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Orbital Planner

From LEO rendezvous to Mars transfer windows — the same NM21 operator, phase-locked to HulyaPulse, solving trajectory math at sub-0.1% Δv.

  • Live app — zeq.dev/apps/orbital-planner/
  • Source — apps/zeq-me/public/apps/_in-development/orbital-planner/ (2,148 lines)
  • Operators — KO42 · NM21 (gravity) · optional GR32, GR33 (relativistic corrections)
  • Error budget — ≤ 0.1% Δv for canonical Hohmann and Lambert transfers

What it solves​

A mission-design workbench. Three tools:

  • Hohmann / bi-elliptic — two-impulse circular-to-circular transfers
  • Lambert's problem — fixed-time-of-flight two-body boundary value solver
  • Patched-conic with gravity assist — Earth → Venus → Earth → Mars, with sphere-of-influence transitions

Optional GR corrections activate when you enable GR35 (gravitational time dilation) — relevant for GNSS-class precision and solar-system-scale Shapiro delay.

The math​

NM21  F = G m₁ m₂ / r²                 (Newton gravity, two-body)
Vis-viva                v² = μ (2/r − 1/a)
Hohmann Δv_1            √(μ/r_1) · (√(2 r_2/(r_1+r_2)) − 1)
Lambert (Izzo)          universal-variable formulation (solved iteratively)
GR32 Ricci              G_{μν} = R_{μν} − ½ R g_{μν}   (post-Newtonian corrections)
GR35 time dilation      ∆t = ∆t₀ √(1 − 2GM/rc² − v²/c²)

Operator picks​

StepDecision
1. PrimeKO42 on
2. LimitKO42 + NM21 = 2 operators (baseline); + GR35 = 3 (GNSS precision)
3. ScaleSolar-system, 10³–10⁹ m, Keplerian
4. Precision≤ 0.1% Δv
5. CompileC_KO42 + C_NM21 (+ C_GR35)
6. ExecuteZ encodes central body μ, orbit radii, time-of-flight
7. VerifyCross-check vis-viva and Hohmann reference

Runnable worked example — LEO to GEO Hohmann​

r₁ = 6,578 km, r₂ = 42,164 km, Earth μ = 398,600 km³/s². Published Δv_total ≈ 3.935 km/s.

The anonymous playground takes a domain plus named inputs and lets the seven-step wizard pick the operators (always KO42 + the domain fit). It returns a sealed envelope:

curl -s -X POST https://zeqsdk.com/api/playground/compute \
  -H "Content-Type: application/json" \
  -d '{
    "domain": "newtonian-mechanics",
    "inputs": { "radius": 6578000, "radius_target": 42164000, "mu": 3.986e14 }
  }' | jq

The response carries value, unit, the operators the wizard chose, the equations it evaluated, and a zeqProof digest. Compare the returned value against the published Hohmann total (Δv_total ≈ 3.935 km/s) yourself — the platform hands you a result any node can recompute, not a printed figure to trust.

Extend it​

  1. Low-thrust spiral — replace impulsive Δv with Edelbaum's analytical; compare payload-mass at Mars
  2. Porkchop plots — Lambert sweep over departure × arrival; shade C₃ and arrival-v∞
  3. N-body perturbations — add Moon and Sun to LEO Δv-budget via patched cowell integration

Seeds​

  • Relativistic trajectory design — activate GR32/GR33 for Mercury perihelion precession (43″/century)
  • Gravitational-wave assist trajectories near compact binaries (GR38 active)
  • Optimal cis-lunar logistics — daily L1/L2 cycler design with the planner running at 1.287 Hz

Papers​

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.