Numerical solutions of the complete two-body system in QUMOND
arXiv:2509.01493 · doi:10.1051/0004-6361/202555656
Abstract
Due to the non-linearity of the QUMOND field equations, in the modelling of binaries so far the two-body system is replaced by an effective one-body system, where the central particle contains the total mass of both binary components and is orbited by a massless test particle. In this work, the discrepancy between the effective one-body treatment and the complete two-body solution in QUMOND is quantified. Particles are treated as limits of Dirac sequences. Then, the QUMOND contribution to the total kinematical acceleration of a particle is expressed as a Green's integral which is calculated numerically. In the non-linear transition regime the kinematical acceleration of the effective one-body system with a total mass of 2 Msun is up to a factor of 1.44 higher than the Newtonian acceleration, whereas the acceleration is only boosted by a factor of 1.2--1.3 in the two-body system in the case of the simple transition function.
arXiv commentaccepted for publication in A&A
References in corpus (26)
- The mass distribution and gravitational potential of the Milky Way
- The Baryonic Tully-Fisher Relation
- Modified Newtonian Dynamics in the Milky Way
- Quasi-linear formulation of MOND
- Constraints on MOND theory from radio tracking data of the Cassini spacecraft
- Milky Way Mass Models and MOND
- Combined Solar System and rotation curve constraints on MOND
- Wide binaries as a critical test of Classical Gravity
- External field effect of modified Newtonian dynamics in the Solar system
- Modified-dynamics predictions agree with ovservations of the HI kinematics in faint dwarf galaxies contrary to the conclusions of Lo Sargent and Young
- Breakdown of the Newton-Einstein Standard Gravity at Low Acceleration in Internal Dynamics of Wide Binary Stars
- Strong constraints on the gravitational law from DR3 wide binaries
- Asymmetrical tidal tails of open star clusters: stars crossing their cluster's prah challenge Newtonian gravitation
- Internal kinematics of GAIA DR3 wide binaries: anomalous behaviour in the low acceleration regime
- Challenging a Newtonian prediction through Gaia wide binaries
- Wide Binaries from GAIA EDR3: preference for GR over MOND ?
- A tale of caution: the tails of NGC 752 are much longer than claimed
- Modified Kepler's Law, Escape Speed and Two-body Problem in MOND-like Theories
- General virial theorem for modified-gravity MOND
- Open star clusters and their asymmetrical tidal tails
- On the degree of stochastic asymmetry in the tidal tails of star clusters
- Sedna and the cloud of comets surrounding the Solar System in Milgromian dynamics
- Towards an explanation of orbits in the extreme trans-Neptunian region: The effect of Milgromian dynamics
- Influence of selection criteria on the interpretation of rotational behaviour of wide-binary star systems
- Asymmetry of the tidal tails of open star clusters in direct N-body integrations in Milgrom-law dynamics
- Central MONDian spike in spherically symmetric systems