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aholinch/sgp4: SGP4 implementations in multiple languages

SGP4 stands for Simplified General Perturbations 4 and is arguably the most widely used propagator for simulating earth satellite orbits. This module is my personal project to produce implementations in multiple languages. There is an official government document released decades ago that describes the theory and the software. That document is known pasak Spacetrack Report #3. In 2006 researchers at the Center for Space Standards and Innovation (CSSI) published a detailed study of the algorithm and more modern software implementations. In addition to the paper they also released the software. Most importantly they produced an extensive adegan of test cases that cover multiple orbit regimes, potential singularities, and other tricky orbits.

Alpha-5 Format

In December 2020 Space-track.org announced a change to the object id format. In tata tertib to accommodate more that 100 000 objects, the object id in TLEs will include alphabetic characters. I’m in the process of updating each TLE and ElsetRec structure to provide basic support. At this time the plan is to simply treat the id gandar a string. There is a schema to convert alpha-5 to integers, but that is not required to parse and simulated TLEs.

This code is released under an unlicense. Do what you want with it completely at your own risk. It is based on code released by the Center for Space Standards & Innovation (CSSI). Their code is based on a US Government standard. No liability and no warranty are offered.

The astrodynamics calculations are all implemented sumbu static functions in the SGP4 class/module. The ElsetRec datastructure is used to maintain initialization state across those methods. For convenience, I have implemented the TLE class. The constructor accepts the two lines of the the two-line element set poros arguments. To then propagate (simulate) the orbit, I have implemented a few getRV methods in each language. One will accept the number of minutes since the epoch aksis an argument. In most languages, I've also implemented a version of getRV that accepts a Date or DateTime object to simulate the orbit at a specific point in time. Sometimes, if I didn't find a helper class in the korban language that I liked, I simply used the number of milliseconds since January 1, 1970 poros the argument.

I've delivered production code in all of these languages.

I've only done my own projects in these languages.

gcc -o testsgp4 SGP4.c TLE.c TestSGP4.c -lm

./testsgp4

Typical errors r=6.722191e-03 mm, v=4.812040e-04 mm/s

g++ -o testsgp4 TestSGP4.cpp TLE.cpp SGP4.c

Typical errors r=6.722191e-03 mm, v=4.812040e-04 mm/s

Tested with dotnet framework on Linux. Versions 2.1 and 5.0. Adjust sgp4.csproj as necessary for your environment.

dotnet run

Typical errors r=0.00672218292027499 mm v=0.00481204064816902 mm/s

I'm a bit proud of this port myself. I've been seeing SGP4 in FORTRAN for decades now. However, all the other versions I've seen were using COMMON data blocks. By porting the code from C to FORTRAN 90, I was able to organize the code in modules and take advantage of custom data types, ElsetRec and TLE. Now others can include these modules in their code without having to have the common block.

gfortran ElsetRec.f90 SGP4.f90 TLE.f90 TestSGP4.f90 -o testsgp4

Typical errors r= 6.7121279555256517E-003 mm, v= 4.8048366357605730E-004 mm/s

javac -d . *.java

java -classpath . sgp4.TestSGP4

Typical errors r=0.006722149979022173 mm v=4.812041812093286E-4 mm/s

In the js directory open sgp4.html in a browser to view the results. Calling javascript from the cli, you can run testsgp4.js which will call the verify() method.

Typical errors r = 0.006722036443346485 mm, v = 0.00048120408916018905 mm/s

The first implementation of SGP4 I ever wrote was in VBA in Excel. I did the implementation by converting a printout of the SpaceTrack Report #3 FORTRAN code to VBA pivot I typed it in. I don't have Excel on my dev laptop, so I ported the C version of code to LibreOffice Basic. Very little documentation for this language exists (compared to other languages). I was able to implement a episode of macros in a Calc spreadsheet. Most users will want to use the parseLines and getRV macros in the TLE module. To verify the code with the standard test cases run the Main macro in the TestSGP4 module. The velocity errors are similar to other languages. However the position errors are about five times greater. I'm not sure why that is, but many of the data types in Basic have a limited resolution compared to the other languages.

Typical errors

3.33434E-02 mm

4.80742E-04 mm/s

The code has been tested with Matlab 7.9.1

ans = Typical errors r=6.721676E-03 mm v=4.812042E-04 mm/s

The code has been tested with Octave 4.0.0

octave TestSGP4.m ans = Typical errors r=6.722191E-03 mm v=4.812040E-04 mm/s

The SGP4 and TLE code works in both Python 2 and Python 3. The TestSGP4 code should also work in both versions and has a dependency on the standard json package. Simply execute your preferred version of python from the python src directory.

python2 TestSGP4.py

Typical Errors 0.00651341005177 mm 0.000481251231334 mm/s

python3 TestSGP4.py

Typical Errors 0.006513410051766991 mm 0.0004812512313336876 mm/s

If you run RStudio from the r directory, call source('TestSGP4.R') to run the test script.

Typical errors r=2.852996E-03 mm v=4.277355E-06 mm/s

The Ruby version was ported from the Python version. To run the code go to the ruby directory and type:

ruby TestSGP4.rb

Typical Errors 0.006722191115878764 mm, 0.0004812040288887651 mm/s

The Rust version was ported from the C version. To run the code go to the rust directory and type:

cargo run

Typical errors r=0.006589293163823231 mm, v=0.00048047055139244986 mm/s

The Swift version was ported from C and Rust. To run the code, go the swift/sgp4 directory. You can compile with "swift build" To execute, you can run .build/debug/sgp4

Typical errors r=0.007046565385144334 mm, v=0.0004804350487733351 mm/s

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