Negligible MOND effects on the orbits of planets

Abstract First proposed in 1983, modified newtonian dynamics (MOND) provides an alternative picture to dark matter theory. However, recently, there have been several reports that MOND is inconsistent with, or at least difficult to reconcile with, the orbits of planets in the Solar System. As with all the other studies so far, they assumed that the planetary accelerations can be computed without considering their own gravity (i.e. their self-gravity). Nonetheless, we demonstrate that, according to the original MOND theory, instead of its variants, each planet essentially follows a Newtonian orbit when its self-gravity is taken into account; the relative increase in gravitational acceleration due to MOND is at most 3 × 10 −11 for Mercury, which has the highest relative increase among planets, while the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> value has a relative error of approximately 6 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> 10 −11 , rendering the deviation from the Newtonian orbit undetectable with today’s technology. It is in stark contrast to the two major variants of MOND, namely AQUAL and MOND, where it has been proven that self-gravity can be ignored in a suitable limit when determining the MOND acceleration, which significantly deviates from the Newtonian acceleration. Consequently, attempting to constrain or falsify MOND through the analysis of planetary orbits becomes largely meaningless if the original MOND theory, rather than AQUAL or QUMOND, is valid. As a result, it is unjustified to argue that MOND is incorrect due to the observed lack of its influence on the orbits of planets, unless one of the variants of MOND theory, instead of the original one, is correct.