Empirical density function for Jovian planets?

Question

I did the terrestrial planets, and here is the result:

rho = 0.5286 (log M)^2 + 2.144 log M + 5.515

Where

M is the planet's mass in Earth masses

rho is the average density in grams per cubic centimeter

the logarithm function is base 10

It works for Mars, Earth, Venus, and the Moon. Mercury is a little off though.

So what would the similar equation be for the Jovian planets?

Answer 1

That doesn't seem possible. Take a look here:

J 1.33 318

S 0.70 95

N 1.76 17

U 1.30 14

The letter indicates the planet, the first number is the density in g/cm^3, the second number is the mass in Earth masses. I sorted the list by mass. One immediately sees that the densities are not ordered as the masses. This seems the indicate that Neptunus and Uranus have rocky cores, while Jupiter and Saturn have not.