The Gaps In Saturn's Rings

We saw recently in "The Infinity Deception" how, from any finite distance, there is a difference between a planet's center of mass and it's center of gravity. I find that an ideal example of this is the gaps between the rings of Saturn.

Saturn is the planet that is known for it's spectacular ring system. All of the outer planets actually have rings around them, but those of Jupiter, Uranus and, Neptune are faint. Saturn's rings are not visible from earth with the unaided eye, but are easily visible in a small telescope.

The current Wikipedia article on "Rings of Saturn" give the reason for the gaps in Saturn's rings, other than "gravitational resonance" with Saturn's moon's, as "unexplained". Image from that Wikipedia article.

The gaps in Saturn's rings are actually simple to explain if we use the difference between the center of mass and the center of gravity, from a finite distance.

Without thinking further we might presume that the "center of mass" and the "center of gravity" of a planet are the same. But they aren't.

The "center of mass" of a planet is constant. It is the point from where the planet's concentration of mass is equal in all directions. We should expect that the center of mass of the planet will be just about exactly the same as it's geometric center.

But the "center of gravity" of the planet is relative, and not constant. According to the Inverse Square Law, the force of gravity is inversely proportional to the square of the distance. In other words, an object at three times the distance will exert 1 / 9 of the gravitational force.

The reason that the center of gravity is relative is that, if we are at a finite distance from a planet, the close half of the planet will have a greater gravitational effect on us than the far half of the planet. This means that the center of gravity would be closer to us than the center of mass. It is only if the planet were infinitesimal in scale, or if we were an infinite distance from the planet, that the center of gravity would be the same as the center of mass.

If we were in a spacecraft, orbiting a planet at a finite distance from the planet, the planet's center of mass would remain constant but the center of gravity would be continuously changing. The center of gravity of the planet would follow our orbit, within the planet, and always closer to us than the center of mass.

It is very unlikely that a planet will be of uniform density throughout. Almost certainly the innermost parts of the planet will be the most dense. The earth, for example, consists of a heavy iron core, above which is the mantle which consists of dense rock but not as dense as the core. Above the mantle is the less-dense crust.

The closer the spacecraft, or observation point, is to the planet, the closer the effective center of gravity is to the surface of the planet, meaning the furthest from the center of the planet. This is simply because the closer we are to the planet the greater the gravitational effect of the close half of the planet, relative to the far half.

Now, back to Saturn's rings. The rings are made mostly of particles of ice. The particles of ice closest to the planet have their real center of gravity in the least-dense outermost part of the planet. But those particles of ice in orbit at a somewhat higher altitude have their real center of gravity in a denser layer beneath that.

The effect of this is as if the particle at the higher altitude is in orbit around a more dense planet. An orbit around a more dense planet would mean that an object in orbit, at the same altitude around the heavier planet, would have a higher orbital energy. 

In orbit around the same planet, a higher altitude means a higher orbital energy. The orbital energy is governed by the same Inverse Square Law that governs gravity. If there is an object in orbit, and we give it 3x the orbital energy, it would then orbit at 9x the altitude, but would move at only 1 / 3 the speed.

So if one of the particles of ice composing Saturn's rings is in orbit, with it's effective center of gravity in a less-dense outer part of the planet, and a particle in a little bit higher orbit has it's effective center of gravity lower than that, in a more-dense inner part of the planet, the higher particle will have to have more orbital energy, than that which would be proportional to altitude, if the planet were of uniform density.

Since orbital energy is proportional to altitude, with a higher orbit having a higher orbital energy, this means that the particle in higher orbit, with it's real center of gravity in the lower and denser part of the planet, will have to gain more altitude to reflect it's higher orbital energy because it is, in effect, in orbit around a more-dense planet.

This is why there are gaps in Saturn's rings. The gaps are a reflection of the layers of material composing the planet, with the denser layers deeper inside the planet making necessary a higher orbital energy for the particles of ice with their effective centers of gravity within those denser layers. Since a higher orbital energy means a higher orbital altitude, this creates the gaps in the rings that reflect the layers of different density within the planet.

The following diagram shows an approximation of the internal density layers of Saturn, getting more dense toward the center. The black dot, Point 1, is it's center of mass. The diagram actually looks like the rings of Saturn, and that is no coincidence. An object in orbit close to Saturn might have it's center of gravity at the red dot, Point 2. An object in orbit still further away might have it's center of gravity at Point 3, the blue dot, and one still further away at Point 4, the green dot. 

Only if an object were an infinite distance from Saturn would it's center of gravity be the same as the planet's center of mass. But having the center of gravity in a high density region means the object will have more orbital energy and thus must be in a higher orbit. If the density layers within the planet change suddenly then the higher orbital energies would also have to change suddenly. This is why there are gaps in Saturn's rings, it is a reflection of the internal structure of the planet.