What are $($a$)$ the speed and $($b$)$ the period of a $380$ kg satellite in an approximately circular orbit $470$ km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of $2\mathrm{.}3\backslash$times $105$ J per orbital revolution. Adopting the reasonable approximation that the satellite's orbit becomes a $\text{'}\text{'}$circle of slowly diminishing radius,$\text{'}\text{'}$ determine the satellite's $($c$)$ altitude, $($d$)$ speed, and $($e$)$ period at the end of its $1278$ th revolution. $($f$)$ What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth$$s center conserved for $($g$)$ the satellite and $($h$)$ the satellite$$Earth system $($assuming that system is isolated$)?$