Derived equation initial speed

[7randomapples]

Homework Statement

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. Homework Equations
-Derived equation provided:
Finward = Fg
m1 v^2 / r = Gm1m2/r
v^2 = Gm2/r
v= (square root of) Gm2/r

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?

 

[cepheid]

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.

 

[dr_k]

...
v = 6.3x10^5 m/s ?

Is this initial velocity though? Or did I miss a step?

Draw a picture, and ask, what is r?
http://img705.imageshack.us/img705/790/fma3.jpg

 

[7randomapples]

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?

 

[cepheid]

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.

 

[7randomapples]

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?

 

[cepheid]

It would give you the orbital speed of the satellite (which is constant in magnitude).