Re: ILE - The Ideal Lane-Emden Equation

On 20 Jul, 17:22, Thomas Smid <thomas.s...@xxxxxxxxx> wrote:

I think it makes sense to describe all these planets as consisting
largely of an ideal gas, because even for Neptune, the internal
temperature (as given by the gravitational potential over the virial
theorem) is still about 15,000 K, which should make it impossible for
organized structures of the matter in the form of a fluid or a solid
to develop. So essentially, we are still dealing here (like in the
case of the sun) with a 'plasma soup' of nuclei and electrons. Because
no atoms (and thus no excitation of atomic transitions) can exist at
this temperature and density, one can consider it as an ideal gas (in
fact more ideal than gases in the usual sense).

You've enough data to find a coincidence;
not enough to show a connection. (Note that Uranus and Neptune are so
similar they're effectively the same point.)

Well, the point is that these 'coincidences' confirm a mass-radius
relationship R~M^1/3, but invalidate other exponents.



Put it another way: if Uranus and Neptune had the same masses but were 75%
hydrogen instead of 15% and had orbits inside Venus', would you still expect
them to fit your curve?

The fact that they fit the curve suggests that they *do* consist
largely of hydrogen

By the way, the smaller planets also follow a R~M^1/3 law for
themselves, but have a consistently smaller radius by about a factor
0.6 (Mars 0.7) (this agrees with their higher average density compared
to the sun and giant planets).

Thomas



.

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