Source: https://guthlabs.ai/docs/instruments/orbital-eccentricity-apsides-solver/mechanism/

instrument mechanism / verified-clean

# Orbital Eccentricity/Apsides Solver mechanism

The inspectable method record for Orbital Eccentricity/Apsides Solver, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The exact ambiguity requiring review is whether r_p and r_a mean center-to-body radii or surface altitudes, and whether the advertised 'any two' input mode includes all pairwise inverse calculations. The current name and computes field also imply broader orbital-element functionality than the supplied formulas provide.

- The stated formulas r_p=a(1-e) and r_a=a(1+e) are correct for an elliptical orbit when a, r_p, and r_a are center-to-body distances and all distances use the same units.

- The advertised 'any two of a, e, r_p, r_a' capability requires additional inverse formulas that are not specified, including a=(r_p+r_a)/2, e=(r_a-r_p)/(r_a+r_p), e=1-r_p/a, e=r_a/a-1, a=r_p/(1-e), and a=r_a/(1+e).

- The formulas do not apply to unbounded parabolic or hyperbolic trajectories as an apsis solver: e=1 has no finite apogee, and e>1 has no apogee.

## Units and conventions

- Eccentricity e is dimensionless.

- a, r_p, and r_a must be expressed in identical distance units; the formulas do not perform unit conversion.

- Perigee and apogee are Earth-specific terms and conventionally mean distances from Earth's center, not altitudes above the surface. If altitudes are intended, Earth-radius conversion is required.

- The formulas assume a bound Keplerian ellipse with 0<=e<1 and positive a.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "a": 10000,
    "e": 0.2,
    "distance_unit": "km"
  },
  "expected_outputs": {
    "r_p": 8000,
    "r_a": 12000,
    "distance_unit": "km"
  },
  "working": "r_p = a(1-e) = 10000(1-0.2) = 10000(0.8) = 8000 km.\nr_a = a(1+e) = 10000(1+0.2) = 10000(1.2) = 12000 km."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The solver can encounter an undefined division when a=0. It also needs explicit validity and convention handling at e=1, across e=1, and for negative semimajor axis hyperbolic inputs; otherwise it may return misleading apsides.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/orbital-eccentricity-apsides-solver/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/orbital-eccentricity-apsides-solver/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/orbital-eccentricity-apsides-solver/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`