Serial of year 15

In this problem we analyse and interpret measurements made in 1994 on radio wave emition from a source consisting multiple bodies within our galaxy. The distance to the central celestial body from Earth is estimated to be $R = 3,86.10^{20}$ m. The angular velocities of two objects ejected from the centre in opposite directions were measuredyo be: $\omega _{1} = 9,73.10^{-13} rad.s^{-1}$ and $\omega _{2} = 4,42.10^{-13} rad.s^{-1}$. We calculate the transverse velocities: $v_{1} = R\omega _{1} =3,76.10^{8} m.s^{-1}$ and $v_{2} = R\omega _{2} = 1,71.10^{8} m.s^{-1}$. The first object is faster than light! How is it possible?

Let's consider an object moving with velocity $v$. The angle between the velocity vector and the direction to the observer is $\varphi$. The distance to the observer is denoted $R$. Calculate the angular velocity as seen by the observer. Can $Rω$ be greater than the speed of light? Using your results calculate the real velocities of the two objects. Assume that the velocities are equal.