For any given launch, a direct ascent due east will produce an orbit whose inclination is the latitude of the launch site. So, out of the Cape, latitude 28-ish degrees, a due east ascent produces a orbit with a latitude of 28 degrees. G* orbit is 52, so, the Delta out of the Cape had to do a left hand turn 14 deg to the north.
When launching out of Vandenberg, the ascent is essentially due south. Then it needs to make a left hand turn and 90 deg at the equator would put it due east, but that is still short of the 52 deg goal. The exact number depends on several factors, and rocket trajectories is not my area of expertise, so I don't want to say something that is not exactly correct, but hopefully this provides an idea of the magnitude of what is required.
But this is still only part of the story. The energy required to make that "left hand turn" is proportional to both the sine of the angle and the velocity at the time the turn is made. Launching out of the Cape and making a turn to the north when the rocket is going relatively slow is common and the delta V (energy) required is much less than when making the turn when the rocket is at altitude, and going much faster.
The reason that this is necessary is that the manifest out of the Cape is pretty full -- to get more Delta launches required the testosterone approach out of Vandenberg. I, for one, think it is way cool! |
