Gravitational waveforms for 2- and 3-body gravitating systems

Different numbers of self-gravitating particles (in different types of periodic motion) are most likely to generate very different shapes of gravitational waves, some of which, however, can be accidentally almost the same. One such example is a binary and a three-body system for Lagrange's solution. To track the evolution of these similar waveforms, we define a chirp mass to the triple system. Thereby, we show that the quadrupole waveforms cannot distinguish the sources. It is suggested that waveforms with higher $\ell$-th multipoles will be important for classification of them (with a conjecture of $\ell \leq N$ for N particles).