# Is it possible to plot the ground track of a satellite with just azimuth & elevation angles without range?

I came across this question on StackOverflow about Satellite Trajectory plot. In the code mentioned in the question, the user takes only the Azimuth & Elevation angles (radians) & converts them into cartesian (x, y) coordinates & plots the Satellite trajectory onto a polar plot.

However, to convert from Spherical to Cartesian coordinates, one needs Range, Azimuth & Elevation. But the formula used in the code is
$$x = \frac{(\pi/2) - Elevation} {(\pi/2)*cos(Azimuth - (\pi/2))}$$
$$y = \frac{Elevation - (\pi/2)} {(\pi/2)*sin(Azimuth - (\pi/2))}$$
How was the OP able to draw a satellite ground track using only Azimuth & Elevation? How to arrive at the above equations from
$$x = r*cos(Elevation)*cos(Azimuth)$$
$$y = r*cos(Elevation)*sin(Azimuth)$$
$$z = r*sin(Elevation)$$

• You should ask questions about that plot there, although the question is from 2012. It's not a ground-track plot at all as far as I can tell, it's just a plot of altitude and azimuth of several GPS satellites, shown only when they are above the horizon for that viewing location. – uhoh Jun 15 '18 at 13:04

As far as I can tell, in the question by the link, the OP is not trying to plot satellites' ground tracks in any way. He simply plots their elevations and azimuths, that's all, so he doesn't need to know the ranges. The $x$ and $y$ his program computes have nothing to do with satellite's Cartesian coordinates; they are just the coordinates of the point which represent the given elevation and azimuth on the plot.