Effect of Galactic Rotation on Radial Velocities and Proper Motion. Part II

We express the geometrical and algebraic aspects of the problem of galactic rotation on the motion of the stars represented by fig. (2). We verify the equations involving third order terms of the orbits of the stars. That means taking into account higher order terms in our analysis, namely up to O(r=R0)3. These terms allow a generalization and high precision for the results. We acquired a higher order Taylor’s expansion for V as denoted in fig. (2). U′, V ′ are the linear components of the velocity of the group of stars S. After some lengthy expansions and reductions, we obtained the formulae for U′, V ′. Consequently ξ, ƞ, Ϛ the linear components of S corresponding to the two proper motion equalities in galactic longitude and latitude and radial velocity Δρ. Expansions are performed up to the third order in (r=R0).