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As it's well known, assuming the earth fixed and non rotating, the trajectory of a falling body with initial speed $v_0 = \{v_{0x},v_{0y},{v_{0z}}\}$ is contained in a plane. Assuming an observer in the origin of a fixed reference frame, he will measure three coordinates of the falling body: $P=\{\rho,\theta,\phi\}$. We can suppose to be $\rho$,distance, $\theta$, elevation and $\phi$, azimuth. How is it possible to find a reference frame in which the azimuth $\phi$ is zero? Thanks in advance.

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The observer has to be in the plane of the motion. The surfaces where $\phi$ is constant are planes; the observer just has to orient her axes appropriately for one of these planes to be the plane of motion.

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    OK. Suppose I measure three points of the trajectory in my reference frame: $P_1$, $P_2$ and $P_3$. The equation of the plane defined by this points is: $a(x-x_1)+b(y-y_1)+c(z-z_1)$ where $a$,$b$ and $c$ are calculated from the three points coordinates. Assuming I know the impact point of the particle on the trajectory belonging to this plane. In this case I can put the origin of the new reference frame in this point and put, for example, the $(x,z)$ plane coincident with the trajectory plane. What kind of rotation and translation have I do?2012-10-19