Light Deflection / Pointing Correction Calculator

First-order PPN angular deflection $\alpha = (1+\gamma)\,2GM/(c^2 b)$ of a light ray passing a massive body at impact parameter $b$.

📊 Sample calculation — Solar-limb deflection: lab agrees with Eddington (1919) within stated tolerance — canonical first-order GR solar-limb value 1.7505″ to 0.04 %

Inputs

Central body

Impact-parameter units

Impact parameter $b$ Default = 1.0 body-radii → solar-limb case when body is Sun.

PPN $\gamma$ GR = 1. Cassini bound: $\gamma - 1 = (2.1 \pm 2.3)\times10^{-5}$.

Pointing tolerance (µrad) Above tolerance → KEEP. Below 1% → IGNORE.

Result

Deflection

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Deflection (arcsec)

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Deflection (mas)

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Tolerance

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Formula registry entry — light_deflection_ppn_v1

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Breakdown

Body: —

$GM$: — m³/s²

Impact parameter $b$: —

$\alpha_{\rm GR}$ ($\gamma=1$): —

$d\alpha/d\gamma$ sensitivity: —

Reference (solar-limb, $\gamma=1$): $\alpha_\odot = 4GM_\odot/(c^2 R_\odot) \approx 1.7505\,\text{arcsec}$

Formula

First-order PPN light deflection $$\alpha \;=\; (1+\gamma)\,\frac{2GM}{c^2 b}$$ General relativity ($\gamma=1$) $$\alpha_{\rm GR} \;=\; \frac{4GM}{c^2\,b}$$

Assumptions

First-order PPN (post-Newtonian) weak-field expansion.
Static, spherically symmetric body; no oblateness ($J_2$), no spin, no internal-structure terms.
Photon trajectory approximated as a straight line at impact parameter $b$ (test-particle null geodesic at leading order).
$b > R_{\rm body}$ (photon clears the body's surface). For $b \le R_{\rm body}$ the path would intersect the body.
Observer and source effectively at infinity; finite-distance corrections of order $b/r$ are neglected.

What this would need for mission-grade use

Show requirements

Full PPN higher-order terms (beyond first-order $(1+\gamma)\,2GM/(c^2 b)$)
Frame-dragging (Kerr / Lense-Thirring)
Solar oblateness $J_2$
Finite-distance corrections (observer / source not at infinity)
Plasma / coronal refraction (radio wavelengths)
Full VLBI calibration pipeline (clock offsets, troposphere, ionosphere, instrumental delays)

Warnings

First-order PPN only. Higher-order $(GM/c^2 b)^2$ terms, frame-dragging (Kerr), and finite-size / oblateness contributions are not included.
If $b \le R_{\rm body}$, the photon path passes through the body, which is physically impossible; the calculator flags this case.
Solar-corona plasma refraction can dominate over GR deflection for grazing solar limbs at radio wavelengths; this calculator returns the GR term only.

Source notes

Formula: standard first-order PPN deflection; see Will, Theory and Experiment in Gravitational Physics, §6 (2018 ed.).
Canonical first-order GR solar-limb value $\alpha_\odot \approx 1.7505$ arcsec (Eddington 1919; modern VLBI/Gaia constrain PPN $\gamma$ to sub-mas precision).
Constants from CODATA / IAU; full table on the Validation page.

Certificate

Each computed result can be exported as a JSON or Markdown certificate. Certificate v2 splits the deterministic result_hash (same inputs + version + constants + formulas → same hash) from a timestamped receipt_hash (unique per export).