$($adopted from Prob. $5,$ Wiesel, p$.42)$ A future radiotele$-$

scope might be constructed with a very large reflector and

a separate spacecraft located at the focal point, a fixed dis$-$

tance $R($perhaps several kilometers$)$ from the main reflec$-$

tor. 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.