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Full Version: converting a state vector to C3, RLA and DLA
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This HP Prime program, named demo_rv2hyper, can be used to calculate C3 (twice the specific (per unit mass) orbital energy), RLA (the right ascension) and DLA (declination) of the asymptote of a hyperbolic trajectory. This computer program assumes that the hyperbolic targets, state vector and classical orbital elements are all in the same Earth-centered-inertial (ECI) coordinate system.

This demo program uses "hard-wired" x, y and z components of the position and velocity vectors of a typical hyperbolic orbit. For this example

// eci position vector (kilometers)

r(1) := -6.28143245744413e3;
r(2) := -1.71886519445504e3;
r(3) := -8.16419427413681e2;

// eci velocity vector (kilometers/second)

v(1) := 3.30316298967422;
v(2) := -9.56155991173246;
v(3) := -5.28351302498913;

The zipped archive for this program and its documentation can be downloaded from

Reference URL's