# ⚛  L1 Principle — Satellite Orbit Determination

**ID:** `L1-467` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geodesy — *Orbital mechanics*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 6D orbital state vector
> **📡 Carrier:** RF · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555298

---

## 🧠 1. Introduction

**Satellite Orbit Determination** is a **parameter-estimation problem** whose unknown lives in **6D orbital state vector** space, within the **Orbital mechanics** sub-domain of **Geodesy**.

Measurements consist of RF coil signals (typical of MRI) via a **range range rate tracking** sensing mechanism.

The forward operator applies, in order: time evolution of the state; S · kalman · orbit filter operator; O · least squares · batch operator.

Observations are corrupted by additive Gaussian noise. Existence of the recovered 6D_orbital_state_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 200); atmospheric_drag_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → Time derivative → O · least squares · batch → **y** (detector).

```
y = `O.least_squares.batch` ∂_t x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `D.time` | Time evolution of the state |
| `O.least_squares.batch` | O · least squares · batch operator |

**🛰 Estimator components** _(used inside the solver, not in the forward equation)_:

| Primitive | What it does |
|---|---|
| `S.kalman.orbit_filter` | S · kalman · orbit filter operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geodesy |
| Sub domain | Orbital mechanics |
| Carrier | RF |
| Problem class | parameter_estimation |
| Solution space | 6D_orbital_state_vector |
| Noise model | gaussian |
| Integration axis | orbital_arc |
| Difficulty delta | 3 |
| L dag | 3.2 |

## 📡 4. Measurement Model

Existence of the recovered 6D_orbital_state_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 200); atmospheric_drag_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | position_prediction_error_km |
| Secondary | velocity_error_m_s |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `range_range_rate_tracking`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Altitude km | km | 500 |
| N observations | — | 1000 |
| Arc length days | — | 3 |
| Drag cd uncertainty | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Altitude km | km | 200 – 36000 |
| N observations | — | 50 – 10000 |
| Arc length days | — | 0.5 – 10.0 |
| Drag cd uncertainty | — | 0.01 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.1 position_prediction_error_km

| Metric | Range |
|---|---|
| Position prediction error km | 0.01 – 5.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **position_prediction_error_km**, with κ = `5000` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x86246f83246228f4bb276e90e41f317760dc9848e2085c2f9f0c7ffaedca22dd`
- **Chain tx hash:** `0x803c02ae02ab4e8f9645574a3ef360e4e99f8dda68d669ed1002fb880a8a2c72`
- **Chain block:** `41555298`

---

## File Mapping

This bundle consists of: `L1-467.md`, `L1-467.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-467.md` | Source of truth — edit this | Human or LLM |
| `L1-467.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-467`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._