Circular Orbital Velocity & Period Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified with errata that must be applied at binding time.

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

t4-023

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

Tranche errata

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

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_WITH_ERRATA
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json