Pitch over maneuver after launch

Hello everyone,

I am after clarification concerning payload delivery to orbit. A rocket,
at a certain point after launch, pitches over to form a closed orbit
around the earth. My questions are concerning the pitch over timing and
angle.

1. Is the time of pitch over determined by the vehicle velocity or
possibly the vehicle velocity versus target orbit velocity?

2. The orbit is expressed by an ellipse, but can the behaviour / path of
the booster be defined by the equation of an ellipse while it is still
producing thrust?

Any information or book recommendations would be great.

Thanks,

Stephen (refsmmat at gmail dot com)

Stephen wrote:

1. Is the time of pitch over determined by the vehicle velocity or
possibly the vehicle velocity versus target orbit velocity?

2. The orbit is expressed by an ellipse, but can the behaviour / path of
the booster be defined by the equation of an ellipse while it is still
producing thrust?

The first thing a rocket headed for orbit needs to do is get out of
the thickest parts of the atmosphere, because travelling at high speed
through thick air generates lots of heat and drag. This is the
principal factor determining when pitch-over begins.

A ellipse is the trajectory followed by an object subject only to the
inverse-square law of gravity. If other forces are acting, the
trajectory will not be an ellipse. I doubt that there is any simple
curve describing the trajectory followed to orbit: these things need
to be calculated numerically, step by step.