The principle also applies to our own star, the Sun
The principle, evidently, also applies to our own star, the Sun. The Sun's mass-density is roughly the same as that of the planet Jupiter. If the Sun was a sphere of hydrogen gas, its mass-density would be a thousand times greater, because of the gravitational compression at the center of the Sun. Jupiter is twice as large in volume than Saturn. Consequently, Jupiter has double the mass-density, because of the greater mass compression, with both being gas planets. By this principle, the Sun should have a thousand times greater mass-density than Jupiter, with it having a thousand times greater volume. But that's not the case. However, with the Sun being a sphere of plasma that is largely empty inside, being essentially but a shell of plasma, the low mass-density that it is known to have, is just about right.