How to calculate semiMajorAxis and trueAnomaly from TLE file

Hi,

I am trying to add satelltie to satellite scenario by following the documentaion.

The general way is to simply use the TLE file

sat1 = satellite(sc,tleFile,"Name","Sat1")

If I want to find the Keplerian elements the function orbitalElements(sat1) can give eccentricity, inclination, rightAscensionOfAscendingNode and argumentOfPeriapsis. But how does MATLAB computes semiMajorAxis and trueAnomaly?

Any help is appreicated.

Thank you

Answer 1

[Sam Chak]

Hi @Raghav Rathi

Use the tleread() command.

Otherwise, you can also manually extract the info as detailed here:

https://www.mathworks.com/help/aerotbx/ug/satelliteScenario-key-concepts.html#mw_e08739b4-c5da-4983-898b-56e18cc71f87

After that, apply the equations that you learned in Orbital Mechanics to determine the Semi-major axis.

[Raghav Rathi]

Hi @Sam Chak

Thanks for your reply, but tleread() is pretty much the same as orbitalElements() in terms of output.

When you create a satelliteScenario() using a TLE file, it also generates the orbit of the satellite.

For instance below is an example created using TLE file.

Since it can create the orbit of the satellite, I was wondering if there was a way to get the information about the semi major axis through a matlab function, as most of the information that is needed for the calculation is present.

Answer 2

[Garmit Pant]

Hello Raghav,

I see that you require MATLAB functions to compute the 'semiMajorAxis' and 'trueAnomaly' of a satellite from its TLE file. This can be achieved by the following two methods:

• Using the “orbitalElements” Function: The “orbitalElements” function calculates the ‘SemiMajorAxis’ and ‘TrueAnomaly’ of a satellite if the “OrbitalPropagator” property is set to ‘two-body-keplerian’. The following code snippet adds the satellite to the scenario using the “satellite” method to read the file and returns the orbital elements using the “orbitalElements” function:

sc = satelliteScenario;
tleFile = "eccentricOrbitSatellite.tle";
sat1 = satellite(sc,tleFile,OrbitPropagator="two-body-keplerian");
elements1 = orbitalElements(sat1)

elements1 = struct with fields:
                    SemiMajorAxis: 2.6609e+07
                     Eccentricity: 0.7401
                      Inclination: 60.0625
    RightAscensionOfAscendingNode: 29.8255
              ArgumentOfPeriapsis: 279.8444
                      TrueAnomaly: 210.1601
                           Period: 4.3196e+04

• Using the “ijk2keplerian” Function: The “ijk2keplerian” function is used to calculate Keplerian orbit elements using position and velocity vectors. You can read the data from a TLE file using “tleread”, use it as an input to “propagateOrbit” to calculate the position and velocity of the satellite corresponding to an input time, and subsequently use the position and velocity data to calculate Keplerian orbit elements using “ijk2keplerian”. The following code snippet demonstrates this workflow:

tleStruct = tleread('leoSatelliteConstellation.tle');
[r,v] = propagateOrbit(datetime(2022, 1, 3, 12, 0, 0),tleStruct);
[SMA,ecc,incl,RAAN,argp,nu,truelon,arglat,lonper] = ijk2keplerian(r(:,:,1), v(:,:,1))

SMA = 7.2168e+06

ecc = 0.0020

incl = 55.1282

RAAN = 284.6862

argp = 50.6712

nu = 200.9497

truelon = NaN

arglat = NaN

lonper = NaN

For further understanding, kindly refer to the following MathWorks Documentation:

• Refer to the ‘Output Arguments’ section to understand the different elements returned based on the OrbitPropagator: https://www.mathworks.com/help/releases/R2023b/satcom/ref/matlabshared.satellitescenario.satellite.orbitalelements.html
• Refer to the ‘Output Arguments’ section to understand the different elements returned: https://www.mathworks.com/help/releases/R2023b/aerotbx/ug/ijk2keplerian.html

I hope you find the above explanation and suggestions useful!

[Raghav Rathi]

Hi @Garmit Pant,

Thanks for your answer.

I tried the above method but the values seems to be off.

I generally use the below method to calculate the orbital elements.

% Contents of TLE_file.tle (I have attached it as .txt)
% 1 48133C 21027AT  24181.44840278 -.00013871  00000+0 -92894-3 0  1813
% 2 48133  53.0545  67.0105 0001358  83.1645   3.7056 15.06430375    12
  

startTime = datetime('29-Jun-2024 16:54:32'); 
stopTime = startTime + seconds(20);
sampleTime = 1;
sc = satelliteScenario(startTime,stopTime,sampleTime);
sat = satellite(sc, 'TLE_file.tle');

mu = 3.986004418*1e14;
n = 15.06430375;
semiMajorAxis = nthroot(mu,3)/(((2*n*pi)/86400)^(2/3)) ;
orbitalElements(sat)

OUTPUT: 
                       MeanMotion: 0.0628
                     Eccentricity: 1.3580e-04
                      Inclination: 53.0545
    RightAscensionOfAscendingNode: 67.0105
              ArgumentOfPeriapsis: 83.1645
                      MeanAnomaly: 3.7056
                           Period: 5.7354e+03
                            Epoch: 29-Jun-2024 10:45:42
                            BStar: -9.2894e-04
                    semiMajorAxis: 6.9252e+06

Now, using the method you suggested,

tleStruct = tleread('/home/raghav/dbg/sig9.tle');
[r,v] = propagateOrbit(datetime('29-Jun-2024 16:54:32'),tleStruct);
[SMA,ecc,incl,RAAN,argp,nu,truelon,arglat,lonper] = ijk2keplerian(r(:,:,1), v(:,:,1))

OUTPUT:
SMA = 6.9273e+06
ecc = 0.001386
incl = 53.1830
RAAN = 65.6127
argp = 87.2706
nu = 309.2472

If I understasnd your previous explaination correctly, even though both the methods are initializing the satellite using TLE file, the 2nd method we are calculating keplerian elements from the i-j-k sysyem, hence they are different?