Approximate Solutions of the Equations of Motion of a Charged Particle in the Field of a Magnetic Dipole

Three differential equations of the first order (26)—(28) which determine the trajectory are deduced. An approximate integration by means of elementary functions yields a set of formulas (in chapt. 13. Conclusions) that give a „window” in the sky inside of which the radiation point of a high energy cosmic ray (monotonely bent in the magnetic field) must lie.