dSGP4 ($\partial\textrm{SGP4}$)

Differentiable SGP4 in PyTorch.

This repository contains the implementation described in:

Acciarini, Baydin, Izzo, Closing the gap between SGP4 and high-precision propagation via differentiable programming, Acta Astronautica (2025), https://doi.org/10.1016/j.actaastro.2024.10.063.

What dSGP4 provides

• A PyTorch implementation of SGP4 with autograd support.
• Gradients of propagated states with respect to time and TLE-derived parameters.
• Parsing, writing and conversion of both TLEs and CCSDS OMMs (JSON/XML/KVN/CSV).
• Single-object and batched propagation APIs.
• A hybrid model (mldsgp4) for learning corrections around SGP4 dynamics.

Primary use cases include state transition matrix estimation, covariance transformation/propagation, gradient-based orbit estimation, and ML-augmented orbit prediction.

Installation

From PyPI:

pip install dsgp4

From conda-forge:

conda install conda-forge::dsgp4
# or
mamba install dsgp4

From source:

git clone https://github.com/esa/dSGP4.git
cd dSGP4
pip install -e .

Quick start

1. Parse a TLE and propagate

import torch
import dsgp4

tle = dsgp4.TLE([
    "1 25544U 98067A   24060.50000000  .00016717  00000-0  30134-3 0  9990",
    "2 25544  51.6403 124.7938 0005102 220.2782 248.4427 15.50010353440289",
])

# Initialize once, then reuse for multiple propagations.
dsgp4.initialize_tle(tle, gravity_constant_name="wgs-84")

# tsince is in minutes from TLE epoch.
tsince = torch.tensor([0.0, 10.0, 20.0])
state = dsgp4.propagate(tle, tsince)

# state shape: (N, 2, 3) when tsince has N elements
# state[:, 0, :] -> position [km], state[:, 1, :] -> velocity [km/s]
print(state.shape)

2. Parse an OMM and propagate

Space-Track distributes the same SGP4 mean elements in the CCSDS OMM (Orbit Mean-Elements Message) format, which dSGP4 reads in all its four serializations (JSON, XML, KVN and CSV):

import torch
import dsgp4

omm = dsgp4.OMM({
    "OBJECT_NAME": "ISS (ZARYA)",
    "OBJECT_ID": "1998-067A",
    "EPOCH": "2024-02-29T12:00:00.000000",
    "MEAN_MOTION": "15.50010353",
    "ECCENTRICITY": "0.0005102",
    "INCLINATION": "51.6403",
    "RA_OF_ASC_NODE": "124.7938",
    "ARG_OF_PERICENTER": "220.2782",
    "MEAN_ANOMALY": "248.4427",
    "NORAD_CAT_ID": "25544",
    "BSTAR": "0.00030134",
    "MEAN_MOTION_DOT": "0.00016717",
    "MEAN_MOTION_DDOT": "0",
})

# OMM objects are used exactly like TLE ones:
dsgp4.initialize_tle(omm)
state = dsgp4.propagate(omm, torch.tensor([0.0, 10.0]))

# whole files (one message or many) are read with:
omms = dsgp4.omm.load("gp.json")

# and the two formats convert into each other:
tle = omm.to_tle()
omm = tle.to_omm()

Unlike a TLE, an OMM is not constrained by two fixed-width lines: objects whose catalog number is above 339999 (i.e. beyond what the Alpha-5 convention can encode) can only be represented this way, and to_tle() raises a ValueError for them.

3. Differentiate through propagation

import torch
import dsgp4

tle = dsgp4.TLE([
    "1 25544U 98067A   24060.50000000  .00016717  00000-0  30134-3 0  9990",
    "2 25544  51.6403 124.7938 0005102 220.2782 248.4427 15.50010353440289",
])

time_min = torch.tensor(15.0, requires_grad=True)
state = dsgp4.propagate(tle, time_min, initialized=False)

# Example scalar objective: x-position at time_min.
loss = state[0, 0]
loss.backward()
print(time_min.grad)

4. Batched propagation

import torch
import dsgp4

tles = [
    dsgp4.TLE([
        "1 25544U 98067A   24060.50000000  .00016717  00000-0  30134-3 0  9990",
        "2 25544  51.6403 124.7938 0005102 220.2782 248.4427 15.50010353440289",
    ]),
    dsgp4.TLE([
        "1 40967U 15058A   24060.50000000  .00000033  00000-0  00000+0 0  9992",
        "2 40967   0.0187  89.2881 0002035  82.1068 220.3980  1.00270014 30754",
    ]),
]

times = torch.tensor([5.0, 30.0])
states = dsgp4.propagate_batch(tles, times, initialized=False)
print(states.shape)  # (2, 2, 3)

Technical notes and limitations

• Time input (tsince) is in minutes from the TLE epoch.
• Output units are km (position) and km/s (velocity).
• Supported gravity models: wgs-72, wgs-84, wgs-72old.
• Deep-space propagation is supported.
• Default torch dtype is set to float64 when importing dsgp4.

MCP server (LLM/agent integration, experimental)

dSGP4 ships an optional Model Context Protocol server that exposes the library to LLM clients and agents (Claude Desktop, Claude Code, IDEs, ...) as tools, resources and prompts.

Note: this layer is experimental. The library functionality behind it is stable, but the MCP Python SDK is still evolving quickly, so the server surface (tool names, output fields) may be adjusted in future releases.

Install the extra (requires Python >= 3.10) and run it:

pip install dsgp4[mcp]
dsgp4-mcp                        # stdio transport, all tool domains
dsgp4-mcp --domains tle,propagation
dsgp4-mcp --transport streamable-http --port 8000

For a Claude Desktop / Claude Code style client configuration:

{
  "mcpServers": {
    "dsgp4": {
      "command": "dsgp4-mcp"
    }
  }
}

The tools are organized in six domains, each selectable via --domains:

• tle: parse, describe, validate, build and convert element sets (TLE and CCSDS OMM formats);
• propagation: dSGP4 propagation (single and batched), Cartesian-to-Keplerian and time conversions;
• gradients: autodiff Jacobians of the state w.r.t. the TLE parameters and time, covariance transformations;
• estimation: differentiable Newton-Raphson TLE determination (re-epoch a TLE, fit a TLE to a state);
• ml: forecasts with trained ML-dSGP4 models;
• plot: rendered PNG orbit and element-distribution plots.

Reference resources (dsgp4://reference/..., e.g. the TLE format, the differentiable SGP4 parameters and their units, example element sets) and workflow prompts (orbit characterization, orbit comparison, uncertainty analysis, TLE determination, ML-dSGP4 training) are always available. The server can also be created programmatically with dsgp4.mcp.create_server().

See the MCP page of the documentation for how to connect the server to Claude Desktop, Claude Code and other MCP clients, the full tool listing, and the HTTP transport.

Development

Run tests:

pytest -q

Documentation and notebooks

• Full docs: https://esa.github.io/dSGP4
• Tutorials and examples are in doc/notebooks/.

Citation

If you use dsgp4, please cite:

@article{acciarini2024closing,
  title = {Closing the gap between SGP4 and high-precision propagation via differentiable programming},
  journal = {Acta Astronautica},
  volume = {226},
  pages = {694-701},
  year = {2025},
  issn = {0094-5765},
  doi = {https://doi.org/10.1016/j.actaastro.2024.10.063},
  url = {https://www.sciencedirect.com/science/article/pii/S0094576524006374},
  author = {Giacomo Acciarini and Atılım Güneş Baydin and Dario Izzo},
  keywords = {SGP4, Orbital propagation, Differentiable programming, Machine learning, Spacecraft collision avoidance, Kessler, Kessler syndrome, AI for space, Applied machine learning for space}
}

Authors

• Giacomo Acciarini
• Atılım Güneş Baydin
• Dario Izzo

The project originated from work at the University of Oxford AI4Science Lab.

Acknowledgements

We thank Dr. T.S. Kelso for support and validation guidance against the official Space-Track SGP4 release: https://www.space-track.org/documentation#/sgp4.

License

dSGP4 is distributed under GNU GPL v3. Contact the authors for alternative licensing options.

Contact

• giacomo.acciarini@gmail.com