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Astronomy

ESA PB05-Style Brouwer–Lyddane Averaged-Element Orbit Propagator (J2–J6 + Luni-solar)

Propagate near-Earth and GNSS-region orbits with a semi-analytical averaged-element model in the Brouwer–Lyddane / PB05 tradition: orbit-averaged secular drift of the mean elements under the EGM96 zonal field J2–J6 (numerical Gauss-equation averaging — the Delaunay-normalisation analogue with the closed-form J2 rates as a built-in cross-check), first-order J2 short-period mean↔osculating reconstruction, long-period J3 frozen-orbit analysis (e = −J3·sin i/(2·J2·p), ω = 90°), double-averaged luni-solar quadrupole secular effects on an elliptical inclined perturber orbit (the Celletti/Kozai–Lidov term with the 39.23° critical mutual inclination), tesseral ground-track resonance checks (1:1, 2:1, 3:2, 5:2 and small-rational commensurabilities with Earth rotation), sun-synchronous inclination solving, and an in-report RK4 numerical-propagation cross-validation of the averaged model.

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Quick start

Call this tool from your code in three languages.

cURL
curl -X POST 'https://api.elysiatools.com/en/api/tools/esa-pb05-pce-pck-reddy-porter-keplerian-equation-averaged-element-propagator' \
  -H 'Content-Type: application/json' \
  -d '{"semiMajorAxisKm":8000,"eccentricity":0.05,"inclinationDeg":52.5,"raanDeg":30,"argPerigeeDeg":70,"meanAnomalyDeg":0,"durationDays":30,"zonalDepth":"j2-j4","lunisolar":"none","showReconstruction":true}'

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API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP
POST https://api.elysiatools.com/en/api/tools/esa-pb05-pce-pck-reddy-porter-keplerian-equation-averaged-element-propagator

Parameters

NameTypeRequiredDescription
semiMajorAxisKmnumberNo—
eccentricitynumberNo—
inclinationDegnumberNo—
raanDegnumberNo—
argPerigeeDegnumberNo—
meanAnomalyDegnumberNo—
durationDaysnumberNo—
zonalDepthselectNo—
lunisolarselectNo—
showReconstructioncheckboxNo—

Response format

HTML result

JSON
{
  "result": "<div>Processed HTML content</div>",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json
{
  "mcpServers": {
    "elysiatools-esa-pb05-pce-pck-reddy-porter-keplerian-equation-averaged-element-propagator": {
      "name": "esa-pb05-pce-pck-reddy-porter-keplerian-equation-averaged-element-propagator",
      "description": "Propagate near-Earth and GNSS-region orbits with a semi-analytical averaged-element model in the Brouwer–Lyddane / PB05 tradition: orbit-averaged secular drift of the mean elements under the EGM96 zonal field J2–J6 (numerical Gauss-equation averaging — the Delaunay-normalisation analogue with the closed-form J2 rates as a built-in cross-check), first-order J2 short-period mean↔osculating reconstruction, long-period J3 frozen-orbit analysis (e = −J3·sin i/(2·J2·p), ω = 90°), double-averaged luni-solar quadrupole secular effects on an elliptical inclined perturber orbit (the Celletti/Kozai–Lidov term with the 39.23° critical mutual inclination), tesseral ground-track resonance checks (1:1, 2:1, 3:2, 5:2 and small-rational commensurabilities with Earth rotation), sun-synchronous inclination solving, and an in-report RK4 numerical-propagation cross-validation of the averaged model.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=esa-pb05-pce-pck-reddy-porter-keplerian-equation-averaged-element-propagator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list
{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call
{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "esa-pb05-pce-pck-reddy-porter-keplerian-equation-averaged-element-propagator",
    "arguments": {
  "semiMajorAxisKm": 8000,
  "eccentricity": 0.05,
  "inclinationDeg": 52.5,
  "raanDeg": 30,
  "argPerigeeDeg": 70,
  "meanAnomalyDeg": 0,
  "durationDays": 30,
  "zonalDepth": "j2-j4",
  "lunisolar": "none",
  "showReconstruction": true
}
  }
}
Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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