How to plot a satellite trace wrt a ground station using polar plot view?

Question

I have a ground station which is tracking a satellite. I have the Azimuth & Elevation angles of this trace per second. I want to visualize this using a polar plot which would indicate the trace of the satellite. How to do it correctly?

How do I convert these angles into coordinates of a polar plot? I searched the web for possible answers but couldn't find anything meaningful. I found a MATLAB function "polar" but it only takes one angle as input (novice, so I maybe wrong about this).

Elevation   Azimuth
11.31693268 19.14014857
12.69233985 19.52583539
14.1401434  19.94125872
15.66863156 20.39098266
17.28724858 20.88052782
19.00675835 21.41663385
20.83941898 22.00761262
22.79915889 22.66383037
24.90173605 23.39837633
27.16484691 24.22800675
29.60812765 25.17450351
32.25295023 26.26667162
35.1218531  27.54334561
38.23734641 29.05803185
41.61967464 30.88627821
45.28287159 33.13771907
49.228037   35.97633442
53.43205048 39.65532946
57.61559325 45.56022473

Here are some sample values in degrees. I want to convert these values into a trace on a polar plot. I would also like to do this using MATLAB, so help regarding that would be appreciated too.

Answer 1

More context has been added to the question, so I feel it appropriate to expand on my comments.

I don't have MATLAB, so I will use Mathematica functionality, and hopefully, that can be translated to MATLAB functionality.

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First, to plot elevation ($\varepsilon$) and azimuth ($\alpha$) into standard polar coordinates, I would use the Stereographic Projection rotated so that an azimuth of $0$ is north, $\theta=\frac\pi2$: $$ \begin{align} r&=\tan\left(\frac\pi4-\frac\varepsilon2\right)\\ \theta&=\frac\pi2+\alpha \end{align}\tag1 $$ Applying this conversion, as well as the conversion from degrees to radians, the following function gives the polar coordinates $(\theta,r)$ that can be passed to ListPolarPlot:

f[{elev_,az_}] := {Pi/2+Pi/180 az,Tan[Pi/4-Pi/360 elev]}

Adding some decorations, I get the following visualization:

The circle is the horizon and the grey lines intersect at the zenith.

Answer 2

It seems that you want spherical coordinates (because the motion is in a 3D space). I suppose that your ''Elevation'' is the complementary angle of the polar angle.