Why this exists
Deep-space optical links are sensitive to small effects. A term that looks negligible in one geometry can matter in another: Shapiro delay near solar conjunction, Sagnac timing from rotating frames, point-ahead angle from transverse velocity, diffraction loss from aperture and wavelength, gravitational redshift in precision clock comparisons, and phase accumulation over long integration times.
The purpose of this lab is not to hide those effects inside a black box. The purpose is to make them visible. Each calculator shows the formula, units, assumptions, approximation order, tolerance test, and an exportable certificate.
Calculators — simple, single-term physics checks
Correction Budget Ranker MVP
Purpose. Compare timing, pointing, frequency, phase, and optical-link terms against user tolerances.
Inputs. scenario geometry, range, velocity, frequency, tolerances.
Outputs. ranked table: KEEP WATCH IGNORE.
Best for. "Can I safely ignore this correction?"
Shapiro Delay MVP
Purpose. Compute weak-field gravitational light-time delay near a massive body.
Inputs. central body, $GM$, $r_1$, $r_2$, $R$, PPN $\gamma$.
Outputs. delay in seconds and range-equivalent meters.
Best for. solar-conjunction / light-time correction checks.
Deep-Space Optical Link Budget MVP
Purpose. Estimate beam divergence, received power, photon rate, photons per bit, point-ahead angle, and link margin.
Inputs. wavelength, aperture, power, range, data rate, losses.
Outputs. photon budget and link margin.
Best for. optical communications sanity checks.
Sagnac Correction MVP
Purpose. Estimate rotating-frame timing corrections for Earth-based or rotating-body links.
Inputs. emitter/receiver vectors, rotation vector, frame convention.
Outputs. time correction and range equivalent.
Best for. ground station / rotating-frame timing checks.
Frequency / Clock Shift MVP
Purpose. Estimate gravitational redshift, Doppler, and transverse-Doppler terms.
Inputs. potential difference, velocities, carrier frequency.
Outputs. fractional frequency shift, Hz shift, accumulated cycles.
Best for. clock, phase, and precision frequency checks.
Light Deflection / Pointing MVP
Purpose. Estimate first-order angular light deflection near massive bodies.
Inputs. $GM$, impact parameter $b$, PPN $\gamma$, pointing tolerance.
Outputs. deflection in radians, arcsec, mas, tolerance status.
Best for. pointing correction near solar limb or planets.
Validation Cases MVP
Purpose. Reproduce public or textbook benchmark calculations.
Inputs. preloaded cases.
Outputs. expected value vs calculator output.
Best for. checking implementation correctness.
Certificate Generator In every tool
Purpose. Export calculator inputs, constants, formulas, assumptions, outputs, warnings, and SHA-256 hash.
Inputs. live calculator result.
Outputs. JSON / Markdown certificate.
Best for. reproducible engineering notes and review packets.
Every calculator above includes an "Export Certificate" action.
PPN Sensitivity Explorer Phase 3
Purpose. Vary PPN $\gamma, \beta$ and see which observables move.
Status. planned. The MVP calculators already expose $\gamma$ as an input so a manual sweep is possible.
How the calculators are built
Each calculator is built as a visible chain:
- User inputs
- Physical constants (CODATA / IAU; see Validation)
- Formula set (visible on every tool page)
- Unit conversions
- Correction terms
- Tolerance tests (KEEP / WATCH / IGNORE)
- Warnings and assumptions
- Certificate export (JSON + Markdown, SHA-256 hashed)
Geometry + link inputs
↓
Standard formulas + constants
↓
Term-by-term correction budget
↓
Tolerance ranking
↓
Validation check
↓
Exportable certificate
Physics and math checking
The lab is designed as a calculator suite and as a physics-check workbench. Each result is broken into named terms, and each term is tied to a formula, unit, assumption, and validation case where possible. This makes the tools useful for engineering estimates and also for finding mistakes: wrong units, wrong signs, invalid approximations, hidden frame assumptions, and terms that exceed tolerance.
| Check | What every page exposes |
|---|---|
| Formula check | The equation used for each correction |
| Unit check | Input units, output units, conversion notes |
| Sign-convention check | Direction and frame assumptions |
| Approximation check | Weak-field, first-order, static-body, or low-velocity assumptions |
| Magnitude check | Order-of-magnitude comparison |
| Tolerance check | Whether a term is keep / watch / ignore |
| Validation check | Known benchmark or public example |
| Reproduction check | Exportable JSON / Markdown certificate with SHA-256 hash |
Suggested workflow
- Choose a scenario. Select range, body geometry, velocity, optical-link parameters.
- Run the correction ranker. See which timing, pointing, frequency, and optical-link terms matter.
- Open the dominant terms. Use dedicated calculators for Shapiro delay, point-ahead angle, Sagnac, frequency shift, etc.
- Check formulas and assumptions. Inspect equations, units, signs, and approximation warnings on each tool page.
- Export a certificate. Save inputs, outputs, formulas, constants, assumptions, and SHA-256 hash.
Motto: start broad, rank terms, drill down, export proof.
Validation
The validation page contains public or textbook-level cases the calculators reproduce. These are implementation checks, not proprietary mission validations.
| Validation case | Calculator | What it checks |
|---|---|---|
| Solar-limb light deflection | Light deflection | $4GM_\odot / (c^2 R_\odot) \approx 1.75\,\text{arcsec}$ |
| Solar conjunction Shapiro delay | Shapiro delay | logarithmic light-time correction |
| 1550 nm photon energy | Link budget | $E_\gamma = hc/\lambda$ |
| Airy divergence | Link budget | $\theta_{\rm div} = 1.22\lambda/D$ |
| Simple Sagnac geometry | Sagnac | $\vec\Omega\cdot(\vec r_1\times\vec r_2)/c^2$ |
| Point-ahead scaling | Link budget | $v_\perp/c$ |
Certificate / reproducibility
Every calculator can export a certificate. The certificate records the tool version, timestamp, inputs, constants, formulas, assumptions, outputs, warnings, tolerance tests, and a SHA-256 hash of the canonical JSON. This makes a result easy to share, reproduce, and audit.
{
"tool": "shapiro-delay",
"version": "0.1.0",
"inputs": { "central_body": "Sun", "r1_AU": 1.0, "r2_AU": 1.5, "gamma": 1.0 },
"outputs": { "delay_seconds": 0.000123, "range_equivalent_m": 36874 },
"warnings": [ "one-body weak-field approximation" ],
"hash": { "sha256": "…", "short": "abc123" }
}
Assumptions and limits
| Area | MVP includes | MVP does not include |
|---|---|---|
| GR light-time | one-body weak-field Shapiro | full multi-body relativistic ephemeris |
| Timing frames | simple convention notes | full TDB / TCB / TT / UTC transformation stack |
| Rotation | simple Sagnac | full station-motion / Earth-orientation pipeline |
| Optical link | diffraction, photon rate, point-ahead | turbulence, adaptive optics, detector internals |
| Pointing | first-order light deflection | full pointing-control simulation |
| Validation | public / textbook cases | proprietary mission validation |
Suggested first use cases
"Can I ignore Shapiro delay?"
Sun as central body, Earth-spacecraft geometry, tolerance in nanoseconds or meters → keep/watch/ignore decision.
"How hard is this optical link?"
Wavelength, apertures, range, power, data rate → photon rate, photons-per-bit, link margin.
"What pointing angle matters?"
Transverse velocity, range, aperture, wavelength, impact parameter near Sun → ranked pointing terms.
"Which correction dominates?"
Saved scenario → full ranked correction budget across timing, pointing, frequency, and optical-link terms.
Registries
Authoritative sources for every formula, constant, and validation case used by the calculators above.
- Formula registry — every equation by
formula_id - Constants registry — every numerical constant by
constant_id(CODATA / IAU / IERS / WGS-84) - Source registry — every textbook, standards body, and public mission fact by
source_id - Reproducibility bundle — downloadable bundle for re-running the lab
- Validation cases — public / textbook benchmark reproductions
More Advanced Calculators
Design-Space Dominance Map Advanced
Purpose. Find the active optical-link constraint across a high-dimensional design space — before spending compute on full wave-optics or high-fidelity Monte Carlo.
Inputs. design vector (range, wavelength, aperture, power, etc.) and sweep ranges.
Outputs. dominant-limiter map, closure margin $G(z)$, regime classification, boundary-case list, high-fidelity recommendations.
Best for. "Which constraint dominates in this region of design space?"
Optical Link Reliability Emulator Advanced
Purpose. Estimate deep-space optical-link closure probability under declared assumptions and uncertainties — fast triage before high-fidelity simulation.
Inputs. nominal scenario + per-input uncertainty distributions.
Outputs. $P_\text{close}$, margin percentiles $M_{05}/M_{50}/M_{95}$, dominant failure mode, high-fidelity escalation list.
Best for. "Will this link close reliably under uncertainty?"
Wave-Optics / Atmosphere / AO Surrogate Advanced
Purpose. Estimate atmospheric turbulence, adaptive-optics residual, pointing, and coupling penalties — fast surrogate triage before high-fidelity wave-optics simulation.
Inputs. optical scenario + atmosphere ($r_0$, zenith, $T_\text{atm}$) + AO model + receiver coupling.
Outputs. Strehl ratio, coupling efficiency, penalty distribution, fade probability, dominant impairment, high-fidelity recommendation.
Best for. "How much penalty does the atmosphere + AO actually cost on this site?"
Research context
This lab was developed alongside a broader geometric-physics manuscript. The calculators themselves use standard public formulas, public constants, and public validation cases.