Orbital Mechanics Vis Viva Equation Question

[FQVBSina_Jesse]

In the case of a satellite orbiting the Earth. Would the relative velocity calculated by the Vis Viva equation the same as the orbital speed of the satellite? If the satellite is in an ellipse, would Vis Viva give the circular tangential velocity V_t=rω, or would it give the orbital velocity V_o=V_t/cos(Φ), where Φ is the flight path angle?

Thanks!

 

[FQVBSina_Jesse]

Additionally, is the following relationship between circular tangential velocity, V_t, orbital speed, V_o, radial speed, r_dot, and flight path angle, Φ, correct?
V_t² + r_dot² = V_o²
Therefore,
Φ = tan^-1(r_dot/V_t)