In Self-contradiction, Machian Geocentrism Entails Absolute Space
  Luka Popov has attempted to advance Machian physics by maintaining that the heliocentric system must be replaced by Tycho Brahe's geocentric system. We show that while geocentrism relies on Mach's contention that accelerations are relative, this contention is untenable because, inter alia, the consequences of an acceleration of an object with respect to the fixed stars cannot be duplicated by acceleration of the stars with respect to this object and, if the universe and a co-rotating observer have the same angular velocity, this motion is detectable because they have different linear velocities. Also, geocentrism precludes the relativity of accelerations and leads to an absolute space while Mach argued against absolute space, Popov's result that the force exerted by the Earth on the Sun depends on the square of the Sun's mass but is independent of the Earth's mass is paradoxical, and the annual asymmetry of the Cosmic Microwave Background falsifies all geocentric or 'Tychonic/Brahean) systems. 
Herbert I. Hartman and Charles Nissim-Sabat
physics.hist-ph