# Which reference frame for space shuttle PEG orbital insertion?

Which frame were the space shuttle's orbital insertion attitude targets specified in?

The shuttle had three frame choices: LVLH, INRTL, and REF (an inertial frame whose attitude the crew could lock in by pressing a button).

For attitude display, LVLH was selected early in launch. But would this be the same frame the closed-loop orbital insertion targets would have been specified in?

Since LVLH depends on the velocity vectors, whose direction is still changing during orbital insertion, it seems LVLH would be a poor choice to specify the attitude targets...

The orbital insertion targets for shuttle were

1. Inertial velocity magnitude
2. Altitude
3. Inertial flight path angle
4. Orbital plane

From Unified Powered Flight Guidance page 1-3 (see also table on 3-3)

Some explanation:

We will tackle the second difficulty by deciding on a non-rotating Earth-centric XYZ coordinate frame: X and Y axes will lie in the equatorial plane (X aligned with the 0° meridian at some given time), Z will point north. It's easy to convert spherical coordinates (longitude, latitude & altitude) into XYZ - we just have to remember that the Earth constantly rotates, thus the launch site coordinates will also be continuously changing. Converting Keplerian coordinates of the target orbit into XYZ is more difficult. Since it is not a single, unique point in position&velocity space but rather a set of points, we can only express the desired state in terms of constraints. We will write them in the following form:

• plane - defined by desired inclination and longitude of ascending node,

• altitude - desired radius at MECO,

• velocity - magnitude of the desired velocity vector,

• flight path angle - angle between desired velocity vector and local horizontal.

The first constraint can be easily and uniquely written in XYZ form as a vector normal to the target plane (we can use Euler formulas to calculate it knowing INC and LAN angles), explicitly describing where the orbit will be and what will be the direction of motion. Next three describe what the orbit will look like: knowing altitude (radius) and corresponding velocity and angle, we can draw an ellipse in a unique way.

From here - written by a person who sat down and wrote their own version of PEG by poring through the shuttle documents