Using his theory of relativity, he calculated what would happen. It turns out that the body should indeed feel a tiny gravito-magnetic force. Further evidence in favour of Mach's principle comes from cosmology. In Newton's theory, it is entirely possible for the entire cosmos to spin about some axis. Given that almost all astronomical systems are observed to rotate to some extent, we might expect, if Newton is right, to observe a universal rotation too.
Astronomers find no evidence for a systematic rotation of the universe.
Their observations imply that the universe cannot have turned by even one degree since the big bang. If rotation is absolute, the absence of a universal rotation seems to be a very special and contrived state of affairs, but if as Mach claimed it is relative, then the observations are explained. All this looks promising, but other features of Einstein's theory of relativity are decidedly anti-Machian, and in spite of occasional claims that Einstein's theory incorporates Mach's principle in a subtle manner, the jury has remained out for decades. Now three American physicists have published a completely new idea that goes part way to restoring Newton's view of absolute space. However, physicists have discovered that what might appear to be a vacuum is in fact far from empty in the ordinary sense of the word.