Two-Body Barycenter / Reduced Mass Calculator mechanism

Model scope

The algebra is correct, but the specification is incomplete because it declares separation as an input while the barycenter formula requires r1 and r2, or an explicit coordinate convention such as r1=0 and r2=separation along a selected axis.

• Both formulas are standard and correct: r_cm=(m1*r1+m2*r2)/(m1+m2) and μ=m1*m2/(m1+m2). However, the declared inputs omit r1 and r2; separation alone cannot determine the absolute barycenter position without a coordinate origin and direction. If r1=0 and r2=separation are intended, that convention must be stated explicitly.
• The barycenter formula must support scalar coordinates or componentwise vector coordinates consistently. Separation is a scalar distance and does not by itself specify vector positions.

Units and conventions

• m1 and m2 use the same mass unit; μ has that same mass unit.
• r1, r2, and separation use the same length unit; the barycenter position has that length unit.
• For vector positions, all components use the same length unit and the formula is applied componentwise.
• Masses should be nonnegative, with m1+m2>0 for both formulas to be defined.
• If the origin is placed at body 1, then r1=0 and r2 may be represented by the separation only along a chosen axis.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "m1": 6e+24,
    "m2": 7.5e+22,
    "r1": 0,
    "r2": 384000000,
    "separation": 384000000,
    "mass_unit": "kg",
    "length_unit": "m"
  },
  "expected_outputs": {
    "barycenter_position": 4740740.740740741,
    "reduced_mass": 7.407407407407407e+22
  },
  "working": "m1+m2 = 6e24 + 7.5e22 = 6.075e24 kg. r_cm = (6e24*0 + 7.5e22*384000000) / 6.075e24 = (7.5e22/6.075e24)*384000000 = (1/81)*384000000 = 4740740.740740741 m. μ = (6e24*7.5e22)/6.075e24 = 4.5e47/6.075e24 = 7.407407407407407e22 kg."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification permits zero-mass inputs but does not state a rejection rule. With m1=m2=0, both outputs become 0/0 and are undefined. The specification also omits the coordinate origin and endpoint-orientation convention, so a numeric barycenter coordinate can differ while the reduced mass remains unchanged.

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