Correction Budget Ranker

For one mission geometry, compute every relativistic and optical correction term, rank by magnitude against your tolerances, and export a reproducible certificate. The flagship aggregator for the Relativistic Optics Lab.

📊 Sample calculation — Earth–Mars superior conjunction at solar grazing: lab agrees with Will (2018) within stated tolerance 250 μs to 1 %

Scenario

Preset Preset auto-fills all inputs below. "Custom" leaves your values alone.

Tolerances

Timing (ns)

Range (m)

Pointing (µrad)

Frequency (Hz)

watchFrac / keepFrac

ratio = |value|/tol. KEEP if ratio ≥ keepFrac; WATCH if ≥ watchFrac.

Geometry

Shapiro / deflection body

Distance units (r1, r2, R, b)

$r_1$ — emitter to body

$r_2$ — receiver to body

$R$ — emitter→receiver range

$b$ — impact parameter Same units as $r_1, r_2, R$.

PPN $\gamma$

Sagnac surrogate area $A$ (m²) Δt_Sag = 2 Ω⊕ A / c². Simplified scalar form — see Sagnac calculator for full vector form.

Optical

Wavelength λ (nm)

Transmit aperture $D_t$ (m)

Transverse velocity $v_\perp$ (m/s)

Transmit power $P_t$ (W)

Frequency / clock

Line-of-sight velocity $v_\parallel$ (m/s)

Carrier frequency $f_0$ (Hz)

Emitter potential $U_e$ (J/kg) Blank → auto-fill $-GM/r_1$.

Receiver potential $U_r$ (J/kg) Blank → auto-fill $-GM/r_2$.

Emitter speed $v_e$ (m/s)

Receiver speed $v_r$ (m/s)

Decision summary

KEEP

—

WATCH

—

IGNORE

—

Dominant term

—

Formula drawer (registry-backed equations, assumptions, sources)

Loading formula registry…

Compare scenario A vs B

Workflow: pick / edit a preset, click Save current as Scenario A; pick / edit another preset, click Save current as Scenario B; the side-by-side appears below. Both snapshots persist in localStorage.

Ranked corrections

Click any column header to re-sort. Default sort: descending by tolerance ratio (largest budget hit first).

#	Term	Value (native)	In tolerance units	Tolerance	Ratio ▼	Decision	Refs (formula_id · source_ids)
Press Rank corrections to compute.

Formulas used

Shapiro delay (one-body PPN) & range-equivalent $$\Delta t_{\rm Shap} = (1+\gamma)\,\frac{GM}{c^3}\,\ln\!\frac{r_1+r_2+R}{r_1+r_2-R},\qquad \Delta\rho_{\rm Shap}=c\,\Delta t_{\rm Shap}$$ Sagnac (simplified scalar surrogate) · Light deflection (1st-order PPN) · Airy half-angle · Point-ahead $$\Delta t_{\rm Sag}\!\approx\!\frac{2\Omega A}{c^{2}},\quad \alpha_{\rm defl}\!=\!(1+\gamma)\frac{2GM}{c^{2}b},\quad \theta_{\rm Airy}\!=\!1.22\lambda/D_t,\quad \alpha_{\rm pa}\!=\!v_\perp/c$$ Low-order frequency shift · Photon rate $$\frac{\Delta f}{f}\!\approx\!-\frac{v_\parallel}{c}+\frac{U_e-U_r}{c^{2}}-\frac{v_e^{2}-v_r^{2}}{2c^{2}},\qquad \dot N = P_t\lambda/(hc)$$

Assumptions

Single mission geometry, single point in time. No ephemeris, no time-averaging.
Shapiro and light deflection: one-body weak-field PPN form, γ user-set (γ = 1 is GR).
Sagnac uses a simplified scalar surrogate Δt ≈ 2 Ω⊕ A / c²; full vector form Δt = Ω·(r₁×r₂)/c² is on the Sagnac page.
Frequency shift uses the standard low-order decomposition (first-order Doppler, gravitational redshift, SR transverse term). Higher-order cross-terms omitted.
Photon rate is informational only and is not rank-tested.
Each frequency term is rank-tested in Hz (ratio = |Δf|/tol_Hz); the fractional Δf/f and equivalent fractional tolerance tol_Hz/f₀ are shown alongside.

What this would need for public engineering surrogate use

Full ephemeris. Time-tagged JPL DE-series planetary state vectors for every relevant body, not a single static geometry.
Frame transformations. ICRF ↔ BCRS ↔ GCRS ↔ topocentric chain with the IAU 2006/2010 precession-nutation, polar motion, UT1-UTC, and station-displacement models.
Instrument models. Antenna phase centre, group delay, on-board oscillator behaviour, detector timing jitter, link-budget calibration.
Light-time iteration. Numerical iteration of the down-leg (and up-leg, where applicable) light-time equation rather than instantaneous-geometry approximation.
Mission calibration. Spacecraft-specific calibration tables, range bias, clock-offset fits, and post-fit residual treatment.
Multi-body Shapiro. Summed weak-field delays from Sun, Jupiter, Saturn, Earth, Moon, and any nearby bodies — not a single-body PPN form.
Plasma / atmospheric corrections. Solar-corona, ionospheric, and tropospheric path-delay models (e.g. dual-frequency calibration, ZTD mapping functions).

Warnings

Simplified single-body, single-point geometry. Per-term calculators in other pages (Shapiro, Sagnac, Light deflection, Frequency shift, Optical link) give more rigorous treatments — use those for any number you intend to publish or fly.
If $r_1 + r_2 - R \le 0$ the Shapiro denominator goes singular; the ranker reports NaN and a warning instead of a spurious value.
For photon paths close to the body ($r_{\min} \lesssim$ a few body radii), the weak-field expansion degrades; treat all gravity terms as order-of-magnitude only.
Tolerance thresholds (watchFrac / keepFrac) are engineering policy, not physics. Defaults 1 % / 10 % are reasonable; set your own.
Public engineering surrogate. Not affiliated with NASA / JPL. Not a substitute for public engineering surrogate pipelines (full multi-body relativistic ephemeris, frame transformations, instrument-specific corrections).

Certificate

Inputs, tolerances, every computed term, and the ranked decisions are exported with a SHA-256 hash of the canonical content.