What is the formula for gravity loss on a rocket launch and how was it derived?

[Januz Johansen]

Hello all!
Lately i have been looking at many rocket equations, and i was wondering about the gravity loss on a rocket launch. I found the formula for the gravity loss

where g is of course the gravitational acceleration, and y is the flight path angle, but can someone explane why it looks like this? How has this been deduced?
Thanks

 

[mfb]

It is the component of the gravitational force along the velocity of the rocket (=the component changing the velocity), integrated over the whole rocket flight time.

 

[Januz Johansen]

It is the component of the gravitational force along the velocity of the rocket (=the component changing the velocity), integrated over the whole rocket flight time.

Okay thanks
But why do we have to take the Angle into accound?

 

[mfb]

Acceleration orthogonal to the direction of motion does not change the speed.

 

[Januz Johansen]

Acceleration orthogonal to the direction of motion does not change the speed.

Okay thank you