Exact semianalytical calculation of rotation curves with
  Bekenstein-Milgrom nonrelativistic MOND
  Astronomers use to derive MOdified Newtonian Dynamics (MOND) rotation curves
using the simple algebraic rule of calculating the acceleration as equal to the
Newtonian acceleration ($a$) divided by some factor $\mu (a)$. However, there
are velocity differences between this simple rule and the calculation derived
from more sophisticated MOND versions such as AQUAL or QMOND, created to expand
MOND heuristic law and preserve the conservation of momentum, angular momentum,
and energy, and follow the weak equivalence principle. Here we provide recipes
based on Milgrom's proposal to calculate semianalytically (without numerical
simulations) MOND rotation curves for any density distribution based on AQUAL,
applying it to different models of thin disks. The application of this
formalism is equivalent to the creation of a fictitious phantom mass whose
field may be used in a Newtonian way to calculate iteratively the MOND
accelerations. In most cases, the differences between the application of the
simple algebraic rule and the AQUAL-MOND calculations are small, $\lesssim 5$%.
However, the error of the algebraic solution is larger than 5% when more than
half of the mass is in the MONDian regime (where Newtonian and MOND rotation
speeds differ by more than 10%), reaching in some cases $>70$% discrepance,
such as in Maclaurin disks, representative of galaxies for which the rotational
velocity rises to the edge of the disk as is seen in irregular galaxies. The
slope of the rotation speed in the dependence with the radius or the vertical
distance of the plane is also significantly changed.
