Source: https://guthlabs.ai/docs/instruments/hohmann-transfer-delta-v/mechanism/

instrument mechanism / verified-clean

# Hohmann Transfer Delta-V mechanism

The inspectable method record for Hohmann Transfer Delta-V, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The underlying approach is the standard idealized two-impulse Hohmann calculation and is consistent with the stated honest label. Review is required because the formula set, transfer-time definition, GM-table precision, radius reference, and unit contract are not fully specified.

- The stated method is standard, but the actual equations are underspecified: use a_t=(r_initial+r_target)/2, v=sqrt(mu(2/r-1/a_t)), Δv1=|v_transfer,perigee-sqrt(mu/r_initial)|, and Δv2=|sqrt(mu/r_target)-v_transfer,apogee|.

- Transfer time is not explicitly defined; for a Hohmann half-ellipse it should be t_transfer=pi*sqrt(a_t^3/mu).

- The implementation must handle both outward and inward transfers with absolute delta-v magnitudes; an unsigned subtraction would produce an incorrect negative burn.

- The central-body GM table and its authoritative values are not specified, so reproducibility depends on hidden table precision and epoch/convention.

- The input must clarify that orbit radii are distances from the central body's center, not altitudes above the surface.

## Units and conventions

- All radii in the first three vectors are kilometers and mu is in km^3/s^2, so velocities are km/s and transfer time is seconds.

- The Earth value used is mu=398600.4418 km^3/s^2.

- The fourth vector uses SI units: radii in meters and mu=398600441800000 m^3/s^2, producing velocities in m/s and time in seconds.

- Both orbits are assumed circular, coplanar, and prograde; radii must be positive and the central-body GM must use units consistent with radius.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "central_body": "Earth",
    "mu_km3_s2": 398600.4418,
    "initial_radius_km": 7000,
    "target_radius_km": 14000
  },
  "expected_outputs": {
    "transfer_semi_major_axis_km": 10500,
    "delta_v1_km_s": 1.16738,
    "delta_v2_km_s": 0.97915,
    "total_delta_v_km_s": 2.14653,
    "transfer_time_s": 5353.83
  },
  "working": "a_t=(7000+14000)/2=10500 km. v_c1=sqrt(398600.4418/7000)=sqrt(56.9429203)=7.546053 km/s. v_p=sqrt(398600.4418*(2/7000-1/10500))=8.713432 km/s. Δv1=|8.713432-7.546053|=1.167379 km/s. v_c2=sqrt(398600.4418/14000)=5.335865 km/s. v_a=sqrt(398600.4418*(2/14000-1/10500))=4.356716 km/s. Δv2=|5.335865-4.356716|=0.979150 km/s. Total=1.167379+0.979150=2.146529 km/s. t=pi*sqrt(10500^3/398600.4418)=5353.83 s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-radius input causes division by zero and undefined orbital quantities; the instrument must reject it. The specification also leaves signed-versus-magnitude delta-v and unit conventions ambiguous.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/hohmann-transfer-delta-v/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/hohmann-transfer-delta-v/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/hohmann-transfer-delta-v/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`