Is it except the center of mass, the other part of the object do not have weight ?
why when we do the calculations , we always neglect the other part out of the center of mass ?

Good question!
the answer is because in an object, the mass is distributed about the axis. So in the centre, there is equal amounts of mass along each side of each axis from that point.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.