# Help understanding centre of mass

So basically the question I posed myself a few days ago was for a torus shaped planet, what would the gravitational field be like inside the torus? After viewing some answers on the internet, (Gravity on a doughnut-shaped/Möbius planet, and also having my friend code http://ideone.com/s9tlyM for me to check), it seems that anywhere inside the torus, you would experience a force towards the .centre (ie the centre of mass). TORUS RING misinterpreted results oops

So what does the centre of mass really mean for an object, if when I'm in the torus planet, and I'll fly to the edges, instead of being attracted to the centre of mass (which seems logical to me) Or does centre of mass have no relation to gravity at all? http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy) As best as I understand this article, it says that a system of stars will orbit around their centre of mass, so if you treat me and the torus planet as two stars shouldn't I be attracted to the centre of mass?

Thanks for any help clearing this up.