On the MOND External Field Effect in the Solar System

In the framework of the MOdified Newtonian Dynamics (MOND), the internal dynamics of a gravitating system s embedded in a larger one S is affected by the external background field E of S even if it is constant and uniform, thus implying a violation of the Strong Equivalence Principle: it is the so-called External Field Effect (EFE). In the case of the solar system, E would be A_cen\approx 10^-10 m s^-2 because of its motion through the Milky Way: it is orders of magnitude smaller than the main Newtonian monopole terms for the planets. We address here the following questions in a purely phenomenological manner: are the Sun’s planets affected by an EFE as large as 10^-10 m s^-2? Can it be assumed that its effect is negligible for them because of its relatively small size? Does $\bds E$ induce vanishing net orbital effects because of its constancy over typical solar system’s planetary orbital periods? It turns out that a constant and uniform acceleration, treated perturbatively, does induce non-vanishing long-period orbital effects on the longitude of the pericenter of a test particle. In the case of the inner planets of the solar system and with E\approx 10^-10 m s^-2, they are 4-6 orders of magnitude larger than the present-day upper bounds on the non-standard perihelion precessions recently obtained with by E.V. Pitjeva with the EPM ephemerides in the Solar System Barycentric frame. The upper limits on the components of E are E_x <= 1 x 10^-15 m s^-2, E_y <= 2 x 10^-16 m s^-2, E_z <= 3 x 10^-14 m s^-2. This result is in agreement with the violation of the Strong Equivalence Principle by MOND.

💡 Research Summary

The paper investigates whether the External Field Effect (EFE) predicted by Modified Newtonian Dynamics (MOND) can produce observable signatures in the orbital motions of the Solar System planets. In MOND, a system embedded in a larger gravitating structure feels a modification of its internal dynamics due to the external gravitational field of the host, even when that field is uniform and constant. This phenomenon violates the Strong Equivalence Principle (SEP) and is one of the few experimentally testable consequences of MOND.

The authors focus on the Milky Way’s centrifugal acceleration acting on the Solar System, A_cen ≈ 10⁻¹⁰ m s⁻², which is many orders of magnitude smaller than the Newtonian monopole acceleration experienced by the planets (e.g., ≈6 × 10⁻³ m s⁻² for Earth). Nevertheless, within the MOND framework a constant external acceleration E can induce secular perturbations in the Keplerian orbital elements. By treating E as a small perturbing acceleration, the authors derive the long‑period rates of change of the orbital elements using standard Lagrange planetary equations. The most relevant result is a non‑zero secular precession of the longitude of perihelion (ω):

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