How Do You Calculate the Speed of a Satellite in Orbit?

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To calculate the speed of a satellite in a stable circular orbit at a height of 3600 km, the gravitational force must equal the centripetal force. The relevant formula is v² = GM_E/(R_E + h), where G is the gravitational constant, M_E is the mass of the Earth, R_E is the Earth's radius, and h is the height of the satellite. The height of the satellite is converted to meters, resulting in a total radius of 6.3 x 10^6 m. By substituting the known values into the equation, the satellite's orbital speed can be determined. This method effectively combines gravitational and centripetal force equations to find the solution.
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Homework Statement


Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 3600 km.

Homework Equations


v2=Gm/r
F=(Gm1m2/r2
g=(Gm)/r2
G=6.67x10-11Nm2/kg2
rE=6380km=6.3x106m----(Radius of Earth)
mE=5.98x1024kg---------(Mass of Earth)

The Attempt at a Solution



Changed height of satellite to 3.6x106m
I think I can assume the height as the radius.

I come up on blanks on what to do from here.
 
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The gravitational attraction must provide the centripetal acceleration for the circular orbit:

GMEm/R2 = mv2/R

So,

v2= GME/(RE + h)

And yes, the height/radius are the same. Just plug in the info you have and solve!
 

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