1. ROLE

3. GETTING STARTED

Minimum I need (pick one):

• "Design a sun-synchronous orbit for an Earth observation satellite at 500 km"
• "Calculate the Hohmann transfer from LEO to GEO"
• "Design a Walker constellation for global coverage with 24 satellites"
• "What's the launch window to Mars in 2026?"

Helpful if you have it:

• Altitude and inclination requirements
• Revisit time or coverage requirements (for constellations)
• Launch site latitude
• Mission lifetime (affects altitude selection due to drag)
• Payload field-of-view (affects swath width for coverage)

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

• "Circular or elliptical?" — fundamentally changes the analysis
• "Sun-synchronous needed?" — constrains inclination to altitude
• "What revisit time?" — drives constellation size

4. CONNECTORS

Shared Tools (in shared/tools/)

Shared Data

Cross-skill

5. TAXONOMY

5.1 Keplerian Orbital Elements

5.2 Common Orbit Types

5.3 Key Equations

Vis-viva (velocity at any point):

v = √(μ × (2/r - 1/a))

Circular orbit velocity:

v_circ = √(μ/r)

Orbital period:

T = 2π × √(a³/μ)

Hohmann transfer delta-v:

a_transfer = (r₁ + r₂) / 2
Δv₁ = √(μ/r₁) × (√(2r₂/(r₁+r₂)) - 1)
Δv₂ = √(μ/r₂) × (1 - √(2r₁/(r₁+r₂)))
Δv_total = Δv₁ + Δv₂
TOF = π × √(a_transfer³/μ)

Inclination change (circular):

Δv_inc = 2 × v × sin(Δi/2)

Sun-synchronous inclination:

cos(i) = -T × ṅ_sun × (a/R_E)^3.5 / (1.5 × π × J₂)
≈ For 500 km: i ≈ 97.4°

Ground track repeat:

Revolutions/day = k/d  (k revolutions in d days)
a = (μ × (d × 86400 / (2π × k))²)^(1/3)

5.4 Planetary Reference Data

6. PROCESS

Step 1: Define Mission Orbit

• Altitude (perigee × apogee) or semi-major axis
• Inclination (mission-driven or SSO)
• Eccentricity (circular preferred for most missions)
• Special constraints: frozen orbit, repeat ground track, sun-sync

Step 2: Calculate Orbit Parameters

Given: altitude h (circular) above Earth
r = R_E + h = 6371 + h  [km]
v = √(μ/r)              [km/s]
T = 2π√(r³/μ)           [seconds]

Worked Example — 525 km SSO:

r = 6371 + 525 = 6896 km
v = √(398600/6896) = 7.603 km/s
T = 2π√(6896³/398600) = 5700 s = 95.0 min
i_SSO = 97.5° (from J₂ regression matching solar rate)

Step 3: Transfer Orbit Design

Worked Example — LEO (400 km) to GEO:

r₁ = 6771 km, r₂ = 42164 km
a_t = (6771 + 42164)/2 = 24467.5 km
Δv₁ = √(398600/6771) × (√(2×42164/48935) - 1) = 2.400 km/s
Δv₂ = √(398600/42164) × (1 - √(2×6771/48935)) = 1.457 km/s
Δv_total = 3.857 km/s
TOF = π × √(24467.5³/398600) = 19,042 s ≈ 5.29 hours

Step 4: Constellation Design (if applicable)

Walker notation: T/P/F

• T = total satellites
• P = number of orbital planes
• F = phase factor (0 to P-1)

Example — 12/4/1 Walker at 525 km SSO:

• 4 planes × 3 satellites each
• Planes spaced by 360°/4 = 90° RAAN
• In-plane spacing: 360°/3 = 120°
• Phase offset: F=1 → 30° between adjacent planes
• Revisit at equator: ~6 hours (for SAR swath ~20 km)

Step 5: Station-Keeping Budget

Step 6: Verify & Report

• Check delta-v against propulsion budget (→ propulsion skill)
• Check altitude vs mission lifetime (drag decay)
• Check coverage vs revisit requirements
• Generate orbit parameter table

7. OUTPUT TEMPLATE

# [Mission] — Orbital Analysis

## Orbit Definition
| Parameter | Value |
|-----------|-------|
| Type | [SSO/LEO/GEO/...] |
| Altitude | [h] km ([perigee] × [apogee]) |
| Inclination | [i]° |
| Eccentricity | [e] |
| Period | [T] min |
| Velocity | [v] km/s |
| RAAN | [Ω]° (or free) |

## Transfer (if applicable)
| Maneuver | Δv (m/s) | Duration |
|----------|----------|----------|
| [burn 1] | [value] | [time] |
| [burn 2] | [value] | [time] |
| **TOTAL** | **[value]** | **[total]** |

## Constellation (if applicable)
| Parameter | Value |
|-----------|-------|
| Walker | [T/P/F] |
| Revisit | [time] at [latitude] |

## Station-Keeping
| Budget item | Δv/year (m/s) |
|-------------|---------------|
| [item] | [value] |
| **TOTAL** | **[value]** |

8. CLASSIFICATION

9. VARIATIONS

• A: LEO/SSO Design — Altitude trade (drag vs coverage), SSO inclination calc, LTAN selection
• B: GEO Mission — GTO injection, apogee kick, E-W/N-S station-keeping, longitude slot
• C: Constellation — Walker optimization, coverage vs revisit, deployment phasing
• D: Interplanetary — Porkchop plots, patched conics, gravity assists, C3 requirements
• E: Proximity/Rendezvous — CW equations, V-bar/R-bar approach, safety ellipse

10. ERRORS & PITFALLS

• E1: Using μ_Earth for interplanetary (must use μ_Sun outside SOI)
• E2: Forgetting plane change cost (inclination changes are extremely expensive: 28° at GEO = 3.6 km/s)
• E3: SSO altitude confusion (each altitude has ONE valid inclination — not a free variable)
• E4: Circular orbit assumption for elliptical analysis (v varies along ellipse!)
• E5: Ignoring J₂ effects on RAAN drift (5-7°/day at LEO — kills constellation geometry)
• E6: TOF in wrong units (vis-viva gives seconds, not minutes)
• E7: Mixing radius and altitude (r = R_Earth + h, NOT just h)
• E8: Ground track repeat error (15.x revs/day ≠ 15 — fractional part matters)

11. TIPS

• T1: Always draw r₁, r₂, a_transfer before computing — prevents sign errors
• T2: For SSO: use i ≈ 96.7° + 0.15°×(h/100km) as quick estimate (400-800 km)
• T3: Hohmann is optimal only for r₂/r₁ < 11.94. Above that, bi-elliptic wins
• T4: GEO longitude slot accuracy requires <0.1° — budget 46-52 m/s/yr total S/K
• T5: Constellation phase factor F: try all values 0 to P-1, coverage can vary 30%+
• T6: Sanity check: LEO velocity ≈ 7.5-7.8 km/s, GEO ≈ 3.07 km/s, escape ≈ 10.9 km/s
• T7: Low-thrust spiral Δv ≈ |v_final - v_initial| (not Hohmann — different formula)
• T8: For repeat ground track: start with revs/day ≈ 14.5-15.5, solve for exact a

12. RELATED SKILLS