I have read numerous explanations as to why it is beneficial to launch a rocket in the eastern direction. I know that it's true because NASA's website http://spaceplace.nasa.gov/launch-windows/en/ even claims this. But it makes absolutely no sense to me. I understand that the Earth is spinning at about 410 m/s towards the east. I also understand that the 410 m/s is an initial tangential speed that lessons the mechanical energy needed to reach an orbit. So then what advantage does an easterly launch bring? The conservation of angular momentum conserves the tangential speed of 410 m/s, so that will be there whether it is a vertical launch or an easterly launch. Therefore, it seems that any easterly motion is just going to add to the 410 m/s that the rocket starts with. And the vertical launch costs the same amount of potential energy no matter what angle it gets launched at. Can someone please make sense of this. I left out the orbital help of the Earth around the Sun to keep this simple for me.