Solve Orbital Velocity Equation: V=sqrt((g*R^2)/r)

[chris529911]

I have a homework problem that involves the equation v=sqrt((g*R^2)/r) I am confused as to where this equation comes from. I know that Vcirc = sqrt((GM)/r) and Vesc = sqrt((2GM)/r)

 

[ideasrule]

Do you know the formulas a=v^2/r and a=GM/r^2? Equate the two and you get v^2/r=GM/r^2. With a bit of manipulation, you get that equation.

 

[chris529911]

a=v^2/r is the equation for the normal component of acceleration

a=GM/r^2 derived from F= GMm/r^2

a satellite orbiting the Earth only has a normal component of acceleration correct ?

 

[chris529911]

this is the problem. Why can't you just use v^2=GM/r?

 

[ideasrule]

a=v^2/r is the equation for the normal component of acceleration

a=GM/r^2 derived from F= GMm/r^2

a satellite orbiting the Earth only has a normal component of acceleration correct ?

For a circular orbit, yes.

 

[ideasrule]

this is the problem. Why can't you just use v^2=GM/r?

You can. That comes from equating v^2/r with GM/r^2.