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LEO cannon ball

by runner2392
Tags: ball, cannon
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runner2392
#1
Feb29-12, 08:45 PM
P: 11
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
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SHISHKABOB
#2
Feb29-12, 08:53 PM
P: 614
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
#3
Feb29-12, 10:24 PM
P: 11
thanks!


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