Astronomy

Kepler Orbit Solver

Numerically solve Kepler’s equation E − e·sin(E) = M for eccentric anomaly E, true anomaly ν, orbital radius and relative speed, with Newton/bisection/fixed-point methods, convergence history and an SVG orbit diagram

html· HTML resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/kepler-orbit-solver' \
  -H 'Content-Type: application/json' \
  -d '{"M":45,"e":0.3,"a":1,"method":"newton","maxIter":100,"tol":"1e-12"}'

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/kepler-orbit-solver

Parameters

Name	Type	Required	Description
M	number	Yes	—
e	number	Yes	—
a	number	No	—
method	select	No	—
maxIter	number	No	—
tol	select

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-kepler-orbit-solver": {
      "name": "kepler-orbit-solver",
      "description": "Numerically solve Kepler’s equation E − e·sin(E) = M for eccentric anomaly E, true anomaly ν, orbital radius and relative speed, with Newton/bisection/fixed-point methods, convergence history and an SVG orbit diagram",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=kepler-orbit-solver",
      "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": "kepler-orbit-solver",
    "arguments": {
  "M": 45,
  "e": 0.3,
  "a": 1,
  "method": "newton",
  "maxIter": 100,
  "tol": "1e-12"
}
  }
}

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]

Browse tools Open tool