Double-pulse cotangential transfers between coplanar elliptic orbits☆

The geometric characteristics of double-impulse cotangential transfers between coplanar elliptic orbits, which are used to investigate of such transfers, are given. Each argument is accompanied by the development of a corresponding geometric algorithm which illuminates the mechanical problem from a geometric point of view, imparting the clarity to it which is characteristic of a geometric concept. A general method of investigation is developed based on a comparison of the behaviour of a cotangential transfer with an excentre of the transfer orbit which is joined to the excentres of the given elliptic orbits (an excentre is a circle constructed on the major axis of the ellipse which is its diameter). The cotangential transfer trajectory parameters and the values of the velocity pulses controlling the motion of the spacecraft during the transfer are determined in explicit form and depend on the parameters of the specified orbits and the true anomaly of the point of application of the first velocity pulse.