Gavroy said:
and what would be the theoretically best orientation? as far as i see, this angle could not differ that much from 90 degrees, as centrifugal force is compared to the velocity you need to escape from the Earth relatively weak.
What centrifugal force? It is a fictitious force. You do not need to invoke centrifugal force; it is in fact easier to look at things from the perspective of a non-rotating frame in which there is no centrifugal force.
As far as "optimal" is concerned, what are you trying to optimize? There are multiple conflicting variables in play here, so there is no such thing as a trajectory that optimizes everything. The best one can do is some sort of compromise.
Start out easy by looking at launching from an airless, non-rotating planet with no concern for structural issues and with a rocket capable of extremely high (effectively infinite) thrust. Here the "best" thing to do is to launch horizontally with an impulsive burn that places the apofocus at the desired altitude. The rocket will perform a second horizontal impulsive burn to place the rocket in a circular orbit upon reaching apofocus. This is essentially a Hohmann transfer from the ground to on-orbit. Making all of the burns horizontal means there are no gravity losses.
Making the planet rotate just means the first burn needs to be to the east (in the direction of rotation) to minimize fuel consumption. It's still a Hohmann transfer with horizontal burns.
Adding an atmosphere makes things a lot more complicated. Air drag increases with the velocity squared while density decreases more or less exponentially with increased altitude. This means gives some advantage in gaining altitude at a relatively low velocity. However, this increases gravity losses. So a tradeoff.
Adding concerns about structural and payload integrity makes things even more complicated. The only orientations that make sense structurally are vertical and horizontal. Anything in between would require adding lot more structure to both the rocket and to the launch system, and even a horizontal orientation would require more structure in the rocket than would a vertical orientation. Another downside of a horizontal orientation is that this makes it hard to balance increase in velocity versus decrease in pressure. In technical terms, it would make for a very large max Q (maximum dynamic pressure).
As for the optimal trajectory, it's called a "gravity turn" (google that phrase).