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After research, I knew that a certain TLE data can be transformed into another format (I thought about ECI) so geodetic conversion can be applied (to fetch coordinates which can be plotted) .

I wanted to build a software that ground tracks the ISS (I saw many online; so I thought about developing my own).

Though I read here that this conversion should not be applied (because it produces errors) : https://celestrak.com/columns/v04n05/index.asp#FAQ05

I want to ask about the amount of the error the author was meaning.

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The circumspect answer is that I think you can only find this by specific evaluation for the type of object and orbit that you have in mind. Apologies, as I enthusiastically wrote most of what follows before remembering that you said that you want to track the ISS position. The short answer is, give it a whirl, it may well be just fine!

The rest of this is just if you'd like to take more of an interest in it. I don't know where you have got with your own understanding but, as a start, here a couple of points from the reference you cited that are worth looking at more closely:

Firstly, TLEs are already in an ECI frame (see further down the page on the reference):

"To be precise, the reference frame of the Earth-centered inertial (ECI) coordinates produced by the SGP4/SDP4 orbital model is true equator, mean equinox (TEME) of epoch."

With that you may be wondering why they need to be converted at all, this leads to the second point:

"The elements in the two-line element sets are mean elements calculated to fit a set of observations using a specific model..."

Try this little thought experiment to help with the concept of "mean elements" which leads to a very rough way to evaluate the error:

  1. Imagine an ideal keplerian orbit defined by the six orbital elements and time. You can convert this into cartesian co-ordinates and you will see that the orbit is elliptical, by definition.

  2. If you instead look at the orbit of a real object and took observations to plot its course in cartesian co-ordinates then you would see that the "ellipse" was just an approximation and that the real satellite path has lumps in it. It isn't possible to represent this orbit as an ellipse because it isn't one. Typically orbits are either specified as a position/velocity vector for that instant in time, or are converted back to keplerian-looking elements on the express understanding that such ephemeris, the eccentricity, semi major axis, angles etc only apply at that specific instant in time. Strictly this ephemeris would be described as "osculating" elements rather than "keplerian" ones. If you had a propagator to see what the orbit would look like a few minutes later, the ephemeris would have changed.

  3. Imagine now conjuring up some simplfied view of the real satellite path that can still be defined by the 6 keplerian orbit elements, time and a couple of other details. A TLE describes an orbit for which some, but not all, of the bumps have been smoothed out. These are "mean" elements. This simplification will will only be valid if the reader has access to the same underlying set of assumptions that were used to generate it, namely the SGP4 model. If you produce a different tpe of mean elements then, metaphorically, you will get a different mean.

If you try to use elements from one mean algorithm in software for another then you will have errors. If you go a step further and blindly use mean elements, say TLEs, in a propagator meant for osculating elements then the errors will be still larger.

If you try converting each of the above three orbits into cartesian coordinates you should see that 1. is an elipse, 2 is bumpy and 3 is somewhere between the others.

That will give you some idea of the errors that are mentioned.

If you want to get more into this there is another Q&A on this stack exchange here.

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    $\begingroup$ thank you for your answer, I was late due to researching more into this; most of the trackers I saw did use "TLE" as a source of data; then the conversion followed "through SPG4". For other readers though, this tool is what I decided to use to convert the data(C++ & C# Libraries) zeptomoby.com/satellites .I will look more into your answer since I want to educate myself more on this; $\endgroup$ – Mohammed Baashar Nov 24 '15 at 16:20

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