Converting to TLE

Orbit Mean-Elements Messages whose mean elements follow the SGP4 theory can be converted into a classic Two-Line Element set (TLE). This is useful to interoperate with the many tools in the SatelliteToolbox.jl ecosystem that consume TLEs, such as the SGP4 propagator.

This capability is provided by a package extension that is loaded automatically once SatelliteToolboxTle.jl is available in your environment:

julia> using Pkg

julia> Pkg.add("SatelliteToolboxTle")

Performing the Conversion

Load both packages and use Julia's convert function with the target type TLE. Assuming the variable omm holds an OrbitMeanElementsMessage for the Amazonia 1 satellite:

julia> using SatelliteToolboxTle
julia> tle = convert(TLE, omm)TLE:
                      Name : AMAZONIA 1
          Satellite number : 47699
  International designator : 21015A
        Epoch (Year / Day) : 25 / 364.75838581 (2025-12-30T18:12:04.534)
        Element set number : 999
              Eccentricity :   0.00011240
               Inclination :  98.37210000 deg
                      RAAN :  75.08770000 deg
       Argument of perigee :  97.37720000 deg
              Mean anomaly : 262.75450000 deg
           Mean motion (n) :  14.40772474 revs / day
         Revolution number : 25439
                        B* :    0.0001533 1 / er
                     ṅ / 2 :     4.47e-06 rev / day²
                     n̈ / 6 :            0 rev / day³

The conversion maps the OMM fields to their TLE counterparts, including the translation of the OBJECT_ID (e.g. 2021-015A) into the TLE international designator format (e.g. 21015A).

Requirements and Behavior

• Mean element theory. The conversion only succeeds when the metadata field mean_element_theory is equal to "SGP4". Otherwise, an error is raised, since the elements cannot be interpreted as a TLE.

• Mean motion. TLEs are expressed in terms of the mean motion. If the OMM provides mean_motion directly, it is used as is. If only the semi_major_axis is available, the mean motion is computed from it, which additionally requires the gravitational parameter GM to be present:

  \[n = \frac{1}{2\pi}\sqrt{\frac{GM}{a^3}} \times 86400\]

• Required TLE fields. Conversion requires classification_type, norad_cat_id, element_set_number, rev_at_epoch, bstar, mean_motion_dot, and mean_motion_ddot. Missing fields raise an error; they do not receive placeholder values.

• Unsupported alternatives. OMM TLE parameters may represent drag with either bstar or bterm, and the second derivative slot with either mean_motion_ddot or agom. A classic TLE conversion requires bstar and mean_motion_ddot; conversion rejects bterm and agom because they have no direct TLE representation.