# If mass is homogeneously distributed why would there be gravitational attraction between bodies? [duplicate]

Assuming the mass of the universe was spread completely evenly throughout space why would gravitational attraction happen? All bodies in the universe would feel gravitational tug equally in all directions so why would they go anywhere?

• – PM 2Ring Jun 28 '20 at 23:38
• – Gendergaga Jun 29 '20 at 5:39
• The question seems to assume Newtonian gravity, not general relativity – Charles Francis Jun 29 '20 at 18:05
• @CharlesFrancis True, but most of the answers to the nominated duplicate target also cover the Newtonian case. – PM 2Ring Jul 1 '20 at 1:38

Let mass density be constant, $$\rho$$. Take any two points, $$\mathrm A$$ and $$\mathrm O$$, a distance $$R=\mathrm {OA}$$. According to Newton's shell theorem the gravitational force at $$\mathrm A$$ due to any spherical shell containing $$\mathrm A$$ and centred at $$\mathrm O$$ is zero. The gravitational acceleration due to matter inside a sphere of radius $$R$$ centred at $$\mathrm O$$ is $$\frac {4\pi} 3 G \rho R$$
In other words the gravitational tug does not cancel out, but is towards $$\mathrm O$$, which is clearly inconsistent because $$\mathrm O$$ can be any point in the universe.