where M is the mass of each point, and x i are components of the (unit) position vector of one of the points. As they orbit, this x -vector will rotate, which means that it will have a non-zero first, and also a non-zero second time derivative (this is of course true regardless the choice of the coordinate system). Therefore, the system will radiate gravitational waves. Energy lost in this way was first observed in the changing period of the Hulse–Taylor binary, a pulsar in orbit with another neutron star of similar mass.