1. ROLE

3. GETTING STARTED

When you trigger this skill, I'll work with whatever you give me — but the more context, the better the output.

Minimum I need (pick one):

• "Size an ADCS for a 6U CubeSat in 500 km SSO with 0.1 deg pointing"
• "Compare reaction wheels vs CMGs for a 2000 kg agile imager"
• "Build a pointing error budget for a GEO comms satellite"

Helpful if you have it:

• Orbit parameters (altitude, inclination, LTAN)
• Spacecraft mass, dimensions, and inertia tensor
• Pointing accuracy and stability requirements (per axis)
• Slew rate and settle time requirements
• Mission lifetime and radiation environment
• Power and mass constraints for ADCS subsystem
• Launch vehicle and expected tip-off rates

What I'll ask if you don't specify:

• "What orbit? LEO, GEO, deep space?" — disturbance environment changes completely
• "Pointing accuracy needed?" — 5 deg vs 0.01 deg are different worlds
• "Spacecraft inertia?" — if not given, I'll estimate from mass and dimensions
• "Any agility requirement?" — drives actuator sizing dramatically

4. CONNECTORS

Shared Tools (in shared/tools/)

Shared Data (in shared/ — pack-level)

Cross-skill Connectors

5. TAXONOMY

5.1 Attitude Sensors

5.2 Attitude Actuators

*Magnetic torquer torque depends on local B-field: T = m × B, where m = dipole moment (Am²), B ~ 30 uT at 500 km LEO.

5.3 Disturbance Torque Reference (500 km LEO, 1×1×1.5 m, 200 kg spacecraft)

5.4 Control Law Reference

6. PROCESS

Step 1: Requirements Capture

• Pointing accuracy: degrees, arcminutes, or arcseconds (per axis)
• Pointing stability: jitter over integration time (arcsec/s or arcsec RMS over T)
• Slew requirement: degrees per second, or time to slew N degrees and settle
• Orbit: altitude, inclination, eccentricity, LTAN
• Spacecraft: mass, dimensions, inertia tensor, flexible modes
• Lifetime: years (drives wheel bearing life, propellant for dumping)

IF pointing accuracy is not specified → ASK. IF orbit is not specified → ASK (disturbance torques vary by 100x between LEO and GEO). IF inertia is not given → estimate from mass and dimensions: I = (m/12)(a² + b²) for a box.

Step 2: Disturbance Torque Analysis

Calculate all four disturbance torques for the specified orbit:

Gravity Gradient:

T_gg = (3 × mu_Earth) / (2 × r³) × |Iz - Iy| × sin(2×theta)

WORKED EXAMPLE — 500 kg sat, 600 km orbit, Iz=120 kg·m², Iy=85 kg·m²:

r     = 6371 + 600 = 6971 km = 6.971 × 10⁶ m
mu    = 3.986 × 10¹⁴ m³/s²
T_gg  = (3 × 3.986e14) / (2 × (6.971e6)³) × |120 - 85| × sin(2 × 1°)
      = (1.196e15) / (6.772e20) × 35 × 0.0349
      = 1.766e-6 × 35 × 0.0349
      = 2.16 × 10⁻⁶ Nm  (cyclic, worst case at theta = 45°: 61.8 × 10⁻⁶ Nm)

Aerodynamic:

T_aero = 0.5 × rho × v² × Cd × A × L_cp-cm

At 600 km: rho ~ 1.0 × 10⁻¹³ kg/m³, v = 7.56 km/s, Cd = 2.2, A = 2 m², L = 0.05 m:

T_aero = 0.5 × 1.0e-13 × (7560)² × 2.2 × 2.0 × 0.05
       = 0.5 × 1.0e-13 × 5.715e7 × 2.2 × 2.0 × 0.05
       = 6.29 × 10⁻⁷ Nm  (secular — accumulates momentum)

Solar Radiation Pressure:

T_srp = (F_s / c) × A_illum × (1 + q) × L_cp-cm

F_s = 1361 W/m², c = 3×10⁸ m/s, A = 3 m², q = 0.6, L = 0.02 m:

T_srp = (1361 / 3e8) × 3.0 × 1.6 × 0.02
      = 4.537e-6 × 3.0 × 1.6 × 0.02
      = 4.35 × 10⁻⁷ Nm

Residual Magnetic Dipole:

T_mag = M_residual × B_local

M = 1 Am² (typical smallsat), B at 600 km ~ 25 × 10⁻⁶ T:

T_mag = 1.0 × 25e-6 = 2.5 × 10⁻⁵ Nm  (cyclic)

Total worst-case secular: T_secular ~ T_aero = 6.29 × 10⁻⁷ Nm Total worst-case cyclic (RSS): T_cyclic = sqrt(T_gg² + T_srp² + T_mag²) ~ 2.5 × 10⁻⁵ Nm

Step 3: Reaction Wheel Sizing

Two independent requirements drive wheel sizing:

Momentum storage (absorb cyclic disturbance over quarter orbit):

H_cyclic = T_cyclic × (P_orbit / 4)
P_orbit  = 2 × pi × sqrt(r³ / mu)

WORKED EXAMPLE:

P_orbit = 2 × pi × sqrt((6.971e6)³ / 3.986e14) = 5807 s  (96.8 min)
H_cyclic = 2.5e-5 × (5807 / 4) = 2.5e-5 × 1452 = 0.0363 Nm·s

Momentum storage (secular — between dumps): If momentum dumping once per orbit:

H_secular = T_secular × P_orbit = 6.29e-7 × 5807 = 3.65 × 10⁻³ Nm·s

Slew torque requirement:

H_slew = I × omega_max
T_slew = I × alpha = I × (4 × theta_slew) / t_slew²   (bang-bang profile)

For 30° slew in 60 s, I_max = 120 kg·m²:

alpha  = (4 × 0.524 rad) / (60)² = 2.095 / 3600 = 5.82 × 10⁻⁴ rad/s²
T_slew = 120 × 5.82e-4 = 0.0698 Nm
omega_peak = alpha × (t/2) = 5.82e-4 × 30 = 0.01746 rad/s (1.0 deg/s)
H_slew = 120 × 0.01746 = 2.095 Nm·s

Wheel selection: Need H > 2.095 Nm·s per axis and T > 0.070 Nm per axis. Apply 2× margin: H_wheel > 4.2 Nm·s, T_wheel > 0.14 Nm. → Select medium RW class (e.g., 5 Nm·s, 0.2 Nm). Use 4-wheel pyramid for single-fault tolerance: 4 wheels in tetrahedral mount.

Step 4: Momentum Dumping Design

For LEO (magnetic torquers):

T_dump = m_dipole × B_field

Need to dump H_secular per orbit = 3.65 × 10⁻³ Nm·s. With B = 25 × 10⁻⁶ T, required dipole moment:

m = T_needed / B = (H_secular / t_dump) / B

If dumping over 10% of orbit (581 s):

T_needed = 3.65e-3 / 581 = 6.28 × 10⁻⁶ Nm
m = 6.28e-6 / 25e-6 = 0.25 Am²

Minimum dipole: 0.25 Am². With margin (4×): select 1 Am² torquer per axis. Typical rod torquer: 0.3 kg, 0.3 W.

Step 5: Pointing Error Budget

RSS (Root Sum Square) all contributors:

Margin check: If requirement is 30 arcsec (3-sigma) → margin = (30 - 21) / 30 = 30% → PASS (>20%).

Step 6: Control Mode Design

7. OUTPUT TEMPLATE

# [Mission Name] — ADCS Architecture

## Mission & Orbit Parameters
| Parameter | Value |
|-----------|-------|
| Orbit | [alt] km × [alt] km, [inc]° |
| Spacecraft mass | [X] kg |
| Inertia (Ix, Iy, Iz) | [X, Y, Z] kg·m² |
| Pointing accuracy (3-sigma) | [X] arcsec / [X] deg |
| Pointing stability | [X] arcsec/s over [T] s |
| Slew requirement | [X] deg in [T] s |
| Mission lifetime | [X] years |

## Disturbance Torque Environment
| Source | Magnitude (Nm) | Character |
|--------|----------------|-----------|
| Gravity gradient | [X] | Cyclic |
| Aerodynamic drag | [X] | Secular |
| Solar radiation pressure | [X] | Cyclic + secular |
| Residual magnetic | [X] | Cyclic |
| **Total secular** | **[X]** | |
| **Total cyclic (RSS)** | **[X]** | |

## Sensor Suite
| Sensor | Qty | Performance | Role |
|--------|-----|-------------|------|
| [sensor] | [N] | [accuracy] | [primary/backup/safe] |

## Actuator Suite
| Actuator | Qty | Capability | Role |
|----------|-----|-----------|------|
| [actuator] | [N] | [torque, momentum] | [primary/dump/backup] |

## Reaction Wheel Sizing
| Parameter | Required | Selected | Margin |
|-----------|----------|----------|--------|
| Momentum (Nm·s) | [X] | [X] | [X]% |
| Torque (Nm) | [X] | [X] | [X]% |

## Pointing Error Budget (3-sigma, arcsec)
| Source | Allocation | Type |
|--------|-----------|------|
| [source] | [X] | [bias/random] |
| **RSS Total** | **[X]** | |
| **Requirement** | **[X]** | |
| **Margin** | **[X]%** | |

## Control Modes
| Mode | Sensors | Actuators | Performance |
|------|---------|-----------|-------------|
| [mode] | [sensors] | [actuators] | [metric] |

## Mass & Power Budget
| Component | Qty | Unit Mass (kg) | Total Mass (kg) | Avg Power (W) |
|-----------|-----|----------------|-----------------|----------------|
| [component] | [N] | [X] | [X] | [X] |
| **ADCS Total** | | | **[X]** | **[X]** |

## Recommendation
[Selected architecture, rationale, risks, next steps]

8. CLASSIFICATION

9. VARIATIONS

• A: LEO Nadir-Pointing (EO) — Gravity gradient dominant disturbance, medium RW (2-10 Nm·s), star tracker + magnetometer, magnetic dumping every orbit, 0.05-0.5 deg pointing, ~500 km altitude, PD control adequate
• B: Sun-Pointing (Solar Science / Power) — Single-axis precision (sun line), coarse cross-axis, fine sun sensor + star tracker, low disturbance (GG small for symmetric S/C), 1 deg pointing sufficient, simple PD on sun vector
• C: Agile / Fast Slew (Imaging) — CMGs or large RW (50-200 Nm·s), dual star trackers + FOG gyros, 3-5 deg/s slew, settle <5 s, eigenaxis slew + PID with feedforward, biggest driver is slew torque not disturbance
• D: Spin-Stabilized — No reaction wheels, passive gyroscopic stability, nutation damper, spin rate 1-60 rpm, sensors: sun sensor + magnetometer, precession maneuvers via thrusters or mag torquers, heritage: early commsats, Explorer
• E: Deep Space / Interplanetary — Star tracker + sun sensor (no magnetometer, no GPS), thruster-based momentum management (no B-field for mag torquers), very low disturbances (SRP dominant), long autonomy between ground contacts, 0.01-0.1 deg for nav and science pointing

10. ERRORS & PITFALLS

• E1: Sizing wheels for disturbance torque only — slew torque and momentum often dominate by 10-100×; always check both
• E2: Forgetting secular vs cyclic — gravity gradient is cyclic (averages to zero) but aero drag is secular (accumulates); momentum storage vs dumping are different problems
• E3: Using star tracker accuracy as system pointing — thermoelastic alignment, control error, and latency add 2-5× to the budget; the tracker is one term in the RSS
• E4: No magnetic torquer sizing for momentum dumping — wheels saturate in hours to days without desaturation; mag torquers need dipole moment matched to secular disturbance at the specific orbit B-field
• E5: Ignoring tip-off rates at separation — launch vehicles deliver 1-5 deg/s tip-off; ADCS must detumble from this before any nominal mode; size the detumble actuator accordingly
• E6: Star tracker blinding by Sun/Earth/Moon — star trackers have exclusion angles (typically 25-45 deg from Sun, 15-30 deg from Earth limb); a single tracker has availability gaps; always fly 2+ trackers with offset boresights
• E7: Flexible mode interaction — control bandwidth must be 5-10× below the first flexible mode frequency; a 0.5 Hz flex mode limits control to ~0.05-0.1 Hz; ignoring this causes oscillation and instability
• E8: Wrong inertia tensor — using principal axes when products of inertia are significant, or not updating inertia for fuel depletion; a 20% inertia error can cause 20% torque authority error and control instability

11. TIPS

• T1: Start with disturbance torque analysis — this sets the floor for actuator sizing and drives sensor accuracy requirements
• T2: Use 4-wheel pyramid (tetrahedral) config for single-fault tolerance — 3 orthogonal wheels have zero redundancy; 4-wheel pyramid gives full 3-axis control with any 1 failure
• T3: Pointing budget should have >20% margin at system level — allocate sensor noise, alignment, control, thermoelastic, jitter, then verify RSS is <80% of requirement
• T4: Magnetic torquers are free momentum dumping — in LEO (B ~ 20-40 uT), a 1 Am² rod torquer (0.3 kg, 0.3 W) dumps ~0.02 Nm·s per orbit; always include them
• T5: Slew sizing dominates for agile missions — for a 500 kg sat slewing 45° in 30 s, you need ~100 Nm·s wheels; disturbance-only sizing might give you 1 Nm·s
• T6: Star tracker + gyro is the standard combo — tracker gives absolute attitude at 4-10 Hz with 1-10 arcsec; gyro propagates between updates at 100+ Hz with <0.01 deg/hr drift; together they give best of both worlds
• T7: Sanity check: ADCS mass ~ 5-15% of dry mass for LEO, 3-8% for GEO; power ~ 3-10% of orbit average power; if your numbers are outside this, investigate
• T8: Calibrate against known missions — Sentinel-2 (pointing 0.066 deg, 4× RW 12 Nm·s), Hubble (0.007 arcsec, 4× RW 300 Nm·s + FGS), ISS (4× CMG 258 Nm each, 4600 Nm·s total)

12. RELATED SKILLS