# How to measure mass of planets' core from orbit

I am told in an astrophysics lecture the following.

The mass of Saturn's core was measured by Cassini when it completed its final flyby between the rings and the planet itself. It was also found that its core has a sharp boundary.

Juno measured the mass of Jupiter's core & found that its boundary is a bit fuzzy.

How were these measurements done in principle?

(Ie what was measured from which we can deduce core mass?)

• Commented Mar 13, 2021 at 19:11

$$I = \frac{8\pi}{3}\int_0^R \rho r_0^4 dr_0 = \frac{8\pi}{15}R^5$$
$$r_0$$ is the mean radius of a shell within the planet (because planets generally aren't round). Then you take a simple two-layer model for a planet where $$\rho(r) = f\rho_0$$ for $$0\leq r \leq xR$$ and $$\rho(r) = \rho_0$$ for $$xR < r \leq R$$, where $$R$$ is the radius of the planet. The moment of inertia factor is then $$I/MR^2 = 2[1 + (f - 1)x^5]/5[1 + (f - 1)x^3]$$ which is the curve that you see in the figure.