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We discuss a novel MOND effect that entails a correction to the dynamics of isolated mass systems even when they are deep in the Newtonian regime: systems whose extent  R  ≪  r  M , where  r  M  ≡ ( GM  t / a  0 ) 1/2  is the MOND radius and  M  t  is the total mass. Interestingly, even if the MOND equations approach Newtonian dynamics arbitrarily fast at high accelerations, this correction decreases only as a power of  R / r  M . The effect appears in formulations of MOND as modified gravity, governed by generalizations of the Poisson equation. The MOND correction to the potential is a quadrupole fieldϕ  a   ≈  G    Q  ̂    i  jr  i    r  j    , where   r   is the radius from the centre of mass. In quasilinear MOND (QUMOND),Q  ̂    i  j    =  −  α   Q   i  jr   M    −  5, where  Q   ij   is the quadrupole moment of the system and α &gt; 0 is a numerical factor that depends on the interpolating function. For example, the correction to the Newtonian force between two masses,  m  and  M , a distance ℓ apart (ℓ ≪  r  M ) isF  a   =  2  α    (  ℓ  /   r  M   )   3(  m  M  )   2    M   t    −  3a  0(attractive). Its strength relative to the Newtonian force is    2  α   (  m  M  /   M   t   2   )(   a  0   /   g  N   )    5  /  2( g  N  ≡  GM  t /ℓ 2 ). For generic MOND theories, which approach Newtonian dynamics quickly for accelerations beyond  a  0 , the predicted strength of the effect in the Solar system is rather much below present testing capabilities. In MOND theories that become Newtonian only beyond κ a  0 , the effect is enhanced by κ 2 .

A novel MOND effect in isolated high‐acceleration systems