# Moving objects in retarded gravitational potentials of an expanding spherical shell/Brief historical review

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## Brief historical review

The finiteness of the propagation speed of gravity and its influence on gravitational forces was originally published by the Austrian astronomer Josef von Hepperger (1855–1928) in 1888 in Vienna.
The German physicist Paul Gerber (1854–1909) published 1898 his paper on "The spatial and temporal expansion of gravity", where he established that the perihelion precession of the planet Mercury is related to the propagation speed of gravity, which is quite close to that of electromagnetic radiation. His formula for the perihelion precession of the planet Mercury wasn't known to Albert Einstein (1879–1955), but six years after Paul Gerber's death, Einstein found an identical formula in his publication "Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie" (English: "Explanation of Mercury's perihelion motion from the general theory of relativity") by applying the laws of General Relativity. However, the contemporary scientists couldn't reproduce the derivation of Paul Gerber for the formula, and furthermore, they stated that some of the prerequisites used by him were wrong.
Shortly before his early death the German astronomer and physicist Karl Schwarzschild (1873–1916) published a paper on "Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie" (English: "On the gravitational field of a sphere of incompressible fluid according to Einstein's theory"), where he described how to compute the smallest possible radius for a sphere with a given mass. He found the radius for a sphere with the mass of the sun to be three kilometres. In recognition of his achievement, the corresponding radius is now called the Schwarzschild radius. It is interesting to notice that Schwarzschild also made important contributions to retarded potentials in electrodynamics already in 1903. According to the electrokinetic potential he claimed:
   Es sind in jedem Raumelement die Werte der Dichte und der Geschwindigkeit zu benutzen, welche dort zu einer um die Lichtzeit zurückliegenden Epoche galten.
   In each spatial element, the values of density and velocity are to be used, which were valid there at an epoch around light time ago.
The Belgian theologian and physicist George Lemaître SJ (1894–1966) is regarded as the founder of the Big Bang theory. In 1931, he introduced the term "atome primitif" (English: "primordial atom") to describe the hot initial state of the universe. Already in 1927 he wrote as the second conclusion of his publication about "a homogeneous universe of constant mass and increasing radius, accounting for the radial velocity of extra-galactic nebulae" with reference to the investigations of Edwin Hubble (1889–1953) in 1926:
   Le rayon de l'univers croit sans cesse depuis une valeur asymptotique $R_{0}$ pour $t=-\infty$
   The radius of the universe increases without limit from an asymptotic value $R_{0}$ for $t=-\infty$
In 1933 the Swiss astronomer Fritz Zwicky (1898–1974) obeserved a gravitational anomaly in the Coma galaxy cluster, and he coined the term dark matter (in German: "dunkle Materie") for the cause of this anomaly.
In his book Relativity, Gravitation and World Structure of the year 1935 the British astrophysicist and mathematician Edward Arthur Milne (1896–1950) introduced the special-relativistic cosmological Milne model. This model assumes an isotropic and for all time linearly expanding, but not homogeneous universe. It is independent of general theory of relativity, but nevertheless equivalent to a special case of the Friedmann–Lemaître–Robertson–Walker metric in the limit of zero energy density. The redshift is explained by the velocity caused by a hypothetical initial explosion of matter. The density of such a universe must be small in comparison to the critical density of the Friedmann equations that were published by Russian physicist and mathematician Alexander Friedmann (1888–1925) in 1924. Decades later, the Milne model fell almost completely into oblivion, whereas the cosmological models based on the general theory of relativity gained more and more attention.
In 1953 the German astrophysicist Erwin Finlay-Freundlich (1885–1964) derived a blackbody temperature for intergalactic space of 2.3 Kelvin according to his theory of tired light. The German-British mathematician and physicist Max Born (1882–1970) immediately recommended taking the problem seriously and pursuing it further.
* Portrait images of early contributing scientists
* Josef Hepperger in the 1920s.
* Paul Gerber around 1900.
* Karl Schwarzschild around 1900.
* Edward Arthur Milne in 1917.
* Albert Einstein in 1921.
* Alexander Friedmann around 1920.
* George Lemaître in 1933.
* Edwin Hubble in 1931.
* Fritz Zwicky in the year 1947.
* Erwin Freundlich in the 1930s.
In 1965 the cosmic microwave background (CMB) was discovered by US-American radio astronomers Arno Allan Penzias (1933–2024) and Robert Woodrow Wilson (born 1936). It has a thermal black body spectrum at a very low temperature of about 2.7 Kelvin. Since the cosmic microwave background was mainly created in the visible area of the electromagnetic spectrum, it must have undergone a strong wavelength extension on its way to the observers. This can happen because of two main reasons:
* The origin of the radiation moves away from us very quickly, which will cause an increase of the wavelength according to the Doppler effect described by Christian Doppler (1803–1853) in 1842.
* There is a huge mass behind the origin of the radiation, which will cause an increase of the wavelength according to the gravitation and the relativity principle of Albert Einstein (1879–1955) of 1907.
In addition, it is discussed that an expansion of the spacetime during the propagation time of a light wave also would increase its wavelength to the same extent.
The redshift factor $z$ is defined as a relation between an emitted wavelength $\lambda _{0}$ and an observed wavelength $\lambda$ of electromagnetic radiation:
    $z={\frac {\Delta \lambda }{\lambda _{0}}}={\frac {\lambda -\lambda _{0}}{\lambda _{0}}}={\frac {\lambda }{\lambda _{0}}}-1$
The redshift of the cosmic microwave background was found to be $z\approx 1089$ in 2003, which is an extremely high value. The age of the universe at the time this background radiation was created by hydrogen atoms has been estimated at around 379,000 years.
Observations of distant type Ia supernovae published by both the Supernova Cosmology Project as well as the High-Z Supernova Search Team in 1998 show that the relative expansion of the universe is accelerating. For the analysis the astronomers Saul Perlmutter, Brian P. Schmidt and Adam Riess were awarded the Nobel Prize in Physics in 2011.
From 2001 to 2010 the NASA spacecraft Wilkinson Microwave Anisotropy Probe (WMAP) was investigating the cosmic microwave background. Its measurements led to the current Standard Model of Cosmology. According to this model the universe currently consists of less than 5 percent ordinary baryonic matter; about 24 percent cold dark matter (CDM) that interacts only weakly with ordinary matter and electromagnetic radiation; and more than 70 percent of dark energy that is used to explain the accelerated expansion of the universe. These data were more or less confirmed by the Planck space observatory that was operated by the European Space Agency (ESA) from 2009 to 2013.
* Evolution of the universe investigated with the Wilkinson Microwave Anisotropy Probe (WMAP)
* The evolution of the universe according to the interpretation of the measurements of the Wilkinson Microwave Anisotropy Probe (WMAP). The acceleration of the expansion leads to the concave outer rim surface of the evolution cone today.
* The contents of of the universe today (top) and 380,000 years after the Big Bang (bottom) according to the interpretation of the Wilkinson Microwave Anisotropy Probe (WMAP) measurements.
In 2013 the Indian researcher Chandrakant Raju proposed to apply the retarded gravitation theory (RGT) to explain the flyby anomaly of spacecrafts in the gravitational field of the earth as well as the acceleration of masses in the retarded gravitational fields of spiral galaxies.
In 2016, researchers from the gravitational-wave observatory LIGO reported the first direct measurement of gravitational waves generated by the collision of two black holes (gravitational wave event GW150914). Already in 2017 the Nobel Prize in Physics was awarded for the first direct observation of gravitational waves.
On 17th August 2017 a merging binary neutron star was observed independently and simultaneously by the Advanced LIGO and Virgo detectors (gravitational wave event GW170817) and the Fermi Gamma-ray Burst Monitor as well as the Anticoincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory (gamma ray burst event GRB 170817A). These observations prove that the propagation velocity of gravitational waves must be extremely close to that of electromagnetic waves.
In January 2024 the very young and very far galaxis JADES-GS-z14-0 was found with the Near-Infrared Spectrograph (NIRSpec) of the James Webb Space Telescope (JWST). This galaxy was observed in a state 290 million years after the big bang. Its redshift measured with the well-known Lyman alpha break at a wavelength about 1.8 micrometres has a very high value of a good 14, which is a very high value for an astronomical object, but much lower than that of the cosmic microwave background.
In February 2024, a study explained the anomalies in the rotation curves of more than hundred spiral galaxies of different types from the SPARC (Spitzer Photometry and Accurate Rotation Curves) Galaxy collection taken with the Spitzer Space Telescope, by accounting for retarded gravitational potentials and without taking into account dark matter or modifying general relativity.

### References

* ↑ Hepperger, Josef von (1888). Über die Fortpflanzungsgeschwindigkeit der Gravitation (in German). Wien: K. K. Hof.-und Staatsdruckerei.
* ↑ Gerber, Paul (1898). Mehmke, R.; Cantor, M. (eds.). "Die räumliche und zeitliche Ausbreitung der Gravitation" [The spatial and temporal expansion of gravity]. Zeitschrift für Mathematik und Physik (in German). Leipzig. 43: 93–104 – via Verlag B. G. Teubner.
* ↑ Einstein, Albert (1915). "Erklärung der Perihelbewegung des Merkur aus der Allgemeinen Relativitätstheorie" [Explanation of Mercury's perihelion motion from the general theory of relativity]. Sitzungsberichte der Preußischen Akademie der Wissenschaften: 831–839.
* ↑ Schwarzschild, Karl (1882). Deutsche Akademie der Wissenschaften zu Berlin (ed.). Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin. Smithsonian Libraries. Berlin : Deutsche Akademie der Wissenschaften zu Berlin. pp. 424–434.
* ↑ Schwarzschild, Karl (1903). "Zwei Formen des Prinzips der kleinsten Action in der Elektronentheorie" [Two forms of the principle of least action in electron theory]. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. Göttingen: Commissionsverlag der Dieterich'schen Universitätsbuchhandlung, Lüder Horstmann (3): 127–128.
* ↑ Hubble, Edwin (1926). "Extra-galactic nebulae". Astrophysical Journal. Mount Wilson, California, USA: Contributions from the Mount Wilson Observatory. 64 (I): 321–369.
* ↑ Lemaître, Georges (1927). "Un univers homogéne de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactiques". Annales de la société scientifique de Bruxelles. 47 A: 49–59.
* ↑ Lemaître, Georges (1931). "Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae". Monthly Notices of the Royal Astronomical Society. 91: 483–490.
* ↑ Fritz Zwicky (1933). "Die Rotverschiebung von extragalaktischen Nebeln" [The red shift of extragalactic neubulae]. articles.adsabs.harvard.edu. Retrieved 2024-06-11.
* ↑ Milne, Edward Arthur (1935). "World picture on the simple kinematic model - Comparison with local Newtonian gravitation and dynamics - §§412-418". Relativity, gravitation and world-structure. Oxford, Great Britain: Clarendon Press. pp. 291–294.
* ↑ Friedman, Alexander (1922). "Über die Krümmung des Raumes" [About the curvature of the space]. Zeitschrift für Physik (in German). 10 (1): 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902.
* ↑ Finlay-Freundlich, Erwin (1953). "Über die Rotverschiebung der Spektrallinien" [On the redshift of spectral lines]. Nachrichten der Akademie der Wissenschaften in Göttingen. Göttingen: Vandenhoeck & Ruprecht (7): 94–101.
* ↑ Born, Max (1953). "Theoretische Bemerkungen zu Freundlichs Formel für die stellare Rotverschiebung" [Theoretical remarks to Freundlich's formula for the stellar redshift]. Nachrichten der Akademie der Wissenschaften in Göttingen. Göttingen: Vandenhoeck & Ruprecht (7): 102–108.
* ↑ Penzias, Arno Allan; Wilson, Robert Woodrow (1965). "A Measurement of Excess Antenna Temperature at 4080 Mc/s". The Astrophysical Journal. 142 (1): 419–421. doi:10.1086/148307.
* ↑ Doppler, Christian (1842). "Ueber das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels" [On the Coloured Light of the Double Stars and some other Celestial Bodies]. Abhandlungen der Böhmischen Gesellschaft der Wissenschaften (5/2): 465–485.
* ↑ Einstein, Albert (1907). "Relativitätsprinzip und die aus demselben gezogenen Folgerungen" [On the Relativity Principle and the Conclusions Drawn from It] (PDF). Jahrbuch der Radioaktivität (4): 411–462.
* ↑ C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, D. N. Spergel, G. S. Tucker, E. Wollack, E. L. Wright, C. Barnes, M. R. Greason, R. S. Hill, E. Komatsu, M. R. Nolta, N. Odegard, H. V. Peirs, L. Verde, J. L. Weiland (2003). "First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results". Astrophys. J. Suppl. 148: 1–27. doi:10.1086/377253.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ "Microwave (WMAP) All-Sky Survey | Guide | Digital Universe | Hayden Planetarium". web.archive.org. 2013-02-13. Retrieved 2024-06-01.
* ↑ "The Nobel Prize in Physics 2011". NobelPrize.org. Retrieved 2024-03-16.
* ↑ Francis, Matthew (2013-03-21). "First Planck results: the Universe is still weird and interesting". Ars Technica. Retrieved 2024-06-11.
* ↑ "ESA Science & Technology - From an almost perfect Universe to the best of both worlds". sci.esa.int. Retrieved 2024-06-11.
* ↑ Raju, Chandrakant (2013-11-27). "Retarded gravitation theory" (PDF). Penang, Malaysia: School of Mathematical Sciences, Universiti Sains Malaysia. arXiv:1102.2945. Retrieved 2024-03-22.
* ↑ LIGO Scientific Collaboration and Virgo Collaboration; Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K. (2016-02-11). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. doi:10.1103/PhysRevLett.116.061102.
* ↑ "The Nobel Prize in Physics 2017". NobelPrize.org. Retrieved 2024-03-16.
* ↑ LIGO Scientific Collaboration; Virgo Collaboration; Monitor, Fermi Gamma-Ray Burst; INTEGRAL (2017-10-20). "Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A". The Astrophysical Journal Letters. 848 (2): L13. doi:10.3847/2041-8213/aa920c. ISSN 2041-8205.
* ↑ Stefano Carniani, Kevin Hainline (2024-05-30). "NASA's James Webb Space Telescope Finds Most Distant Known Galaxy". webbtelescope.org.
* ↑ Glass, Yuval; Zimmerman, Tomer; Yahalom, Asher (2024-02-20). "Retarded Gravity in Disk Galaxies". Symmetry. 16 (4): 387. doi:10.3390/sym16040387. ISSN 2073-8994.