Circular Orbital Velocity & Period Calculator mechanism

Model scope

Core velocity and period formulas PASS under the stated honest-label assumptions, but the overall specification NEEDS_REVIEW because units, GM-table conventions, and the formulas or thresholds for the advertised LEO/GEO markers are not specified.

• The formulas v=√(GM/r) and T=2π√(r³/GM) are standard for a circular two-body orbit when r is measured from the central body's center and G and M use a consistent unit system.
• The claimed output "altitude equivalents (LEO/GEO markers)" has no specified formula, threshold, or classification rule; LEO and GEO markers therefore cannot be verified from this spec.
• The planetary GM table is unspecified, including its source, precision, and supported bodies.

Units and conventions

• Use SI units: G in m³·kg⁻¹·s⁻², M in kg, r in m, v in m/s, and T in seconds.
• If altitude h is supplied, compute orbital radius as r=R+h, with h and body radius R in the same units before conversion.
• Use G=6.67430×10⁻¹¹ m³·kg⁻¹·s⁻² in the test vectors.
• The central body's mass is treated as much larger than the orbiting object's mass; otherwise use the total system mass.
• The quoted outputs are rounded approximations.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "central_body": "Earth",
    "mass_kg": 5.972e+24,
    "G_m3_kg_s2": 6.6743e-11,
    "body_radius_m": 6371000,
    "altitude_m": 400000,
    "orbital_radius_m": 6771000
  },
  "expected_outputs": {
    "orbital_velocity_m_s": 7672.49,
    "period_s": 5544.93,
    "period_min": 92.42
  },
  "working": "GM=(6.67430×10⁻¹¹)(5.972×10²⁴)=3.98589196×10¹⁴ m³/s². r=6,371,000+400,000=6,771,000 m. v=√(GM/r)=√[(3.98589196×10¹⁴)/(6.771×10⁶)]=√(5.886711×10⁷)=7,672.49 m/s. T=2π√(r³/GM)=2π(r/v)=2π(6,771,000/7,672.49)=2π(882.50)=5,544.93 s=5,544.93/60=92.42 min."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The calculator has undefined behavior at zero or negative orbital radius and can produce materially different results if negative altitude is interpreted as signed depth versus an absolute altitude magnitude. The radius-input and altitude-input branches agree for valid positive values.

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