph that surprised me. I really don't know how to account for the rise in density from Saturn outward. Perhaps it has to do with temperature. As you get further out things are getting a lot colder. Elements that were formerly in a gaseous phase are now solids, increasing density. Things like ammonia, methane, nitrogen, etc. It should be possible to test this theory to see if passes muster. The elemental composition of planets is know fairly well. It wouldn't be too hard to check the phase transition temperatures of those elements against the mean temperature of each planet to see whether it is a gas, liquid, or solid. The effect that has on density could then be accounted for. You could plot a sort of "normalized density" against orbital distance to eliminate the effect.

Closing Thoughts

Perhaps it would be better to graph something other than density against orbital distance. Something like oh...shoot, I can't think of anything right now.

It would be interesting to look at mass distribution against orbital distance. If the Momentum Distribution theory is correct, then the distribution of mass in the solar system should tell you something about the general composition of the interstellar medium from which the primordial cloud coalesced. That in turn could give you some clues as to stellar evolution and what generation of star the sun is.