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- The perifocal coordinate (PQW) system is a frame of reference for an orbit. The frame is centered at the focus of the orbit, i.e. the celestial body about which the orbit is centered. The unit vectors and lie in the plane of the orbit. is directed towards the periapsis of the orbit and has a true anomaly of 90 degrees past the periapsis. The third unit vector is the angular momentum vector and is directed orthogonal to the orbital plane such that: And, since is the angular momentum vector, it may also be expressed as: 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, can be expressed as: where is the true anomaly and the radius r may be calculated from the orbit equation. The velocity vector, v, is found by taking the time derivative of the position vector: A derivation from the orbit equation can be made to show that: where is the gravitational parameter of the focus, h is the specific relative angular momentum of the orbital body, e is the eccentricity of the orbit, and is the true anomaly. is the radial component of the velocity vector (pointing inward toward the focus) and is the tangential component of the velocity vector. By substituting the equations for and into the velocity vector equation and simplifying, the final form of the velocity vector equation is obtained as: (en)
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- The perifocal coordinate (PQW) system is a frame of reference for an orbit. The frame is centered at the focus of the orbit, i.e. the celestial body about which the orbit is centered. The unit vectors and lie in the plane of the orbit. is directed towards the periapsis of the orbit and has a true anomaly of 90 degrees past the periapsis. The third unit vector is the angular momentum vector and is directed orthogonal to the orbital plane such that: And, since is the angular momentum vector, it may also be expressed as: where h is the specific relative angular momentum. (en)
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- Perifocal coordinate system (en)
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