Source: https://guthlabs.ai/docs/instruments/vis-viva-elliptical-orbit-energy-calculator/
instrument / verified-clean
# Vis-Viva / Elliptical Orbit Energy Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo
**Tranche**: tranche-4
**Evidence ID**: t4-047
**Ledger rows**: 1
No ledger note is attached.
## Review findings
Core vis-viva and specific-energy formulas PASS under the stated two-body Keplerian approximation. The specification NEEDS_REVIEW because the claimed apoapsis/periapsis outputs require missing inputs, and the unit convention and domain constraints must be made explicit.
### Formula and scope findings
- The vis-viva formula v²=GM(2/r−1/a) is standard and correct for a two-body Keplerian orbit when GM, r, and a use mutually consistent units.
- The specific orbital energy formula ε=−GM/(2a) is standard and correct for a bound two-body orbit; its units are energy per unit mass.
- The claimed apoapsis and periapsis speeds cannot be computed from only GM, current radius r, and semi-major axis a. The specification must also provide apoapsis/periapsis radius, eccentricity, or equivalent orbit-shape information.
- The claim is specifically for an elliptical orbit, so the input constraints must exclude r≥2a and require a>0, r>0, and a positive GM. The boundary r=2a gives v=0 and corresponds to the degenerate parabolic-limit boundary, not a nondegenerate ellipse.
### Unit assumptions
- GM must be supplied in units of length³/time², such as km³/s² or m³/s².
- r and a must use the same length unit as GM; the resulting speed uses the corresponding length/time unit.
- Specific orbital energy ε has units of length²/time², equivalently J/kg when using SI units.
- All calculations assume a point-mass central body, negligible test-body mass, and no drag, thrust, third-body perturbations, or relativistic effects.
- A GM table is only valid if the selected body's GM and the supplied r and a are in compatible units.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The advertised apoapsis and periapsis speeds cannot be computed from the stated inputs GM, current radius r, and semi-major axis a alone; eccentricity or both apsis radii are required. The calculator also needs explicit rejection handling for r=0 and for negative square-root radicands, especially at and beyond r=2a.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"GM": 398600.4418,
"r": 7000,
"a": 7000,
"units": "km, km³/s²"
},
"expected_outputs": {
"speed": 7.54605329,
"specific_energy": -28.47146013,
"apoapsis_speed": null,
"periapsis_speed": null
},
"working": "v²=398600.4418×(2/7000−1/7000)=398600.4418×(1/7000)=56.9429202571 km²/s²; v=√56.9429202571=7.54605329 km/s. ε=−398600.4418/(2×7000)=−398600.4418/14000=−28.47146013 km²/s². Apoapsis and periapsis speeds are not determined because eccentricity or apoapsis/periapsis radius was not supplied."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche4/tranche4-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`