
#1
Dec1109, 11:17 AM

P: 7

1. The problem statement, all variables and given/known data
Use the equation derived about to calculate the exact value of the initial speed that will produce a circular orbit of the satellite at an altitude of 1000 km above earth. 2. Relevant equations Derived equation provided: Finward = Fg m1 v^2 / r = Gm1m2/r v^2 = Gm2/r v= (square root of) Gm2/r 3. The attempt at a solution Finward = Fg m1 v^2 / r = Gm1m2/r v^2 = Gm2/r v = (square root of) Gm2/r v = (square root of) (6.67x10^11)(5.98x10^24)/1000 v = (square root of) 3.98....x10^11 I didn't round of 3.98....on my calculator; I saved the whole number and calculated the square. This gave me: v = 631558.39 v = 6.3x10^5 m/s ???? Is this initial velocity though? Or did I miss a step? 



#2
Dec1109, 11:24 AM

Emeritus
Sci Advisor
PF Gold
P: 5,198

In Newton's law of gravitation, r is the distance from the *centre* of mass 1 to the *centre* of mass 2. This is true for the equation for centripetal force as well  r is the distance from the object to the centre of its orbit. In other words, you have not used the correct distance for r.




#3
Dec1109, 11:59 AM

P: 69





#4
Dec1109, 12:07 PM

P: 7

Derived equation...initial speed...
Finward = Fg
m1 v^2 / r = Gm1m2/r v^2 = Gm2/r v = (square root of) Gm2/r v = (square root of) (6.67x10^11)(5.98x10^24)/(1000/2) v = (square root of) (6.67x10^11)(5.98x10^24)/500 v = (square root of) 7.977...... I didn't round of 7.977....on my calculator; I saved the whole number and calculated the square. This gave me: v = 893158.4406 v = 8.9x10^5 m/s ???? Is this the initial velocity? 



#5
Dec1109, 12:14 PM

Emeritus
Sci Advisor
PF Gold
P: 5,198

Where do you get 1000/2 from? This is not correct. I think you should read my previous post again. The distance 'r' has a very specific definition here.




#6
Dec1109, 12:23 PM

P: 7

Finward = Fg
m1 v^2 / r = Gm1m2/r v^2 = Gm2/r v = (square root of) Gm2/r G= gravitational constant = 6.67x10^11 m2= mass of earth = 5.98x10^24 r= radius of earth + altitude of satellite above earth = 6.37x10^6 + 1000 ????? If everything else is right, would this equation give me initial velocity or average? 


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