LEO cannon ball

runner2392

How long would it take a cannon ball to orbit the earth given that the radius of the
earth is 4000 miles and the height of the (quite fictitious) mountain is 800 miles?

Me = mass of earth
Mc = mass of cannon ball
R = earth's radius
v = 2piR/T
4000 mi = 6437200 meters
a = acceleration of cannon ball
G = 6.67e-11
Using an applet for a previous question, I found Vo to be 15468 miles/hr. But I didn't use Vo... Instead I used Fnet = GMeMc/r^2 as follows.

Fnet = GMeMc/r^2 = Mca = (Mc(2piR/T)^2)/R -->
GMe/r^2 = (4pi^2*R^2)/RT^2 -->
r^2/GMe = T^2/(4pi^2*R) -->
sqrt(4pi^2*R^3)/GMe = T

my result was 5138s, which is about 85.6 minutes.
Does my work and result look all right?? thanks in advance

SHISHKABOB

well, the International Space Station is in Low Earth Orbit and it takes about 90 minutes to orbit the Earth once, so you're in the right ballpark ;)

it's about 200 miles up for comparison, and has an orbital velocity of about 7,000 m/s

runner2392

thanks!