The orbit plane is that defined by R and V. Thus, the orbit normal vector, N, is
Let the inertial coordinate axes be defined by x in the direction of the vernal equinox, z in the direction normal to the Earth's equator, and y such that the coordinate system is orthonormal and right-handed. TTten, the inclination is given by
and the right ascension of the ascending node by fi = arctan(— Nx/Ny) (3-26)
The vector in the direction of the ascending node is Ô=zXN. The semimajor axis is determined by the vis viva equation as:
where ¡i = GM and a negative value of a corresponds to a hyperbolic trajectory. The period for elliptical orbits is then obtained from Kepler's Third Law as:
If we define the heading or flight path angle, ft, by
then the eccentricity, e, and the true anomaly, v, are given by (see, for example, Thomson ):
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