$($adopted from Prob. $5,$ Wiesel, p$.42)$ A future radiotelescope might be constructed with a very large reflector and a separate spacecraft located at the focal point, a fixed distance $R($perhaps several kilometers$)$ from the main reflector. As the reflector changes is orientation the two angles $$ and $$ shown in the figure change with time, but hat$(s{)}_2$ remains in the hat$(i{)}_1-$hat$(i{)}_2$ plane. Write the angular velocity of the $S$ frame shown in the figure, and find an expression for the velocity the spacecraft needs to remain at the focal point.