Planetary Orbital Dynamics Lab

Simulation Framework hosting codebase for a Leapfrog Algorithm-based Python integrator to numerically simulate the orbital evolution of any characterized 3 body (Star-Planet-Moon) system, analyzed and orbitally animated via a Dash Plotly UI. Supports automated parameterization from the NASA Exoplanet Archive and tools accessible to Claude (LLM), via an MCP Server.

Key Functions supported by Claude

The MCP server provides tool endpoints to Claude (or another LLM agent) for:

fetch_exoplanet: Lookup and import system properties from the NASA Exoplanet Archive by planet name.

run_sim & run_sim_years: Run a simulation for the specified or default duration; outputs a Plotly HTML animation.

check_moon_stability, assess_stability, assess_moon_stability, moon_escape_info: Analyze moon orbital stability, estimate escape times, and summarize system evolution.

dash_url: Generate a browser-accessible Dash UI session for real-time visualization and manual parameter tweaking.

Input Parameters

Parameter	Description	Units
Ts	Star effective temperature	Kelvin (K)
rs_solar	Star radius	Solar radii (R☉)
ms_solar	Star mass	Solar masses (M☉)
mp_earth	Planet mass	Earth masses (M⊕)
dp_cgs	Planet mean density	g/cm³
ap_AU	Planet semi-major axis	Astronomical Units (AU)
ep	Planet eccentricity	Dimensionless
mm_earth	Moon mass	Earth masses (M⊕)
am_hill	Moon orbit as fraction of Hill radius	Dimensionless
em	Moon eccentricity	Dimensionless
moon_retrograde	Moon retrograde flag	Boolean
years	Simulation duration (optional)	Years

Constraining Exomoon Habitability and Orbital Stability

Condition A: An exomoon orbit is stable if Planetary Hill Radius > Moon Semi Major Axis, where

$$ r_\mathrm{Hill} = a_p , (1-e_p) \left( \frac{M_p}{3 M_s} \right)^{1/3} $$

Condition B: An exomoon orbit is habitable if Habitable Zone (Inner Boundary) < Moon-Star Distance < Habitable Zone (Outer Boundary)

$$ a_\mathrm{inner} = \sqrt{\frac{L_*}{4 \pi F_\mathrm{inner}}} $$

$$ a_\mathrm{outer} = \sqrt{\frac{L_*}{4 \pi F_\mathrm{outer}}} $$

with,

$$ L_* = 4π R_² σ T_⁴ $$

Numerical Integration (Leapfrog Algorithm)

For every object, the code integrates orbits using the velocity Verlet (leapfrog) scheme:

For each time step:

1. Advance position by half-step:

$$ \mathbf{x}_{i+1/2} = \mathbf{x}_i + \frac{1}{2} \mathbf{v}_i , \Delta t $$

2. Update velocity by full-step (acceleration is sum of pairwise gravitation):

$$ \mathbf{v}_{i+1} = \mathbf{v}i + \mathbf{a}{i+1/2} , \Delta t $$

3. Advance position by half-step:

$$ \mathbf{x}{i+1} = \mathbf{x}{i+1/2} + \frac{1}{2} \mathbf{v}_{i+1} , \Delta t $$

4. Accelerations are calculated via

$$ \mathbf{a}{ij} = -\mu_j \frac{\mathbf{r}{ij}}{|\mathbf{r}_{ij}|^3} $$

for each interacting pair

Building and Testing the MCP Server with Claude Desktop

1. With VSCode installed, run:

   • Windows: 'code $env:AppData\Claude\claude_desktop_config.json'
   • MacOS: 'code ~/Library/Application\ Support/Claude/claude_desktop_config.json'

2. Setup the MCP Server Configuration

   {
    "mcpServers": {
    "exomoon": {
            "command": "C:\\Path\\to\\Python\\Installation",
            "args": ["-m", "exomoon.mcp_server"],
            "env": {
                "PYTHONPATH": "\\Absolute\\Path\\to\\Parent\\Folder"
            }
        }
    }
   }
   

Output

HTML/Plotly animation of the system’s evolution

Numerical summary of stability, escape times, and orbital diagnostics

Option to analyze or download output via Claude or from storage