How does Mach's principle explain the centrifugal force as a result of the relative circular motion of the distant stars? Why does this, in the light of Mach's principle, make a net force although the distribution of stars is almost homogeneous, on average, through space?
The following is not an answer, it is a comment, but it's too long to fit into a comment.
The concept that is referred to as 'Mach's Principle' was not proposed by Ernst Mach.
Ernst Mach's views on how to do science were quite strong-minded. Ernst Mach argued for a very high burden of proof for wat should be regarded as scientifically proven. A striking example of that is that for a long time Mach held the view that the existence of atoms had not been proven beyond doubt. Of course Ernst Mach was well aware of all the circumstantial evidence for the existence of atoms, but Mach held the view that circumstantial evidence was not sufficient.
The distant stars
In his book on mechanics Mach stated the following view: we observe that the inertial frame of reference that co-moving with the the solar system does not rotate with respect to the distant stars. That observation is a scientific fact. We should not speculate why this is the case, as speculation is outside the realm of science.
Again, you should think of Ernst Mach as someone who argued for a very restrained conduct. Keep theories limited to what is supported by direct observation.
Other authors did the very thing that Mach rejected: they speculated on the possible nature of some connection between distant stars and the local inertial frame of reference.
Those other authors would then refer to their speculations as thoughts about 'Mach's principle.'
That is why Ernst Mach is not the originator of what over time has became known as 'Mach's Principle'. It was originated by others, but many of them referred to the idea as 'Mach's principle'.