Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_74

3/74 The spacecraft $P$ is in the elliptical orbit shown. At the instant represented, its speed is $v = 13,244 \text{ ft/sec}$. Determine the corresponding values of $\dot{r}$, $\dot{\theta}$, $\ddot{r}$, and $\ddot{\theta}$. Use $g = 32.23 \text{ ft/sec}^2$ as the acceleration of gravity on the surface of the earth and $R = 3959 \text{ mi}$ as the radius of the earth. Diagram information: Perigee altitude: $200 \text{ mi}$ Apogee altitude: $22,300 \text{ mi}$ Vertical distance from earth center $O$ to spacecraft $P$: $10,450 \text{ mi}$ At the instant shown, velocity $\vec{v}$ is horizontal.