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

We expand Δfi the radial velocity of a group of stars moving around the center of galaxy, firstly in circular orbits. The expansion of Δfi is performed up to the third order of O(r/R0)3. A new result is encountered. The Oort constant is splitted into 3 parts A1, A2, A3 instead of one constant A. Moreover we verify the problem when the motion of the stars is elliptic. For proper motion components, there is no split of the second Oort‘s constant B. In all involved expansions orders of magnitude higher than the third in ΔR or r/R0 are neglected.