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LEO cannon ball 
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#1
Feb2912, 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 = 6.67e11 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 


#2
Feb2912, 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 


#3
Feb2912, 10:24 PM

P: 11

thanks!



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