The Stars

Newton realized that according to his theory of gravity,the stars should attract each other.so it seemed they could not remain essential ly motionless.would they now all fall together at some point?He argued that this would indeed happen if there were only a finit number of stars distributed over a finite region of space but reasoned that if.On the other hand,there were an infinite number of stars,distributed more or less uniformly over infinite space,this would not happen because there would not be any central point for them to fall to .
This argument is an instance of the pitfalls that you can encounter in talking about infinity.In an infinite universe every point can beregarded as the centerbecuase every point has an infinite number of stars on each side of it.The correct approachit was realised only much later,is to consider the finite situation in which the stars all fall in on each other ,and then how to ask how things change if one adds more stars roughly uniformly distriuted outside this region.According to Nwtons law the extra stars would make no difference at all to the original ones on average,so the stars would fall in hust as fast.we can add as many stars as we like,but they will stillalways collapse in on themselves .we now know it is impossible to have an infinite static model of the universe in which gravity is always attractive.