Horizon coordinates:

This is a local coordinate system for a particular observation point $O$ on the Earth, as shown in Fig. . The $z$-axis is defined to be the direction opposite to the local acceleration due to gravity. The $x$-axis is defined to lie in the plane formed by the $z$-axis and the Earth's rotational axis, and to be directed into the northern hemisphere. In this coordinate system, the latitude coordinate is called the altitude and the longitude coordinate is the negative of what astronomers call the azimuth; this sign reversal is due to the fact that astronomers define azimuth to increase clockwise, and our longitudinal coordinates uniformly increase counterclockwise about the $z$-axis.

This coordinate system is related to the geographic coordinate system (below) by the geographic latitude $\phi_z$ and longitude $\lambda_z$ of the observer's $z$-axis direction.

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$\parbox{0.38\textwidth}{\caption{Definition of the geographic (Earth-fixed) coordinate system.}}$