SSA Quick Reference Card¶

Hardware Costs¶

Component	Cost	Quantity	Total
Detection Node (IMX307 + RPi)	$130	50	$6,500
Tracking Station	$550	5	$2,750
Central Server (VPS)	$50/mo	1	$600/yr
Production Total			$9,850

Compare: 1 professional site = $330,000

Performance Targets¶

Metric	Target	Method
Detection limit	Mag 10-11	IMX307 sensor
Astrometry	5-30 arcsec	Plate solving
Timing sync	<50 ms	NTP
Triangulation error	<100 km	3+ sites
Orbit prediction (24h)	<500 km	Particle filter
Tumble period	5% accuracy	Lomb-Scargle

Key Algorithms¶

1. Track-and-Stack¶

SNR improvement = √N frames
100 frames → 2.5 mag improvement
1000 frames → 3.3 mag improvement

2. Admissible Region¶

Generate particles: 10,000-100,000
Constraints: Energy < 0, Perigee > 100 km
Propagate: GPU-friendly
Prune: On new observation

3. Triangulation¶

Minimum sites: 3
Baseline: 500-3000 km ideal
Altitude calculation: Line intersection

File Structure¶

ssa/
├── edge/
│   ├── streak_detector.py     # Hough transform
│   ├── plate_solver.py         # Astrometry
│   ├── timing_sync.py          # NTP
│   └── uploader.py             # API client
│
├── central/
│   ├── models.py               # Database
│   ├── catalog.py              # TLE management
│   ├── track_associator.py     # Link observations
│   ├── triangulator.py         # Multi-site position
│   ├── orbit_solver.py         # Gauss + particles
│   └── api.py                  # REST API
│
└── characterization/
    ├── lightcurve.py           # Tumble detection
    └── material_classifier.py # Color analysis

Detection Limits¶

Object Type	Size	Magnitude	Detectable
LEO large debris	>30 cm	6-8	✅ Yes
LEO small debris	10-30 cm	8-10	✅ Yes
LEO tiny debris	<10 cm	>10	⚠️ Marginal
GEO satellites	All sizes	5-10	✅ Yes
MEO	Most	7-12	✅ Yes

Note: Track-and-stack can improve by 2-3 magnitudes

Timing Requirements¶

Task	Precision	Method
Detection	<1 ms	GPS ideal, NTP acceptable
Triangulation	<50 ms	NTP
Orbit determination	<1 sec	Standard clock
Light curve	<1 sec	Standard clock

Material Classification Colors¶

Material	B-V	V-R	R-I	Notes
S-type	0.5-1.0	0.4-0.8	0.3-0.6	Silicates
C-type	0.3-0.5	0.2-0.4	0.1-0.3	Carbonaceous
M-type	0.4-0.6	0.3-0.5	0.2-0.4	Metallic
Solar panel	0.0-0.2	-0.1-0.1	-0.2-0.0	Active satellite

Tumble Detection¶

Method: Lomb-Scargle periodogram
Input: Time series of magnitudes
Output: Period (seconds), Amplitude (mag)

Tumbling: периодический variation with significance >3σ
Stable: Flat or random variation

Orbit Elements¶

a = Semi-major axis (km)
e = Eccentricity (dimensionless)
i = Inclination (degrees)
Ω = Right Ascension of Ascending Node (degrees)
ω = Argument of Perigee (degrees)
ν = True Anomaly (degrees)

Network Topology¶

Minimum for triangulation: 3 detection nodes
                      Cost: ~$400
              Coverage: Regional

Operational national: 10 detection + 3 tracking
                      Cost: ~$2,300
              Coverage: Continental

Production global: 50 detection + 5 tracking
                      Cost: ~$9,200
              Coverage: Global

Software Dependencies¶

Edge (Raspberry Pi)¶

Python 3.8+
OpenCV (cv2)
NumPy
Astropy
 Requests
Backoff (for retries)

Central (Server)¶

Python 3.8+
PostgreSQL 12+
Redis
Skyfield (orbit propagation)
Orekit (orbit determination)
Scipy (signal processing)

API Endpoints¶

POST /api/v1/streaks          # Upload detections
GET  /api/v1/objects           # List tracked objects
GET  /api/v1/objects/<id>      # Get object details
POST /api/v1/campaigns         # Create observation campaign
GET  /api/v1/campaigns/<id>    # Get campaign status

Success Metrics¶

Milestone	Criteria
Phase 1	Detect ISS from 2 nodes
Phase 2	Triangulate altitude <100 km error
Phase 3	Refine orbit <500 km (24h prediction)
Phase 4	Detect tumble period 5% accuracy
Production	Maintain catalog of 1000+ objects

Common Issues¶

Problem	Solution
No detection	Check threshold, verify camera
Timing drift	Re-sync NTP, consider GPS
False positives	Filter by velocity (planes vs satellites)
Cloud cover	Multi-site redundancy
Light pollution	Background subtraction, dark site
Star confusion	Plate solve, identify stars

Testing Targets¶

Object	Magnitude	Purpose
ISS	-3 to -1	Baseline detection
Hubble	2-3	Medium brightness
Sentinel-6	4-5	Faint detection
GOES	5-7	GEO tracking

CubeSat Cost Estimate¶

Component	Cost	Notes
3U CubeSat bus	$25,000	COTS
Lidar payload	$35,000	Fiber laser + APD
Launch (rideshare)	$30,000	SpaceX/Rocket Lab
Operations	$10,000/yr	Ground station
Total per unit	$90,000-100,000
5-unit constellation	$450-500K	Complete SSA

Key Numbers to Remember¶

IMX307 read noise:      ~1.0 e-    (matches $10K cameras)
Detection threshold:    Mag 10-11
Track-and-stack gain:   √N frames
Timing precision:      <50 ms    (NTP)
Triangulation minimum: 3 sites
Particle filter:       10,000-100,000 particles
Cost ratio:            25× cheaper than traditional
Coverage improvement:  Global vs single-point

File Locations¶

Planning Docs:
├── SSA Session Summary.md          # This conversation
├── SSA Low Cost Architecture.md    # Costs and architecture
├── SSA Implementation Roadmap.md   # Phase-by-phase plan
├── SSA Bulk Coding Handoff.md      # Code specifications
└── SSA Quick Reference.md          # This document

Reference Docs:
├── Science/Projects/SSA.md                    # Technical deep dive
└── Science/Projects/Security cameras SSA.md   # Hardware specs

Speed Reference¶

LEO velocity:      7.8 km/s    (28,000 km/h)
LEO period:        90 minutes
GEO velocity:      3.07 km/s   (11,000 km/h)
GEO period:        24 hours

Streak speed:      0.5-2°/s   (LEO)
Frame rate:       25 fps      (minimum)
Exposure:         40 ms       (1/25 s)
Typical streak length: 100-500 pixels

Useful Formulas¶

Altitude from magnitude:
  size = 2 × distance × 10^((mag - H_sun)/5)
  where H_sun = -26.74

SNR improvement from stacking:
  SNR_stacked = SNR_single × √N

Triangulation error:
  σ_position ≈ baseline / (2 × tan(parallax_angle/2))

Orbital period:
  P = 2π × √(a³/μ)
  where μ = 398,600 km³/s²(Earth)

Admissible region constraints:
  Energy < 0          (bound orbit)
  Perigee > 6471 km   (above Earth surface + 100 km)