The perifocal coordinate (PQW) system is a frame of reference for an orbit is directed towards the periapsis has a true anomaly is the angular momentum vector and is directed orthogonal to the orbital plane such that:

is the unit vector where h is the specific relative angular momentum.

The position and velocity vectors can be determined for any location of the orbit. The position vector, r may be calculated from the orbit equation.

The velocity vector, v, is found by taking the time derivative

is the gravitational parameter of the focus, h is the specific relative angular momentum of the orbital body, e is the eccentricity into the velocity vector equation and simplifying, the final form of the velocity vector equation is obtained as:

Conversion between coordinate systems

The perifocal coordinate system can also be defined using the orbital parameters inclination (i), right ascension of the ascending node) and the argument of periapsis). The following equations convert from perifocal coordinates to equatorial coordinates and vice versa.

Perifocal to equatorial

Following the standard 3-1-3 rotation (see Conversion formulae between formalisms

.

Equatorial to perifocal

Applications

coordinate must be aligned with the eccentricity vector. Circular orbits, having no eccentricity, give no means by which to orient the coordinate system about the focus.

The perifocal coordinate system may also be used as an inertial frame of reference because the axes do not rotate relative to the fixed stars. This allows the inertia of any orbital bodies within this frame of reference to be calculated. This is useful when attempting to solve problems like the two-body problem.

References