Calculating Time for Cannon Ball to Orbit Earth at 4000mi Radius

[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!