I know centrifugal force can be considered as an inertial, actually kind of ficticious force … But not only that way.

Imagine a solid spherical object rotating as artificial satellite around Earth. As all we know, the hole object is globally subjected only to one gravitatory centripetal force, which is producing an acceleration. Being that acceleration perpendicular to the object velocity, it doesn´t change its linear velocity, only its direction, in such a way that the object rotates. To simplify we can consider the orbit is circular.

That is possible only with suitable values of angular speed and distance: those values have to match. The gravitatory force divided by object´s mass has to be equal to the square of the angular speed multiplied by the radius (distance from Earth).

For a given angular speed, centripetal acceleration of that satellite is proportional to the distance, but gravitatory acceleration is inversely proportional to the square of the distance.

If we made the simplification of considering the hole mass of the satellite concentrated in its center of gravity, for a given angular speed there would be a distance suitable to get the object moving as a satellite.

In that case, no centrifugal force would actually be affecting the object. That force, in the fashion I´m using this concept, derives from action/reaction principle: if Earth is producing a gravitatory, centripetal force on the object, this is also producing another equal opposite force on the Earth. But the object does´t suffer that reaction force.

But the object has a size. Different parts of it are at different distances from Earth. Subsequently gravitational forces are different. But the hole object is kind of obliged to rotate at the same angular speed … New internal forces appear affecting different parts of the object!

Let us imagine the object divided into many thin cylindrical slices (with radius equal to distance to Earth). All parts of each slice rotate with same radius. If there were no internal forces, only a central slice could continue rotating with the given global angular speed, but the rest could not.

All parts of the object interact with contiguous ones, but we can consider central parts of the object “ run the show”: they are rotating at the “ correct” speed, and forcing the rest to keep their pace.

Each slice experiences the gravitatory force at that distance, and additional internal forces from contiguous slices. The sum of all those forces has to produce the centripetal acceleration which makes it rotate at the given angular speed.

Going from center slice to further side, slices are being forced by contiguous closer ones to rotate with a centripetal acceleration bigger than what only gravity would produce on each slice. That is acheived by inner direct tensile forces, from closer slices to further contiguous ones. And that fills the centripetal acceleration “gaps”. Due to action/reaction principle, further slices produces an opposite and equal force on closer ones. Those forces are CENTRIFUGAL, not ficticious but real, and affect all those slices of the object.

Something similar happens going from center slice to closer side. In this case gravitatory forces get bigger and bigger than what required to produce the centripetal force at the given angular speed. Further slices force contiguous closer ones to rotate with a centripetal acceleration smaller than what produced by gravity there. That is achieved by direct internal tensile forces from further slices on closer ones, which is also a CENTRIFUGAL, real force.

Those “ internal” imbalances are the cause of the tendency of any celestial object rotating around another (actually around a common axis of rotation) to get an ovoid shape, causing many interesting phenomena, some of them mentioned by Schutz previously linked work as a pdf. And, as far as I can see, they are also the actual cause of the two Earth´s high tides.

I have other arguments that further “ prove” my (?) theory, related to tide cycle due to the other “couple” Sun/Earth, but this post is already too long …

By the way, Schutz (or whoever has written “Investigation 5.1: Tides and eclipses“ at mentioned work), make a bizarre calculation when comparing Sun and Moon gravitatory effects, that I also find wrong ...