Vis-Viva Equation Solver mechanism

Model scope

NEEDS_REVIEW because the formula is valid, but the output requires an unstated square-root operation and the units, central body, GM-table selection, and two-body assumptions are not specified. The honest_label field is empty.

• The vis-viva equation is standard for two-body orbital motion, but the displayed formula computes v², while the stated output is velocity; the implementation must return the positive root v = sqrt(GM(2/r - 1/a)).
• The formula assumes an ideal two-body model with negligible third-body, drag, and non-spherical-gravity effects.

Units and conventions

• GM must be the gravitational parameter of the central body, not G alone.
• GM, r, and a must use mutually consistent units; GM in km³/s² with distances in km produces velocity in km/s, while GM in m³/s² with distances in m produces velocity in m/s.
• r is assumed to be the center-to-object orbital radius, not altitude above the body's surface.
• For an elliptical orbit, a > 0, r > 0, and the radicand must be nonnegative; a physically valid orbit also requires the supplied r to lie within that orbit's periapsis and apoapsis radii.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "GM_km3_s2": 398600,
    "r_km": 7000,
    "a_km": 7000
  },
  "expected_outputs": {
    "velocity_km_s": 7.5460491
  },
  "working": "v² = 398600 × (2/7000 - 1/7000) = 398600 × (1/7000) = 56.9428571 km²/s². v = sqrt(56.9428571) = 7.5460491 km/s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification provides no explicit input validation for r=0 or for a negative square-root radicand. Such inputs produce undefined results and must be rejected. The output also lacks a stated sign convention, so it cannot distinguish velocity direction from speed magnitude.

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