First of all you are posing the issue from a Newtonian perspective. Within that perspective there is no explanation of what gravity is. Form earth it appears to be an attraction between mass. On the other hand, graviton type theories of gravity treat it as a pressure (corpuscular). They end up with the same mathematics as Newtonian.
You are positing that the stars do not matter. If they do not, what causes inertia? Mach’s principle tells us that inertia is caused by resistance to movement by the stars. If the stars are powerful enough to cause inertia, why wouldn’t they factor in in calculating the gravitational balance of the universe? Remeber, though the force from each star may be small, there are billions out there. Things do sum up.
If a corpuscular gravity is the reality, and the corpuscles are generated at the spherical outer edge of space and move radailly inwards (approximately), then gravity would tend to be an earthward force.
When talking about geocentrism you need to consider the possibility of rotational stability mechanisms (i.e., gyroscopic stabilization). Also, if the universe contains an aether as quantam mechanicists say (they don’t call it aether), then really it would be the aether field that determines the universal properties. Note that QM and relativity are incompatible because of this dichotomy (GR posits vacuum space, QM posits corpuscular space with density as high as 10^94 g/cc).
If the aether is stationary, than a Newtonian-like universe is possible. If it is rotating, then a geocentric-like universe is possible.
Please read Parts I and II of my blog. It is hard to get to detailed in a small space like this (or even on my blog, but there is more freedom and space there).
Mark
www.veritas-catholic.blogpsot.com