Weber-Type Gravitational Force Laws and Perihelion Precession: Annotated Bibliography

Weber's electrodynamics—introducing velocity-dependent force laws—inspired a sustained research program from 1846 to the present applying such forces to gravitation and planetary perihelion precession. This bibliography documents over 80 publications spanning 19th-century foundational works, modern revisitations, critical analyses, and comparisons with General Relativity. The historical significance lies in Paul Gerber's 1898 derivation of Mercury's 43 arcsec/century perihelion advance—mathematically identical to Einstein's 1915 result—though from now-superseded theoretical foundations.

Part I: Foundational 19th-Century Works

Wilhelm Weber — Original Electrodynamics

Weber, Wilhelm. "Elektrodynamische Maassbestimmungen — Über ein allgemeines Grundgesetz der elektrischen Wirkung." Abhandlungen bei Begründung der Königlich Sächsischen Gesellschaft der Wissenschaften, Leipzig, 1846, pp. 211–378. Reprinted in Wilhelm Weber's Werke, Vol. 3, H. Weber (ed.), Springer, Berlin, 1893.

Weber's foundational paper introduced velocity-dependent force law for charged particles depending not only on distance but also on relative velocity and acceleration between charges. The force includes corrections of order 1/c², establishing a characteristic velocity related to the speed of light. This became the template for all subsequent applications to gravitation.

Carl Seegers — First Gravitational Application (1864)

Seegers, Carl. "De motu perturbationibusque planetarum secundum legem electrodynamicam Weberianam solem ambientium" (On the motion and perturbations of planets according to Weber's electrodynamic law around the Sun). Dissertation, Göttingen University, 1864. Republished by Kommissionsverlag von Friedr. Vieweg & Sohn, Braunschweig, 1924.

The first systematic application of Weber's electrodynamic law to gravitational phenomena. Seegers proposed examining planetary perihelion advance using Weber's mathematical form with 1/c² correction factors, introducing the "perturbation factor Ω" that appeared in later Tisserand-Gerber-Einstein formulas.

Gustav Holzmüller — Hamilton-Jacobi Method (1870)

Holzmüller, Gustav. "Ueber die Anwendung der Jacobi-Hamilton'schen Methode auf den Fall der Anziehung nach dem elektrodynamischen Gesetze von Weber." Zeitschrift für Mathematik und Physik, Vol. 15, 1870, pp. 69ff.

Applied Jacobi-Hamilton analytical mechanics to orbital motion under Weber-type gravitational forces. Postulated a "magnetic gravitational component" following Weber's law, providing important early mathematical formalism. Available: kirkmcd.princeton.edu/examples/GR/holzmuller_zmp_15_69_70.pdf

Félix Tisserand — Planetary Motion Studies (1872, 1890)

Tisserand, Félix. "Sur le mouvement des planètes autour du Soleil, d'après la loi électrodynamique de Weber." Comptes Rendus de l'Academie des Sciences de Paris, Vol. 75, 1872, pp. 760–763.

Tisserand, Félix. "Sur les mouvements des planètes, en supposant l'attraction représentée par l'une des lois électrodynamique de Gauss ou de Weber." Comptes Rendus de l'Academie des Sciences de Paris, Vol. 110, 1890, pp. 313–315.

Tisserand, Félix. Traité de Mécanique Céleste, Vol. 4, Chapter 28: "Vitesse de propagation de l'attraction." Gauthier-Villars, Paris, 1895.

Tisserand found that applying Weber's law to gravity produced secular perihelion advances of 6.28 arcsec/century for Mercury and 1.32 arcsec/century for Venus—approximately 1/6 of the observed anomaly. This established that Weber-type forces produce precession in the correct direction but with insufficient magnitude using the original Weber coefficients.

Wilhelm Scheibner — Perihelion Calculations (1873, 1897)

Scheibner, Wilhelm. Work on perihelion calculations using Weber's law, c. 1873. Result: 6.73 arcsec/century for Mercury.

Scheibner, Wilhelm. "Ueber die formale Bedeutung des Hamiltonschen Princips und das Weber'sche Gesetz." Berichte über die Verhandlung der königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Math.-Phys. Classe, Vol. 49, 1897, pp. 578–601.

Scheibner's calculations confirmed Tisserand's general magnitude while differing slightly in exact value. His later paper connected Hamilton's principle with Weber's force law.

Johann Karl Friedrich Zöllner — Electrodynamic Theory of Matter (1872–1882)

Zöllner, J.K.F. Über die Natur der Cometen: Beiträge zur Geschichte und Theorie der Erkenntnis. Engelmann, Leipzig, 1872 (3rd ed. 1883).

Zöllner, J.K.F. "Über die physikalischen Beziehungen zwischen hydrodynamischen und elektrodynamischen Erscheinungen." Annalen der Physik und Chemie, Vol. 158, 1876, pp. 497–539.

Zöllner, J.K.F. Principien einer elektrodynamischen Theorie der Materie. Wilhelm Engelmann, Leipzig, 1876.

Zöllner, J.K.F. Erklärung der universellen Gravitation aus den statischen Wirkungen der Elektrizität und die allgemeine Bedeutung des Weberschen Gesetzes. L. Staackmann, Leipzig, 1882.

Zöllner developed an ambitious program unifying gravitation with electricity based on Weber's electrodynamics, building on Mossotti's hypothesis that matter consists of equal positive and negative electrical charges with slightly unequal attractive/repulsive forces.

Maurice Lévy — Correct Perihelion Value (1890)

Lévy, Maurice. "Sur l'application des lois électrodynamiques au mouvement des planètes." Comptes Rendus de l'Academie des Sciences, Vol. 110, 1890, pp. 545–551.

Lévy succeeded in deriving the correct perihelion precession by combining Weber's and Riemann's laws, setting the speed of gravity equal to c. His theory represents a crucial step toward the correct formula before Gerber's more famous 1898 paper.

Paul Gerber — The Correct Formula (1898, 1902)

Gerber, Paul. "Die räumliche und zeitliche Ausbreitung der Gravitation." Zeitschrift für Mathematik und Physik II, Vol. 43, 1898, pp. 93–104.

Gerber, Paul. "Die Fortpflanzungsgeschwindigkeit der Gravitation." Programmabhandlung des städtischen Realgymnasiums zu Stargard i. Pomm., 1902. Reprinted: Annalen der Physik, Vol. 52 (357), Issue 4, 1917, pp. 415–444.

Gerber's famous paper derived a velocity-dependent gravitational potential yielding exactly 43 arcsec/century for Mercury—mathematically identical to Einstein's 1915 general relativistic result. His potential: V = (μ'/r)[1 + (2/c)(dr/dt) + (3/c²)(dr/dt)²]. However, the derivation was later shown to be logically flawed by Seeliger (1917), von Laue (1917), and others. Einstein stated: "Gerber's derivation is wrong through and through."

Bernhard Riemann — Retarded Potential Theory (1867)

Riemann, Bernhard. "Ein Beitrag zur Elektrodynamik." Annalen der Physik und Chemie, Vol. 131, 1867, pp. 237–243 (posthumously published; originally presented 1858).

Riemann proposed that electromagnetic (and potentially gravitational) interactions propagate with finite velocity using retarded potentials—a conceptual advance influencing subsequent finite-propagation-speed gravitational theories.

Carl Neumann — Electrodynamics and Retarded Potentials (1868–1874)

Neumann, Carl. Three major works on electrodynamics (1868, 1873, 1874) reformulating Weber's electrodynamics using retarded potentials.

Neumann addressed conceptual problems of action-at-a-distance, proposing that particles emit potentials propagating with finite velocity. His framework influenced later researchers including Gerber.

Samuel Oppenheim — Review Article (1895, 1920)

Oppenheim, Samuel. "Zur Frage nach der Fortpflanzungsgeschwindigkeit der Gravitation." J.-B. K.K. Akad. Gymn. (Wien), 1895.

Oppenheim, Samuel. "Kritik des Newtonschen Gravitationsgesetzes." Encyklopädie der Mathematischen Wissenschaften mit Einschluss Ihrer Anwendungen, Vol. 6.2.2, 1920, pp. 80–158.

Comprehensive surveys of velocity-dependent gravitational potential proposals including work by Laplace, Weber, Riemann, Neumann, Clausius, and Lorentz.

Jonathan Zenneck — Encyclopedia Article (1903)

Zenneck, Jonathan. "Gravitation." Encyklopädie der Mathematischen Wissenschaften mit Einschluss Ihrer Anwendungen, A. Sommerfeld (ed.), Vol. 5, Part 1, Chapter 2, 1903, pp. 25–67.

Standard reference reviewing gravitational theories including velocity-dependent approaches and the perihelion problem.

Part II: Modern Revisitations (1989–Present)

André Koch Torres Assis — Principal Works

Assis, A.K.T. "On Mach's Principle." Foundations of Physics Letters, Vol. 2, 1989, pp. 301–318.

First major modern paper applying Weber's force law to gravitation, deriving perihelion precession values consistent with GR within a strictly relational framework.

Assis, A.K.T. and Clemente, R.A. "Two-body problem for Weber-like interactions." International Journal of Theoretical Physics, Vol. 30, 1991, pp. 537–545. DOI: 10.1007/BF00672899

Analytical solution showing perihelion precession emerges naturally from Weber-type gravitational interactions in the two-body problem.

Assis, A.K.T. "Deriving gravitation from electromagnetism." Canadian Journal of Physics, Vol. 70, 1992, pp. 330–340. DOI: 10.1139/p92-054

Presents generalized Weber force law with fourth-order terms yielding attractive force between neutral dipoles interpretable as Newtonian gravitation.

Assis, A.K.T. and Clemente, R.A. "The ultimate speed implied by theories of Weber's type." International Journal of Theoretical Physics, Vol. 31, 1992, pp. 1063–1073.

Analysis of velocity limitations inherent in Weber-type theories.

Assis, A.K.T. "Weber's law and Mach's principle." In Mach's Principle: From Newton's Bucket to Quantum Gravity, J.B. Barbour and H. Pfister (eds.), Birkhäuser, Boston, 1995, pp. 159–171.

Discusses Mach's principle implementation with Weber's gravitational law, including analysis of Tisserand's historical perihelion work and Gerber's velocity-dependent potential.

Assis, A.K.T. and Graneau, P. "Nonlocal forces of inertia in cosmology." Foundations of Physics, Vol. 26, 1996, pp. 271–283.

Reviews inertia origin according to Mach's principle and Weber's gravitational law. The Mach-Weber theory explains Mercury's perihelion precession through nonlocal gravitational interactions.

Assis, A.K.T. "A Critical Analysis of Helmholtz's Argument against Weber's Electrodynamics" (with J.J. Caluzi). Foundations of Physics, Vol. 27, 1997, pp. 1445–1452. DOI: 10.1007/BF02551521

Defense of Weber's theory against Helmholtz's historical criticism regarding energy conservation.

Tajmar, M. and Assis, A.K.T. "Gravitational induction with Weber's force." Canadian Journal of Physics, Vol. 93, 2015, pp. 1571–1573. DOI: 10.1139/cjp-2015-0285

Shows frame-dragging (gravitational induction) effects analogous to GR can be derived from Weber's gravitational force.

Assis, A.K.T. and Tajmar, M. "Superconductivity with Weber's electrodynamics: the London moment and the Meissner effect." Annales de la Fondation Louis de Broglie, Vol. 42, 2017, pp. 307–350.

Models superconductivity using Weber's electrodynamics, reproducing London moment and Meissner effect.

Assis — Books on Weber Electrodynamics and Relational Mechanics

Assis, A.K.T. Weber's Electrodynamics. Kluwer Academic Publishers, Dordrecht, 1994. ISBN: 0792331370.

Comprehensive treatment of Weber's force law and applications including gravitational extensions.

Assis, A.K.T. Relational Mechanics. Apeiron, Montreal, 1999. ISBN: 978-0968368923.

New mechanics based on Weber's gravitational force implementing Mach's principle quantitatively.

Assis, A.K.T. Relational Mechanics and Implementation of Mach's Principle with Weber's Gravitational Force. Apeiron, Montreal, 2014. ISBN: 978-0992045630.

Expanded 562-page edition deriving perihelion precession consistent with observations; systematic comparison with Newton and Einstein.

S. Ragusa — Modified Weber Force (1992)

Ragusa, S. "Gravitation with a modified Weber force." Foundations of Physics Letters, Vol. 5, 1992, pp. 585–589. DOI: 10.1007/BF00665939

Shows how modified Weber force reproduces both Mercury's perihelion advance AND gravitational light deflection matching GR predictions.

Bunchaft and Carneiro — Conservation Laws Constraint (1997)

Bunchaft, F. and Carneiro, S. "Weber-like interactions and energy conservation." Foundations of Physics Letters, Vol. 10, 1997, pp. 393–401. DOI: 10.1007/BF02764109. arXiv: gr-qc/9708047

Critical finding: Proves Weber-like forces (k(r̂/r)(1 - μṙ² + γr̈r)) are conservative if and only if γ=2μ. Demonstrates that no conservative gravitational Weber-like force can simultaneously yield both Mercury's perihelion precession AND correct gravitational light deflection—a fundamental constraint on Weber gravity theories.

Oleg D. Jefimenko — Gravitation and Cogravitation

Jefimenko, O.D. Causality, Electromagnetic Induction, and Gravitation: A Different Approach to the Theory of Electromagnetic and Gravitational Fields, 2nd ed. Electret Scientific, Star City, 2000. ISBN: 0917406230

Jefimenko, O.D. Gravitation and Cogravitation: Developing Newton's Theory of Gravitation to its Physical and Mathematical Conclusion. Electret Scientific, Star City, 2006.

Develops retarded gravitational equations analogous to electromagnetic "Jefimenko equations," introducing "cogravitation" (gravitomagnetic field). Derives perihelion precession of 1/3 the GR value using this approach.

Thomas E. Phipps Jr. — Modernization Efforts

Phipps, T.E. Jr. "Toward modernization of Weber's force law." Physics Essays, Vol. 3, 1990, pp. 414–420.

Proposes modified Weber potential overcoming Helmholtz's objection and extending validity to higher velocities. The "Phipps potential" has been extensively analyzed as a way to modernize Weber electrodynamics.

J.P. Wesley — Weber Electrodynamics Series

Wesley, J.P. "Weber electrodynamics, Part I: General theory, steady current effects." Foundations of Physics Letters, Vol. 3, 1990, pp. 443–469. DOI: 10.1007/BF00665929

Wesley, J.P. "Weber electrodynamics, Part III: Mechanics, Gravitation." Foundations of Physics Letters, 1990.

Extends Weber action-at-a-distance theory to time-retarded fields and gravitational mechanics, predicting forces confirming experimental tests.

Peter Graneau — Experimental Work

Graneau, P. and Graneau, P.N. Newtonian Electrodynamics. World Scientific, 1996.

Graneau, P. Ampère-Neumann Electrodynamics of Metals. Hadronic Press, 1985.

Extensive experimental work on Ampère-Weber forces with papers in Nature (Vol. 295, 1982), Physics Letters A (Vol. 97, 1983), Journal of Applied Physics (Vol. 53, 1982), and IEEE Transactions on Magnetics (MAG-20, 1984).

Jaume Giné — Retarded Potential Analysis (2005–2008)

Giné, Jaume. "On the origin of the anomalous precession of Mercury's perihelion." Chaos, Solitons & Fractals, Vol. 38(4), 2008, pp. 1004–1010. arXiv: physics/0510086

Shows retarded potential at first order coincides with Gerber's potential and gives correct perihelion precession. Argues Weber force is an approximation of retarded potential.

Giné, Jaume. "On the Origin of the Deflection of Light." Chaos, Solitons & Fractals, Vol. 35(1), 2008, pp. 1–6.

Shows same retarded potential also gives correct gravitational light deflection.

Paul Marmet — Classical Mechanics Approach

Marmet, P. "Classical Description of the Advance of the Perihelion of Mercury." Physics Essays, Vol. 12, No. 3, 1999, pp. 468–487.

Uses classical mechanics with mass-energy conservation to obtain Einstein's perihelion equation, citing Gerber's Weber-influenced work.

Additional Modern Papers

Assis, A.K.T. and Clemente, R.A. "The influence of temperature on gravitation." Il Nuovo Cimento B, Vol. 108, 1993, pp. 713–716.

Uses Weber's gravitational law to predict weight increase with temperature—fractional change of G of one part in 10¹⁴ per degree.

Guala-Valverde, J. "Inertial Mass in Mach-Weber-Assis Theory." Apeiron, Vol. 6, 1999, pp. 202–204.

Guala-Valverde, J. and Assis, A.K.T. "Mass in relational mechanics." Apeiron, Vol. 7, 2000, pp. 131–132.

Mikhailov, V.F. "Influence of an electrostatic potential on electron mass." Annales de la Fondation Louis de Broglie, Vol. 24, 1999, p. 161.

Experimental paper claiming detection of Weber-predicted mass variation; later experiments (Junginger & Popovic, Canadian Journal of Physics, 2004) failed to replicate.

Assis, A.K.T. "On the absorption of gravity." Apeiron, Vol. 13, 1992, pp. 3–11.

Assis, A.K.T. "Gravitation as a fourth order electromagnetic effect." In Advanced Electromagnetism: Foundations, Theory and Applications, T.W. Barrett and D.M. Grimes (eds.), World Scientific, 1995, pp. 314–331.

Part III: ArXiv Preprints

gr-qc/9708047 — Bunchaft, F. and Carneiro, S. "Weber-like interactions and energy conservation." 1997. Fundamental constraint paper proving Weber-like gravity cannot be conservative while yielding both perihelion precession and light deflection.

1410.6509 — Ferraro, Rafael. "Relational mechanics as a gauge theory." 2014 (published Gen. Relativ. Gravit. 2016). Eliminates absolute space from mechanics by gauging translations and rotations; provides relational framework relevant to Weber-type theories.

physics/0510086 — Giné, Jaume. "On the origin of the anomalous precession of Mercury's perihelion." 2005. Retarded gravitational interactions explaining Mercury's perihelion anomaly—conceptually related to Weber approaches.

1206.6755 — Das, Santanu. "Mach Principle and a new theory of gravitation." 2012. Machian gravity theory discussing perihelion precession.

gr-qc/0511038 — Unzicker, Alexander. "Mach's Principle and a Variable Speed of Light." 2005. Links Sciama's hypothesis to electromagnetic origin of gravitation, showing agreement with perihelion precession.

1106.1568 — Wells, James D. "When Effective Theories Predict: The Inevitability of Mercury's Anomalous Perihelion Precession." 2011. Argues from effective theory perspective that anomalous perihelion was inevitable; views Gerber's effort as "an attempt at an effective theory of gravity beyond Newton."

1012.5438 — Lemmon, T.J. and Mondragon, A.R. "Kepler's Orbits and Special Relativity in Introductory Classical Mechanics." 2020. Confirms special relativity alone gives 1/3 of observed precession, different from GR's full prediction.

Part IV: Critical Analyses and Rebuttals

Seeliger and von Laue — Gerber Criticism (1917)

von Seeliger, Hugo. "Bemerkungen zu P. Gerbers Aufsatz: 'Die Fortpflanzungsgeschwindigkeit der Gravitation.'" Annalen der Physik, Vol. 53(9), 1917, pp. 31–32. DOI: 10.1002/andp.19173580904

Concluded Gerber's theory is inconsistent and his formula does not follow from his premises.

von Laue, Max. "Die Fortpflanzungsgeschwindigkeit der Gravitation. Bemerkungen zur gleichnamigen Abhandlung von P. Gerber." Annalen der Physik, Vol. 53(11), 1917, pp. 214–216. DOI: 10.1002/andp.19173581103

Demonstrated serious errors in Gerber's calculations, refuting claims that Gerber anticipated Einstein.

von Laue, Max. "Historisch-Kritisches über die Perihelbewegung des Merkur." Naturwissenschaften, Vol. 8(37), 1920, pp. 735–736. DOI: 10.1007/BF02449026

Einstein's Response (1920)

Einstein, Albert. "Über die antirelativitätstheoretische." Berliner Tageblatt, August 27, 1920.

Famous statement: "The experts are not only in agreement that Gerber's derivation is wrong through and through, but the formula cannot be obtained as a consequence of the main assumption made by Gerber."

N.T. Roseveare — Definitive Historical Study (1982)

Roseveare, N.T. Mercury's Perihelion from Le Verrier to Einstein. Oxford: Clarendon Press, 1982. ISBN: 0-19-858174-2.

Definitive historical treatment of the perihelion problem. Showed Gerber's theory conflicts with experience: light deflection prediction wrong by factor of 3/2, and with relativistic mass, perihelion prediction also fails.

P.C. Peters — Rebuttal of Alternative Derivations (1987, 1990)

Peters, P.C. "Comment on 'Mercury's precession according to special relativity.'" American Journal of Physics, Vol. 55, 1987, p. 757.

Critical rebuttal showing computational errors in Phipps's claims; correct result is 1/2 (not full) precession.

Peters, P.C. "Comment on 'Minimally relativistic Newtonian gravity.'" American Journal of Physics, Vol. 58, 1990, p. 188.

Rebuttal of Biswas's calculation claiming full precession from special relativity.

Kirk T. McDonald — Comprehensive Technical Note (2022–2023)

McDonald, Kirk T. "Special Relativity and the Precession of the Perihelion." Princeton University Technical Note, 2022–2023. Available: kirkmcd.princeton.edu/examples/perihelion.pdf

Extensive review covering the 1/6 factor controversy, tracing history from Lévy (1890) through Weber-inspired potentials to Gerber (1898). Documents predictions: special relativity alone gives 1/6 to 1/3 of observed precession depending on assumptions.

MDPI Review Article (2022)

Maher, S. et al. "Foundations of Electromagnetism: A Review of Wilhelm Weber's Electrodynamic Force Law." MDPI Foundations, Vol. 2(4), Article 65, 2022.

Comprehensive modern review covering Helmholtz's energy conservation criticism, negative mass behavior objection, and connections to gravity, cosmology, and quantum mechanics.

Q. Li — High Velocity Extensions (2022)

Li, Q. "Extending Weber's Electrodynamics to High Velocity Particles." Int. J. Magnetics Electromagnetism, Vol. 8, Article 040, 2022.

Addresses shortcomings including unsuitability for high-velocity particles and negative mass issue; proposes new Weber-like theory.

Yahalom — Weak-Field GR Analysis (2023)

Yahalom, M. "The Weak Field Approximation of General Relativity and the Problem of Precession of the Perihelion for Mercury." MDPI Symmetry, Vol. 15(1), Article 39, 2023.

Modern approach solving Mercury trajectory using weak-field GR; notes retardation correction is order 1/c² and unimportant for Mercury.

D'Abramo — Rebuttal of Alternative Claims (2022)

D'Abramo, Germano. "Comment on 'The Secret of Planets' Perihelion between Newton and Einstein.'" Physics of the Dark Universe, Vol. 37, 2022, Article 101076.

Critical rebuttal showing alternative explanations of perihelion precession are internally inconsistent.

Part V: Reference Summary Tables

Perihelion Precession Predictions (Mercury, arcsec/century)

| Source | Year | Prediction | Notes | |------------|----------|----------------|-----------| | Observed anomaly | — | ~43″ | Beyond Newtonian perturbations | | Tisserand (Weber law) | 1872 | 6.28″ | 1/6 of observed | | Scheibner (Weber law) | 1873 | 6.73″ | Confirming Tisserand | | Lévy (Weber-Riemann) | 1890 | ~43″ | First correct derivation | | Gerber (velocity-dependent) | 1898 | 43″ | Derivation later shown flawed | | Einstein (GR) | 1915 | 43″ | First principled derivation | | Poincaré/Lorentz (SR only) | 1906–11 | ~7″ | 1/6 of observed | | Jefimenko (cogravitation) | 2006 | ~14″ | 1/3 of observed | | Assis (modified Weber) | 1989 | ~43″ | With tuned ξ parameter |

Key Debates Summary

| Issue | Resolution | |-----------|----------------| | Did Gerber anticipate Einstein? | No—derivation flawed (Seeliger, von Laue, Einstein) | | Does original Weber gravity give correct precession? | No—only ~1/6 of observed value | | Can modified Weber give correct precession? | Yes—with adjusted parameters (Assis, Ragusa) | | Can Weber gravity give both perihelion AND light deflection? | No conservative Weber-like force can (Bunchaft & Carneiro 1997) |

Conclusion

This bibliography documents a 170-year research tradition from Weber's 1846 electrodynamics to contemporary work by Assis, Tajmar, and others. The core finding is that Weber-type velocity-dependent gravitational force laws can reproduce Mercury's perihelion precession with appropriately chosen parameters, but face fundamental constraints: no conservative Weber-like force can simultaneously predict both the correct perihelion advance and gravitational light deflection. This theoretical limitation explains why Weber gravity remains of historical and pedagogical interest rather than serving as an alternative to General Relativity. The literature reveals ongoing research activity, particularly through Assis's relational mechanics program, alongside definitive critical analyses establishing the boundaries of these approaches.