Milgrom (1983a) showed that this theory of gravitation could explain the advance of Mercury's perihelion, first interpreted by Leverier as due to Vulcano, hypothetical intramercurial planet, later "observed" by Lescarbault, and finally explained by General Relativity. Another interesting application concerns the distance of Oort's cometary cloud, as commented below. Milgrom (1983b) applied MOND to the problem of the vertical distribution of stars in relation to the velocity dispersion.
Of course, MOND was successful when applied to galaxies, as it was originally intended to explain rotation curves. It is not remarkable that MOND explains rotation curves, but what is really remarkable is that a very large variety of galaxies can be fitted under this hypothesis, with only one parameter, i.e. the M/L ratio of the bulge.
This task of fitting real data was undertaken by Begeman, Broeils and Sanders (1991) and later continued by Sanders (1996) and Sanders and Verheijen (1998). The method consists basically of obtaining by classical procedures and then considering equation (84) to fit the results. With the sole exception of NGC 2841, the results were very good, excellent in some cases, even better than the multiparameter fitting considering a dark matter halo. About 80 spiral galaxies with a large variety of luminosities and types were compatible with MOND.
The success was particularly interesting in the case of Low Surface Brightness galaxies. These galaxies can be considered to have a low surface density, too, in the absence of dark matter. Accelerations are therefore so low that the whole galaxy can be considered within the MOND regime. Milgrom (1983a, b, c) even deduced that positive slopes in the rotation curve could be expected, which was later confirmed by Casertano and van Gorkom (1991). These galaxies were studied by de Block and McGaugh (1998), who found reasonable and constant M/L ratios, when the use of classical Newtonian Dynamics provides M/L ratios ranging from 10 to 75 (van der Hulst et al., 1993).
As mentioned above, dwarf spheroidal galaxies are also interpreted as being characterized by very large M/L ratios, in the range 10-100 (Mateo, 1994; Vogt et al., 1995). Gerhard (1994) applied MOND to 7 dwarf spheroidals, without finding any agreement. This negative result was confirmed by Gerhard and Spergel (1992), finding unacceptable differences in the M/L ratios required, but Milgrom (1995) reanalyzed these 7 galaxies and obtained a reasonable agreement between MOND and the observations.
De Block and McGaugh (1998) studied 15 galaxies with low surface brightness, finding a low dispersion in the M/L ratios. Sanders and Verheijen (1998) carried out the analysis in the infrared K' band, where extinction and recent star formation effects do not alter the photometric profiles, and obtained values in good agreement with those predicted by MOND.
Rodrigo-Blanco and Pérez-Mercader (1998) have directly considered the modification of the Newtonian acceleration of gravity from the rotation curve of 9 galaxies, also without the need of dark matter.
Van den Bosch and Dalcanton (2000) compared the results obtained with semi-analytical models and with MOND. This search was undertaken because in their opinion "the dark matter scenario is certainly starting to lose its appealing character" due to the mix of baryons, CDM and HDM needed, as well as a non-zero cosmological constant; therefore, other alternatives should be seriously reconsidered. These authors found that both theories can explain rotation curves almost equally well, even if MOND needs a similar amount of fine-tuning.
Milgrom (1983c) also studied a large variety of systems with dark matter problems, such as binary galaxies, small clusters, rich clusters and in particular, Virgo. All these systems are characterized by low acceleration, and no great quantities of dark matter were required. The and White (1988) considered optical and x-ray observations to check MOND in Coma, finding that models without dark-matter are compatible. Sanders (1998) finds a non-negligible difference between the dynamic and the luminous mass, this ratio being about 2, less than that obtained by standard Newtonian Dynamics but far from unity. He attributes this discrepancy to the fact that accelerations in the innermost part of clusters are not much lower than a0 ( 0.5a0). If this application is correct, it could be due to the non-detection of considerable luminous matter at the centre of rich clusters.
Milgrom (1983a) also discussed the determination of mass in clusters by the gravitational lensing method. Qin, Wu and Zou (1995) concluded that no dark matter was needed under the MOND interpretation. The Faber-Jackson (1976) relation, L , where is the velocity dispersion in an elliptical galaxy, is also explained under Milgrom's hypothesis.
More recently, Milgrom (1997) has studied the filaments that characterize the large-scale structure of the Universe, comparing the M/L ratio obtained with that of Eisenstein, Loeb and Turner (1997) who found M/L 450h in solar units in a filament in the Perseus-Piscis supercluster, in contrast with that of Milgrom of only M/L 19, again requiring little or no dark matter.
a0, with a value of about 2 × 10-8cms-2, is very close to that of H0c of the order of 6.5 × 10-8cms-2, which suggests that MOND could have some implications in Cosmology. Milgrom (1983a, b) suggested that a0 could be connected with the cosmological constant. In any case, the matter contained in the Universe could be considerably less. Felten (1984) developed a MOND-Cosmology, proposing that the homogeneous and isotropic universe would not be possible for small scales. Sanders (1998) continued the discussion, finding another law for the growth of the cosmological scale factor. This cosmology also provides a suggestive scenario for the development of large scale structures.