$($a$)(5$ points$)$ A satellite is to be launched into a circular orbit around the Earth so that it orbits the planet once every T seconds. Using Newton's second law F$=$ma for circular motion, where F$=$GMm$/$r$2$ is the gravitational force on the satellite, derive the expression $($by hand, not numerically$)$ for the satellite's altitude h above the Earth$$s surface and show that the form is:

h$=($GMT$24$$2)1/3$R

where G$=6\mathrm{.}671011$m$3$kg$1$s$2$ is Newton's gravitational constant, M$=5\mathrm{.}971024$ kg is the mass of the Earth, and R $=6371$ km is its radius. Part $($b$)(10$ points$)$ Write a program that asks the user to enter the desired value of T and then calculates and prints out the correct altitude in meters. Part $($c$)(5$ points$)$ Extend this program to quit and print the error message Period not allowed if the height turns out to be negative. python $3$