A Meta-Analysis Review Of How Consistently Modified Newtonian Dynamics (MOND) Explains The Rotation Curves Of Galaxies Across Different Types And Mass Ranges

Author: Ahmed Mohamed

Abstract

Modified Newtonian Dynamics (MOND) is a theory that tries to explain galaxy rotation curves without dark matter. MOND works for some galaxies, but it’s unknown if it can explain all types of galaxies with different masses. This study reviews four scientific papers that test MOND calculations to the rotation curves of different galaxies. These include gas-rich galaxies, small spiral galaxies, dwarf galaxies around Andromeda, and galaxies that follow the Universal Rotation Curve. The data from Lelli et al. (2016) were used to calculate how much MOND’s predictions match real observations. The results show that MOND gives the best results in bright and massive galaxies, with an error of 4.95%. However, it fails in low-mass and gas-rich galaxies, where the average error is higher (31.59%). This study helps evaluate where MOND is correct and where it is wrong and fails in different galaxy types and masses.

Keywords: Modified Newtonian Dynamics (MOND), Galaxy rotation curves, Dark matter alternative, Low acceleration gravity, Galaxy kinematics, Meta-analysis High surface brightness galaxies (HSB), Low surface brightness galaxies (LSB)

Introduction

The study of how galaxies rotate has helped scientists learn more about spreading of mass in different galaxies. One of the biggest discoveries in this area is that stars near the edges of galaxies move faster than expected. According to Newton’s laws, these outer stars should move more slowly, like how the planets in our solar system work — the closer the planet to the sun, the faster it rotates. But in galaxies, stars on the edges have high speeds, almost the same as those at the center. This made the scientists puzzled and created a problem because the visible matter (stars and gas) does not provide enough gravity to hold those stars in their place.

To explain this problem, scientists postulated that galaxies contain something we can’t see called dark matter. This dark matter doesn’t interact with normal matter, but it adds extra gravity. Furthermore, in modern theories, dark matter is the component that has the most mass in the universe.

However, not everyone believes in the idea of dark matter. In the 1980s, a new theory called Modified Newtonian Dynamics (MOND) [1] was proposed. MOND suggests that Newton’s laws don’t work the same way when acceleration is very small, in our case at the edges of galaxies. Instead of adding dark matter, MOND modified how gravity works at low accelerations. [1] With this change, MOND could potentially explain galaxy rotation without needing dark matter. Still, MOND is not perfect. Studies show that MOND works very well in some galaxies, but fails in others.

In this research, a meta-analysis of four scientific papers has been performed that tested how well MOND works in different types of galaxies. These include small spiral galaxies, galaxies with lots of gas, and dwarf galaxies that orbit Andromeda. I compared the predictions made by MOND with actual observations of how fast stars move in these galaxies. The goal of this study is to understand when MOND gives good results and when it does not.

Literature Review

Galaxies rotate in a way that cannot be explained with high accuracy by Newton’s laws of motion and gravity if we only consider visible matter. According to classical physics, stars at the edges of galaxies should move more slowly than they do. To explain this situation, many scientists postulate the presence of something that holds these stars during its high speed-movements - dark matter, an unknown type of matter that adds extra mass and hence increases the force of gravitation.

However, an alternative theory called Modified Newtonian Dynamics (MOND) suggests that Newton’s laws need to be modified when acceleration is very low. Instead of adding dark matter, MOND changes the way gravity works in such weak conditions. The representation of MOND mathematically is [2]:

This review looks at four research papers that tested how well MOND works for different types of galaxies.

2.1 Slowly Rotating Gas-Rich Galaxies in MOND [3]

This paper was about gas-rich galaxies with a small number of stars. Because gas is easier to measure and model, they are good tests for MOND. The results show that MOND works well; but in some galaxies - especially in the outer parts - slight inaccuracies arise. This could be due to errors in the gas measurements or other effects like outside forces.

2.2 MOND Rotation Curves of Very Low-Mass Spiral Galaxies [4]

This paper focuses on small spiral galaxies that have very low mass. In such galaxies, the acceleration is low enough for MOND to be most effective. The study found that MOND gives good results for most of them. Some errors appear in galaxies with properties that make measurements harder like irregular shapes or inclination. Still, MOND performs better than regular Newtonian gravity without dark matter.

2.3 Andromeda Dwarfs Considering MOND [1,5]

This tests MOND on dwarf galaxies that orbit the Andromeda Galaxy. These galaxies are affected by the gravity of Andromeda, which makes them a harder test case. MOND works good for some of them but fails for others, especially those with very weak gravity. Furthermore, MOND cannot always work in environments with strong external forces like tidal forces.

2.4 Newtonian Explanation with Baryonic Matter Only [2,6]

This study uses only visible matter and Newton’s laws, no MOND and no dark matter. While this approach can explain some galaxies with strong central mass, it fails for faint and low-mass galaxies. In these galaxies, visible matter alone is not enough to explain the rotation curves. This supports the idea that we need either extra mass (like dark matter) or a new theory like MOND.

Methods

Data Sources and Searches

A meta-analysis review of galaxy kinematics data was conducted using the dataset from Lelli, McGaugh, & Schombert (2016). [7] The study has been published in The Astronomical Journal and contains different rotation curve measurements for a variety of galaxies, which includes high surface brightness (HSB), low surface brightness (LSB), and dwarf systems. The paper provided:

●        Galaxy names and morphological classifications,

●        Observed outer rotation velocities,

●        MOND-predicted velocities,

●        Surface brightness and baryonic parameters.

Additional information was gathered by manually examining figures, and tabulated data within the same source. No additional external sources were used.

Study Selection

All galaxies listed in the main tables of the Lelli et al. (2016) paper were eligible, provided they had complete entries for:

● Observed outer rotational velocity (V_obs)

●  MOND-predicted velocity (V_mond​)

●  Morphological type and surface brightness classification.

Data Extraction

Extracting data from the published tables and figures. The following parameters were found in the Lelli et al. (2016) paper:

● Galaxy name,

●   Morphological type,

●   Surface brightness classification (HSB or LSB),

●   Observed outer rotation velocity,

●   MOND-predicted circular velocity,

●   Calculated percentage error between MOND and observation:

Error (%) = (V_mond - V_obs)/V_obs × 100

Categorization

Galaxies were divided into three groups:

● High Surface Brightness (HSB) Galaxies

●   Low Surface Brightness (LSB) Galaxies

●   Low-Mass and Gas-Rich Galaxies

Each group was analyzed to determine the accuracy of MOND’s predictions in different types and masses of galaxies.

Data Analysis

Data were analyzed using descriptive statistics to evaluate the accuracy of Modified Newtonian Dynamics (MOND) in predicting the outer rotation curves of galaxies across different types and mass ranges. Percentage errors between observed and MOND-predicted velocities were calculated for each galaxy individually.

All calculations and data tabulation were performed using Microsoft Excel 2024. Galaxy classification and data values were sourced exclusively from Lelli et al. (2016).

Results

A total of 29 galaxies were analyzed based on the inclusion criteria. These galaxies were grouped into three special categories:

● 13 High Surface Brightness (HSB) Galaxies

● 9 Low Surface Brightness (LSB) Galaxies

●   7 Low-Mass and Gas-Rich Galaxies

MOND Accuracy Across Galaxy Types

High Surface Brightness (HSB) Galaxies

Table 1 and graph 1 summarize the MOND-predicted and observed velocities with the calculated error for HSB galaxies. MOND showed high agreement in this group, with an average error of 4.95%. In several cases like (e.g., UGC 6973, NGC 4217), the error was less than 1%, which shows performance.

Low Surface Brightness (LSB) Galaxies

Table 2 lists LSB galaxies. Graph 2 summarizes the MOND-predicted and observed velocities. MOND predictions were less accurate in this group, with average errors of 26.66%.

Low-Mass and Gas-Rich Galaxies

Table 3 presents the results for low-mass and gas-rich galaxies.  Graph 3 summarizes the MOND-predicted and observed velocities. This group showed the highest prediction errors, with an average of 31.59%. Galaxies like DDO 168 and NGC 3109 showed particularly large disagreement between predicted and observed velocities.

Discussion

Over the past few decades, much effort has been made to understand the difference between observed galactic rotation curves and predictions based on Newtonian dynamics using visible (baryonic) matter. This difference has been attributed to the presence of cold dark matter. However, Modified Newtonian Dynamics (MOND) offers an alternative explanation that modifies the laws of gravity at low accelerations instead of supposing the presence of dark matter.

This systematic review compared four peer-reviewed studies that applied MOND to various galaxy types and mass ranges, including low-mass spirals, dwarf galaxies orbiting Andromeda, and comparisons to the Universal Rotation Curve (URC). The goal was to know exactly where MOND performs well and where it fails, using error calculations based on data from Lelli et al. (2016).

The overall results indicate that MOND provides a reasonable fit to rotation curves in many high surface brightness (HSB) and more massive galaxies, where the observed accelerations approach or exceed the characteristic MOND scale​. Table 1 in our analysis shows that HSB galaxies had the lowest average prediction error (~4.95%), supporting the idea that MOND does well with data in these regimes.

However, the theory performed significantly worse in low-mass and gas-rich galaxies. As shown in Table 3, this group shows the highest prediction errors, with an average of 31.59%, in galaxies such as DDO 168 and NGC 3109 they show disagreement between observed and MOND-predicted velocities. These results are in contrast with theoretical expectations, as MOND is supposed to perform better in the low-acceleration regime. This discrepancy suggests that other factors such as external gravitational fields, mass-modeling uncertainties have strong effects and MOND can struggle if the galaxy is not in dynamical equilibrium (which is common in such galaxies) or due to measurement errors too.

The performance of MOND in dwarf galaxies, particularly those orbiting Andromeda, was mixed. In some cases, MOND calculated the velocity well, but in others, it failed because of environmental effects, like tidal forces or the external field effect (EFE).

On the other hand, Newton’s laws using only visible matter (like stars and gas) don’t work well at all. As shown in the fourth paper, these models fail to explain how galaxies rotate, particularly in galaxies with low mass and gas rich. These models don’t get correct values because they need something more - like dark matter or modified gravity.

Our results show that MOND has a high accuracy in some cases, particularly in bright galaxies where we know the matter inside. But MOND doesn't work well in gas-rich or small galaxies. MOND can explain some types of galaxies, but it doesn’t give accurate measurements in all types.

It is important to have more accurate data when we study gravity and galaxy rotation. Research in the future should study how the environmental factors affect the measurements of galaxies and improve how we measure the stars and gas inside them.

Conclusion

In this study we found that MOND does not always predict galaxy rotation curves in all types of galaxies and masses. After reviewing four scientific papers and using real data to calculate errors, we found that MOND works well in bright and massive galaxies with low average errors. But it doesn’t perform well in small and gas-rich galaxies, where the errors were high. This means that scientists should keep testing MOND in many different types and masses of galaxies to see where it works best and where it fails, to increase the collected data. Future studies should explore why there are different results for different galaxies based on MOND. This will help in understanding how different galaxies move and act. These studies will also help determine whether MOND can be a good alternative for dark matter.

References

[1] Kazmierczak, J., & Team, N. U. W. (2025, May 2). Dark Matter - NASA Science. NASA Science. https://science.nasa.gov/dark-matter/

[2] Mannheim, P. (2005). Alternatives To Dark Matter And Dark Energy. Progress in Particle and Nuclear Physics, 56(2), 340–445. https://doi.org/10.1016/j.ppnp.2005.08.001

[3] Sánchez-Salcedo, F. J., Hidalgo-Gámez, A. M., & Martínez-García, E. E. (2013). Slowly Rotating Gas-Rich Galaxies In Modified Newtonian Dynamics (MOND). The Astronomical Journal, 145(3), 61. https://doi.org/10.1088/0004-6256/145/3/61

[4] Milgrom, M., & Sanders, R. H. (2007). Modified Newtonian Dynamics Rotation Curves Of Very Low Mass Spiral Galaxies. The Astrophysical Journal, 658(1), L17–L20. https://doi.org/10.1086/513695

[5] McGaugh, S., & Milgrom, M. (2013). Andromeda Dwarfs In Light Of Modified Newtonian Dynamics. The Astrophysical Journal, 766(1), 22. https://doi.org/10.1088/0004-637x/766/1/22

[6] Pavlovich, K., Sipols, A., & Pavlovich, A. (2014). Newtonian Explanation Of Galaxy Rotation Curves Based On Distribution Of Baryonic Matter. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1406.2401

[7] Lelli, F., McGaugh, S. S., & Schombert, J. M. (2016). SPARC: Mass Models For 175 Disk Galaxies With Spitzer Photometry And Accurate Rotation Curves. The Astronomical Journal, 152(6), 157. https://doi.org/10.3847/0004-6256/152/6/157

[8] Gentile, G., Famaey, B., & De Blok, W. J. G. (2010). THINGS About MOND. Astronomy and Astrophysics, 527, A76. https://doi.org/10.1051/0004-6361/201015283