I have a coordinate system that's fixed on the center of the Earth (assume a sphere).
I know two angles, $\alpha$ and $\delta$, as shown in the figure. These angles will be used to find the position of a point outside the sphere (the satellite). Now let's say I moved the coordinate system to a point on the sphere, keeping its orientation. We know the angles of the point as well (latitude and longitude). Here's my question. Given that I know $\alpha$, $\delta$, latitude, longitude, and magnitude of R, can I find the new angles $\alpha_t$ and $\delta_t$, that point(?) to the same point as $\alpha$ and $\delta$ ?
Edit: If it is not possible to do so, then can I find a transformation matrix for a unit vector in the original coordinates?