Vis-Viva / Elliptical Orbit Energy Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

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