Orbital Velocity Homework: Find Velocity of Geostationary Satellite

[zeion]

Homework Statement

Basically says that a geostationary satellite requires a distance of 35 900 km above Earth's surface. I need to find its orbital velocity.

Homework Equations

The Attempt at a Solution

I find the circumference of the orbit = 225566.3525km then change units to m/s but the answer is wrong?

 

[rock.freak667]

The gravitational force between the satellite and the Earth is proving the centripetal force of the satellite. From the equation for centripetal force you have velocity.

 

[zeion]

But I'm not given the mass of the satellite

 

[rock.freak667]

But I'm not given the mass of the satellite

When you equate the two, the mass of the satellite cancels out.

 

[zeion]

Do I need to use the angular velocity?

 

[rock.freak667]

Do I need to use the angular velocity?

No, I believe that they are asking you for the linear velocity which is the 'v' in the expression for centripetal force.

 

[zeion]

So I need to use centripetal acceleration?

 

[rock.freak667]

So I need to use centripetal acceleration?

Essentially yes.

 

[zeion]

How do I calculate that? I only have the radius and the period.

 

[rock.freak667]

How do I calculate that? I only have the radius and the period.

Do you know the expressions for centripetal force and gravitational force?

 

[zeion]

F = (mv^2) / r ?

 

[rock.freak667]

F = (mv^2) / r ?

then put that equal to the expression for gravitational force and find 'v'.

 

[zeion]

Is that F = ma?

 

[rock.freak667]

Is that F = ma?

No you should know that F=GMm/r² where 'r' is the distance between the Earth and the satellite.