Investigating the non-inertial R2BP in case of variable velocity \(\vec{\mathbf{V}}\) of central body motion in a prescribed fixed direction

In this analytical study, we have presented a new type of solving procedure with the aim to obtain the coordinates of small mass m, which moves around primary M_Sun, referred to non-inertial frame of restricted two-body problem (R2BP) with a modified potential function (taking into account the variable velocity \(\vec{V}\) $\overrightarrow{V}$ of central body M_Sun motion in a prescribed fixed direction) instead of a classical potential function for Kepler’s formulation of R2BP. Meanwhile, system of equations of motion has been successfully explored with respect to the existence of an analytical way of presenting the solution in polar coordinates {r(t), φ(t)}. We have obtained an analytical formula for function t = t(r) via an appropriate elliptic integral. Having obtained the inversed dependence r = r(t), we can obtain the time dependence φ = φ(t). Also, we have pointed out how to express components of solution (including initial conditions) from cartesian to polar coordinates as well.