= Solution
The three classic tests probe orbital motion, the propagation of <light>, and clock rates in a <gravitational field>.
\b[<Schwarzschild perihelion precession>.] For an orbit with <semi-major axis> $a$ and <orbital eccentricity> $e$, the leading advance per revolution is
$$
\boxed{\Delta\varpi=\frac{6\pi GM}{a(1-e^2)c^2}.}
$$
The relevant observation for <Mercury (planet)> is the residual advance after the much larger ordinary perturbations have been included, approximately $43$ arcseconds per century.https://ntrs.nasa.gov/api/citations/19870009701/downloads/19870009701.pdf[Physics through the 1990s: Gravitation, cosmology and cosmic-ray physics, 1986: discussion of the anomalous perihelion advance]{ref} An orbital fit must account for the other planets and reference-frame effects before interpreting that residual as a relativistic contribution.
\b[<Schwarzschild light deflection>.] A ray with large <impact parameter> $b$ passing a nearly spherical mass is deflected through
$$
\boxed{\alpha\simeq\frac{4GM}{bc^2}.}
$$
At the <Sun>'s limb this is about $1.75$ arcseconds. The <Eddington experiment> used the 1919 <solar eclipse> to photograph background <stars> near the obscured <Sun>, then compared their positions with reference photographs. The measured effect is an apparent outward displacement of the background <stars>, not a direct photograph of a curved light path. Telescope focus, plate scale and atmospheric effects must be controlled when extracting such small shifts.<A determination of the deflection of light by the Sun's gravitational field by Frank Watson Dyson and others>[1920 paper, observational comparison and deflection analysis]{ref}
\b[<Gravitational redshift>.] For a photon emitted lower in a weak static field and received a height $H$ above it,
$$
\boxed{\frac{\nu_{\rm rec}-\nu_{\rm em}}{\nu_{\rm em}}\simeq-\frac{gH}{c^2}.}
$$
The <Pound-Rebka experiment> used the narrow recoil-free nuclear resonance supplied by the <Mössbauer effect>. A controlled source motion supplies a small <Doppler shift> that compensates the gravitational shift, allowing a change in resonant absorption to reveal it across a laboratory tower.<Apparent Weight of Photons by Robert Vivian Pound and Glen Rebka>[1960 experiment: gamma-ray source and resonant absorber at different heights]{ref} The leading weak-field redshift follows from the <equivalence principle> and therefore does not, by itself, distinguish every competing metric theory of gravity.
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