Mercury's total observed perihelion precession is about 5600 arcseconds per century. Most of this is explained by:
AGeneral relativistic effects from the Sun's curvature of spacetime
BGravitational perturbations from other planets, primarily Venus, Jupiter, and Earth
CThe oblateness (non-spherical shape) of the Sun
DTidal interactions between Mercury and the Sun
The vast majority of Mercury's perihelion precession — about 5557 arcseconds per century — is due to Newtonian gravitational perturbations from other planets. The remaining 42.98 arcseconds per century is the anomalous precession that could not be explained by any Newtonian effect. This is the piece that GR explains. The solar oblateness contributes about 0.03 arcseconds per century — far too small to account for the anomaly. The GR effect, while tiny compared to the planetary perturbations, was measured with sufficient precision to constitute a definitive test.
Question 2 True / False
The GR perihelion precession formula Δφ = 6πGM/(a(1-e²)c²) predicts that the effect is largest for orbits that are close to the central mass and highly eccentric.
TTrue
FFalse
Answer: True
The precession scales as 1/(a(1-e²)), so it increases for smaller semi-major axis a (closer orbits) and larger eccentricity e. Mercury is the best candidate in our solar system because it has the smallest a and the largest e among the inner planets. The factor a(1-e²) is the semi-latus rectum, which is the radius of the orbit at the endpoints of the semi-minor axis — equivalently, it sets the scale of the closest approach distance. Closer approaches mean stronger relativistic corrections.
Question 3 Short Answer
Explain why Newtonian gravity predicts closed elliptical orbits while GR predicts precessing orbits, in terms of the effective potential.
Think about your answer, then reveal below.
Model answer: In Newtonian gravity, the effective potential for a test particle has the form V_eff = -GM/r + L²/(2mr²), where L is the angular momentum. This potential yields closed elliptical orbits — the orbit equation is exactly periodic. In GR, the Schwarzschild effective potential acquires an additional attractive term proportional to -GML²/(mr³c²), which is negligible at large r but becomes significant near the central mass. This extra term slightly deepens the potential near pericenter, causing the particle to spend slightly more angular distance per radial oscillation than the 2π required for a closed orbit. The orbit is nearly elliptical but rotates slowly — the perihelion advances by a small angle each orbit.
The extra -1/r³ term in the effective potential is the relativistic correction that breaks the exact periodicity of Keplerian orbits. It arises from the spatial curvature terms in the Schwarzschild metric and can be derived by solving the geodesic equation with the Schwarzschild effective potential.
Question 4 Short Answer
Modern measurements of perihelion precession extend beyond Mercury. Which binary pulsar system provided the most precise test of this effect?
Think about your answer, then reveal below.
Model answer: The Hulse-Taylor binary pulsar PSR B1913+16 (discovered 1974) and later the double pulsar PSR J0737-3039 provide the most precise tests. In these systems, two neutron stars orbit each other in tight, highly eccentric orbits where GR effects are enormously amplified relative to the solar system. The periastron advance of PSR B1913+16 is about 4.2 degrees per year — over 35,000 times Mercury's rate — and agrees with the GR prediction to better than 0.2%. The double pulsar PSR J0737-3039 achieves even better precision and tests multiple relativistic effects simultaneously.
Binary pulsars are extraordinary GR laboratories because the gravitational fields are much stronger than in the solar system (the surface gravity of a neutron star is about 10¹¹ times Earth's). The precession rate scales with the strength of the gravitational field, making the effect dramatically more prominent and precisely measurable.