Add test verification documentation

Document expected orbital positions and velocities for the simple
test case (configs/test_simple.txt):

- Expected orbital periods (Earth 365d, Mars 687d)
- Expected velocities (Earth 29.789 km/s, Mars 24.323 km/s)
- Verification points at quarter/half/full orbit
- Quick test commands
- Acceptable tolerances for numerical integration

Provides reference values to verify simulation accuracy by comparing
actual output against predicted positions and angles.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

docs/test_verification.md

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+# Test Case Verification Guide
+
+This document explains how to verify the orbital simulation using the `test_simple.txt` configuration.
+
+## Running the Test
+
+```bash
+# Build the simulation
+make
+
+# Run the simple test case with human-readable output
+./orbit_sim configs/test_simple.txt --headless --readable --days 365
+```
+
+## Test Configuration
+
+The `configs/test_simple.txt` file contains:
+- **Sun**: At the origin (0, 0, 0), mass 1.989e30 kg
+- **Earth**: Starts at 1.0 AU on the +X axis, mass 5.972e24 kg
+- **Mars**: Starts at 1.5 AU on the +X axis, mass 6.39e23 kg
+
+Both planets orbit in circular paths in the XY plane (counter-clockwise when viewed from +Z).
+
+## Expected Orbital Periods
+
+Using Kepler's third law: T² ∝ a³ (where T is period, a is semi-major axis)
+
+- **Earth**: T = 365.25 days (by definition)
+- **Mars**: T = 686.98 days (approximately 687 days)
+
+## Expected Velocities
+
+Circular orbit velocity: v = sqrt(G * M_sun / r)
+
+- **Earth**: v = 29.789 km/s
+- **Mars**: v = 24.323 km/s
+
+## Verification Points
+
+### Initial State (Day 0)
+```
+Earth:
+  Position: (1.0, 0.0, 0.0) AU
+  Velocity: (0.0, -29.789, 0.0) km/s
+
+Mars:
+  Position: (1.5, 0.0, 0.0) AU
+  Velocity: (0.0, -24.323, 0.0) km/s
+```
+
+### Quarter Orbit (Day ~91)
+After approximately 1/4 of Earth's year:
+
+```
+Earth:
+  Expected Position: (~0.0, -1.0, 0.0) AU
+  Expected Velocity: (~-29.789, 0.0, 0.0) km/s
+  Distance: ~1.0 AU (circular orbit)
+
+Mars:
+  Expected Position: (~0.987, -1.129, 0.0) AU (only traveled ~57 degrees)
+  Distance: ~1.5 AU (circular orbit)
+```
+
+### Half Orbit (Day ~183)
+After approximately 1/2 of Earth's year:
+
+```
+Earth:
+  Expected Position: (~-1.0, 0.0, 0.0) AU
+  Expected Velocity: (0.0, 29.789, 0.0) km/s
+  Distance: ~1.0 AU
+
+Mars:
+  Expected Position: (~0.72, -1.30, 0.0) AU (traveled ~114 degrees)
+  Distance: ~1.5 AU
+```
+
+### Full Orbit (Day ~365)
+After approximately 1 full Earth year:
+
+```
+Earth:
+  Expected Position: (~1.0, 0.0, 0.0) AU (back to start)
+  Expected Velocity: (0.0, -29.789, 0.0) km/s
+  Distance: ~1.0 AU
+
+Mars:
+  Expected Position: (~-0.87, -1.23, 0.0) AU (traveled ~228 degrees)
+  Distance: ~1.5 AU
+```
+
+## How to Verify
+
+1. **Check orbital stability**: The distance from the Sun should remain constant
+   - Earth should stay at ~1.0 AU
+   - Mars should stay at ~1.5 AU
+
+2. **Check velocity magnitude**: Speed should remain constant in circular orbits
+   - Earth: always ~29.789 km/s
+   - Mars: always ~24.323 km/s
+
+3. **Check orbital period**: Run for 365 days
+   - Earth should return to near its starting position
+   - Mars should complete about half its orbit (687 day period)
+
+4. **Check direction**: Both planets orbit counter-clockwise
+   - Starting at +X axis
+   - Moving in -Y direction
+   - Position angle increases over time
+
+## Quick Test Commands
+
+```bash
+# Run for a quarter year (91 days)
+./orbit_sim configs/test_simple.txt --headless --readable --days 91
+
+# Run for a half year (183 days)
+./orbit_sim configs/test_simple.txt --headless --readable --days 183
+
+# Run for a full year (365 days)
+./orbit_sim configs/test_simple.txt --headless --readable --days 365
+
+# Run for Mars' full orbit (687 days)
+./orbit_sim configs/test_simple.txt --headless --readable --days 687
+```
+
+## Acceptable Tolerances
+
+Due to numerical integration with discrete time steps:
+- Distance variation: ±0.001 AU (~150,000 km) is acceptable
+- Velocity variation: ±0.1 km/s is acceptable
+- Position after full orbit: Within 0.01 AU of starting position
+
+## Understanding the Output
+
+The `--readable` flag converts output to human-friendly units:
+- **Positions**: Shown in AU (Astronomical Units, ~150 million km)
+- **Velocities**: Shown in km/s
+- **Distances**: Shown in both AU and km
+
+Without `--readable`, all values are in SI units (meters, m/s) with scientific notation.