Velocity Vector Transformation for Point Ahead Angle and Doppler Shift Calculation for Inter-Satellite Link

So, I have the Radial and Tangential Velocity Vector (like in Figure 1) and also the Cartesian coordinate of 3D velocity vector. For reference, you can see in this link. Where, $$o_{dot}$$ vector matrix have 3 components (only X,Y component), first element $$V_R$$ and second element $$V_T$$ like in the Figure 1. But to calculate Point Ahead Angle and Doppler Effect I should follow, this velocity vector like in Figure 2. Where Vp is the perpendicular or the tangential (I guess so!) one and Vr is aligned with Line-of-Sight, where radius is the Range between 2 satellites, as describe here by @uhoh But how to transform the velocity vector as in orbital mechanics point of view (lets take we all are in same inertial frame) from derived in Figure 1 to Figure 2 formation. Is it simply rotation of the angle (angle between Earth-Satellite1-Satellite2) where radial velocity must align with line-of-sight, how?

Thank you

• I mentioned you should ask a new question and you did right away, that's great! +1 I did add a little bit more to this answer but I don't think that addresses this.
– uhoh
Sep 26 '19 at 1:55
• Careful with your definitions. In a circular orbit, the tangential and radial velocities of the spacecraft are orthogonal. But in any real orbit, the velocity and the position are not usually orthogonal. Still, the modulus of the tangential velocity is the modulus of the velocity. Oct 16 '19 at 15:37