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Satellite rotation

QUESTION:
Suppose we want a satellite to revolve around the Earth 5 times a day. What should the radius of its orbit be? (Neglect the presence of the moon.)

WORK:

Found the number of second in 24 hours and divided it by 5 to get the period. Then rearranged the gravitational equation with T^2=((4pi^2)/(GM))r^3 and solved for r. I came up with 1.44 × 10^7 m but its wrong. Any insight?
 

Answers and Replies

Dick
Science Advisor
Homework Helper
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That seems pretty reasonable to me. Why do you think there is something wrong with it?
 
My teacher calculated 7.78 x 10^7 m. The difference is our calculations of the period. He did 5 x 12 x 3600 for the period while I did (24 x 60 x 60)/5. I don't understand where he came up with 12. Could someone help me see where my teacher or I made a mistake.
 
Dick
Science Advisor
Homework Helper
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(24*60*60)/5 is 5 times a day. 5*12*3600 is once every 60 hours. If you are reading the same problem I don't see how he could interpret that as '5 times a day'.
 
Yea I don't know why he did it either. Can any else find a reason for it?
 
83
1
I think you are right
5 times a day means 0.2 day for a complete revolution...
 
tony873004
Science Advisor
Gold Member
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Here's an online calculator I made. It does the unit conversions for you. Choose units of days, Earth masses, and seconds. Plug in 0.2 for period (1/5 of a day), 1 for Mass, and it will compute seconds for you: 1.44E7. Your teacher is wrong. You are right.

http://orbitsimulator.com/gravity/articles/formula55.html
 

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