Problem $17\mathrm{.}151$ The satellite $\backslash ($ A $\backslash )$ is in a circular polar orbit $($a circular orbit that intersects the earth's axis of rotation$).$ The radius of the orbit is $\backslash ($ R $\backslash ),$ and the magnitude of the satellite's velocity relative to a non$-$rotating reference frame with its origin at the center of the earth is $\backslash ($ v$\_\{$A$\}\backslash ).$ At the instant shown, the satellite is above the equator. An observer $\backslash ($ B $\backslash )$ on the earth directly below the satellite measures its motion using the earth$-$fixed coordinate system shown. What are the velocity and acceleration of the satellite relative to $\backslash ($ B $\backslash )\text{'}$s earth$-$fixed coordinate system? The radius of the earth is $\backslash ($ R$\_\{\backslash$mathrm$\{$E$\}\}\backslash )$ and the angular velocity of the earth is $\backslash (\backslash$omega$\_\{\backslash$mathrm$\{$E$\}\}\backslash ).($See Example $17\mathrm{.}12.)$