Calculating Elements from Position and Velocity Vectors
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Let r and v be the cartesian position and velocity 
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vectors of an orbiting object in coordinates of a reference frame 
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with respect to which the elements of the orbit are to be calculated (e.g. geocentric equatorial for an 
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orbit around Earth, or heliocentric ecliptic for an orbit around the Sun). We assume a right-handed 
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system with the x-axis pointing towards the vernal equinox (or other reference direction) and the z-axis pointing upwards.
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Compute the following auxiliary vectors: