A closed form solution of the two body problem in non-inertial reference frames

A comprehensive analysis, together with the derivation of a closed form solution to the two-body problem in arbitrary non-inertial reference frames are made within the present work. By using an efficient mathematical instrument, which is closely related to the attitude kinematics methods, the motion in the non-inertial reference frame is completely solved. The closed form solutions for the motion in the non-inertial frame, the motion of the mass center, and the relative motion are presented in the paper. Dynamical characteristics analogue to the linear momentum, angular momentum and total energy are introduced. In the general situation, these quantities may be determined as functions of time, and their derivation is presented within the paper. In the situation where the non-inertial frame has only a rotation motion, these quantities become first integrals in a larger sense, with respect to an adequately defined differentiation rule.