The classical two - body problem has been considered and the exact solution ofrnKepler's problem has been obtained for the general case.rnUsing this solution the spectrum of the radiation from the system of two chargedrnparticles with Coulomb interaction is briefly discussed. In addition the angularrndistribution of the average power radiated by the system is preciselyrncalculated.The effect of the radiation on the system and the spectrum is deeplyrninvestigated. Relativistic circular motion of a charge and the spectrum of thernradiation is considered in the second part in which the direct way of evaluationrnof the average power radiated by the system is considered. The interfernce of thernradiation from a system of two charges in a circular motion is also considered.rnThe Lagrange expansions of the electromagnetic potentials of a relativisticrncharge in a circular motion is considered for far zone. The exact expression ofrnthe s imu 1 taneous electromagnet i c potent i a 1 s of the charge for any distance isrnalso considered as well as their spectrum for a circular motion