Just in case anybody doesn’t understand the difference between space-fixed velocity and earth-fixed velocity, I’ll explain.
Suppose you are witness to a rocket launch. When you see the rocket on the launch pad it appears stationary, but in reality it is moving because Earth is rotating. You don’t see it move because you are moving along with it. At the latitude of Cape Canaveral, the velocity is 409 m/s in a due east direction. The velocity you see is the earth-fixed velocity, or 0 m/s as the rocket sits on the launch pad. However, the velocity relative to the heavens, or the space-fixed velocity, is 409 m/s.
Suppose the rocket lifts off and travels straight up for several seconds, reaching a velocity relative to the launch pad of 20 m/s. Now the earth-fixed velocity is 20 m/s. Meanwhile, the space-fixed velocity has a vertical component of 20 m/s and a horizontal component of 409 m/s. The total space-fixed velocity is SQRT(20²+409²) = 409.49 m/s.
Flight path angle is the angle the velocity vector makes with the local horizon. Since the earth-fixed velocity vector is straight up, the earth-fixed flight path angle is 90 degrees. On the other hand, the space-fixed flight path angle is ATAN(20/409) = 2.80 degrees.
For things like determining the orbit, we use space-fixed velocity, but for things like calculating atmospheric drag, we use earth-fixed velocity.