Circular Orbital Velocity mechanism

Model scope

The algebraic formula v = √(GM/r) is the standard circular-orbit speed formula under the two-body Newtonian model. Verdict is NEEDS_REVIEW because the exact ambiguity is whether the user supplies orbital radius or altitude, and the specification does not define the required unit conventions or radius-table convention.

No additional formula finding is recorded.

Units and conventions

• GM is the central body's standard gravitational parameter μ = GM, expressed in km^3/s^2.
• Orbital radius r is measured from the central body's center in km.
• With altitude input, r = body_radius + altitude, with both distances in km.
• The resulting velocity is in km/s.
• The calculation assumes a two-body point-mass model and a circular orbit.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "central_body": "Earth",
    "mu_km3_s2": 398600.4418,
    "body_radius_km": 6378.137,
    "altitude_km": 0,
    "orbital_radius_km": 6378.137
  },
  "expected_outputs": {
    "velocity_km_s": 7.90537
  },
  "working": "r = 6378.137 + 0 = 6378.137 km\nv = √(398600.4418 / 6378.137)\n  = √(62.4948)\n  = 7.90537 km/s"
}

Failure boundary

• The specification ambiguously allows either orbital radius or altitude but does not define how altitude is converted to radius; it must use r = body_radius + altitude.
• The units for GM, radius, altitude, and output are not explicitly declared in the specification.
• The body-radii table does not specify which radius is used for non-spherical bodies, such as mean, equatorial, or reference radius.
• Reject or explicitly handle altitude values that produce r <= 0; otherwise the division and square root are invalid.
• A missing or incorrect central-body GM or radius table entry produces an incorrect result.
• The formula does not account for atmospheric drag, body rotation, oblateness, third-body perturbations, or non-circular trajectories.
• The empty honest_label is a concern: the result should be labeled as idealized two-body circular-orbit speed, not universally achievable orbital speed.

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