Orbital Deployment Trade Study

An installable preliminary calculator for tangential deployment impulses, phase drift, host recoil and the rigid-body disturbance from a closed internal mass move.

Status: two-body and rigid-body trade study. This does not perform conjunction assessment, replace a launch-provider analysis or establish flight safety. Atmosphere, covariance, flexible modes and host control require higher-fidelity tools and mission data.

_{The left sweep separates orbital-energy change from accumulated phase. The right ledger separates external release recoil from the closed internal-mass disturbance. All curves and bars are regenerated from the two committed cases.}

Why this exists

VOLLEY's astrodynamics record mixes four questions that do not have the same evidence:

1. what a tangential impulse does to a circular orbit;
2. how mean-motion difference accumulates phase;
3. what linear recoil magnitude the host receives;
4. what ideal angular motion follows an internal mass transfer.

Boundary added 2026-08-14: phase drift is not the cheapest route to phase

Question 2 below computes what it says it computes, and a VOLLEY analysis has since shown it is the wrong comparator for a deployment product. Satellites released at different times from the same host arrive at different true anomalies in the same orbit, for no velocity at all: at 450 km the in-track rate is 0.0641 °/s, so 30° costs 468 seconds of waiting against 1.38 days by commanded differential velocity.

Release timing also gives a better answer, not just a cheaper one. It sets a static offset; a differential sets a rate — 21.75 °/day at 10 m/s — that never stops and that a propulsion-less satellite cannot null.

What a differential impulse buys that a clock cannot is a commanded change in orbital energy: +28.8 km of semi-major axis and a 1.602 lifetime multiplier, against 0 m and 1.0000 for timed release. That is a statement about what a deployment interface can command — drag, J₂ and solar radiation pressure change orbital elements too, and question 1 below prices none of them. Question 1, not question 2, is where the value is. VOLLEY records this as P56.

The first three are useful screening calculations. The fourth is here because a VOLLEY audit found that peak rate had been mistaken for residual rate. A symmetric closed move returns to zero ideal residual body rate but leaves an attitude offset. That correction removed a false 18.1 s cadence floor; it did not produce a host-controller or structural-settling model.

_{The overview is regenerated from both committed cases by tools/generate_readme_figure.py. The lifetime plot is retained from the detailed VOLLEY reference. Both are model output, not flight evidence.}

What the calculator does

• derives the post-impulse ellipse from specific energy and angular momentum;
• computes phase-drift time from the difference in mean motion;
• reports host recoil as a magnitude from linear-momentum conservation;
• separates transient peak rate, attitude offset and ideal residual rate;
• rejects unbound or Earth-intersecting trajectories rather than returning plausible numbers;
• includes one VOLLEY reference case and one independent hosted-6U example.

Run it

python -m pip install -e .
orbital-trade cases/hosted_6u_example.json
orbital-trade cases/volley_reference.json --out build/volley_reference.json

Verify it

python -m unittest discover -s tests -v
python tools/verify_repository.py

The tests cover zero impulse, prograde and retrograde geometry, unbound rejection, momentum conservation, recoil sign convention and the corrected closed internal move.

Evidence boundary

The committed VOLLEY astrodynamics, payload-family, attitude and validation sources remain under reference/volley/. Their uncomfortable results remain attached:

Item	Current record
A5	FAIL — GMAT falsified the claimed solar-activity invariance
A6	three probability-spread rows remain VOID; no operational covariance or CDM
A9	NOT RUN against flown public orbital history
A13	corrected zero ideal residual rate; structural settling and control remain open

NASA GMAT reproduced and challenged numerical claims. NASA did not validate or endorse VOLLEY.

Repository layout

• src/orbital_trade/ — two-body, recoil and internal-mass screening functions;
• cases/ — one VOLLEY case and one non-VOLLEY hosted-6U case;
• tests/ — limiting cases, conservation checks and rejection paths;
• reference/volley/ — files retained byte-for-byte from VOLLEY commit aa22a06;
• docs/ — validation boundary, tool versions, provenance, decisions and roadmap.

See summary, validation, toolchain, provenance, and open problems.

Licence

CC BY 4.0 — full text in LICENSE, attribution form in NOTICE. Attribution requires credit, a link to the licence, and an indication of whether changes were made.

Not retroactive: snapshots taken before this change remain available under the MIT licence they carried at the time, retained at LICENSE-MIT-superseded.

This repository carries copies of VOLLEY analysis code under reference/volley/. CC BY 4.0 does not license patent rights, which is why a patent-granting licence was not used here.