Category: Cosmology

Cosmology is the scientific study of the universe’s origin, evolution, large-scale structure, and future, combining physics and astronomy to understand the cosmos as a whole. It uses observations and theories to explain how galaxies, stars, and planets form and change over vast timescales, addressing fundamental questions about existence.

The three-body problem and the five Lagrangian points

Joseph-Louis Lagrange (1736-1813) was a great mathematician of the 18th century. His main studies on mechanics led him to tackle the gravitational three-body problem, which, however, remains unsolved to this day because the system is inherently chaotic and unpredictable in the long term, as small initial variations cause drastically different results.
Lagrange found the equilibrium solutions (the five Lagrangian points, see figure taken from the ESA website) for the system in the simplified yet highly interesting case where the third body has negligible mass compared to the other two (e.g., the Sun, a planet, and an asteroid or an artificial satellite). The first three points (L1, L2, L3) had already been found by Leonhard Euler (1707-1783), another huge mathematician of the 18th century, while Lagrange found the so-called ‘triangular’ points (L4, L5), because they form perfect equilateral triangles with the two main bodies.
For details about these points, please refer to the easy explanations on the
link  ESA (European Space Agency) website.

Obviously, Lagrange could never have known about the evidence supporting his conjecture (it was only in 1906 that astronomers confirmed his theory by discovering Trojan asteroids captured at points L4 and L5 of Jupiter’s orbit) or its current usefulness in positioning our space exploration vehicles.
Thanks to their ‘gravitational stability’, which saves positioning energy (and in the case of L2 also provides partial shielding from the Sun), it is conceivable that, in the future of space exploration, advanced bases for deep space exploration will be located at Lagrangian points.

 

The 5 Lagrangian points, from the link  ESA (European Space Agency) website; the orbits of points L1 and L2 are not to scale, the distance from Earth is about 1/100 of the radius of Earth’s orbit.

Lagrangian points

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Note for laymen – what is the dark matter?

Let’s consider a disc galaxy with billions of stars forming the disc, which rotates (the Andromeda galaxy in the photo, to give a well-known example). We can consider for each of these stars that the centripetal acceleration
[1]    a’ = v²/R
is equal to the gravitational acceleration
[2]    a” = G M/R²
therefore from  [1] = [2]  we obtain:
[3]    v = √(G M/R)
where  v  is the local velocity of the source considered,  R  is its distance from the galactic center,  G  is the gravitational constant,  M  is the total mass contained within the radius  R  (which determines the gravitational attraction).
Measuring the rotational velocities of galaxies is relatively easy, if they are not seen face on, and it is generally observed that throughout the disk the rotational velocities of the sources (stars but also gas clouds) are almost constant. Therefore, from relation  [3]  it follows that the mass  M  must increase in proportion to the radius  R , since  G  is a constant. Indeed, the mass contained within the radius  R  increases as  R  increases, but what is observed is not sufficient to justify the constant value of  v . These considerations leads to the hypothesis that there is a substance that is invisible and non-baryonic in nature (i.e., not made up of protons and neutrons, which are not detected) that manifests itself only through gravitational behavior, which is called dark matter.

Processed photograph of M31, Andromeda. It was not possible to obtain the author of this beautiful photograph.


Andromeda

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A note on the Measurement Dispersion at Low Redshift in Pantheon+ database

A brief note on the dispersion of low-redshift measurements in the Pantheon+ database. This is part of my study of the alternative interpretation of redshift that does not involve the expansion of the universe.
The Pantheon+ database is one of the largest and most precise cosmological data collections in the world, consisting of 1,701 light curves from 1,550 Type Ia supernovae (SnIa).

pdf  Brussi 2026_Pantheon+ low z issue

 

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Here I am

After a hiatus from 2021, I’m resuming my online presence with this small collection of suggestions, seeking intellectual dialogue. Let me know what you think in the comments or via email.
Thanks

p.s. I posted with the dates of the original documents

 

 

That's me

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My thesis work

My thesis work (written in italian) is published in the University of Padova archive:
pdf_ita  Brussi 2025_Epistemology of time and cosmological interpretations

As an appendix to the same thesis I put a first development draft of the non-standard framework, which, after significant revisions, later became my work
link  The URD Framework.

Abstract
The aims of this study on time are first to explore its ontological meaning in the historical developments that have accompanied its interpretative evolution, and then to examine some theoretical critical issues raised by recent literature. With some original theses, some alternative explanations for the expansion of the universe are then analyzed, which the current interpretation claims to be observed experimentally, by means of a model based on the ‘specific time’ of photons as an alternative to the ‘universal time’. Furthermore, it is hypothesized a model that considers the presence of an energy density in the cosmic fluid (called aether) that interacts with the incident radiation, thus determining a redshift effect in the wavelength, or an even longer time for the same radiation to diffuse. The consistency of ‘specific time’ has been verified with Minkowski spacetime, with Einstein’s principles of special relativity, and with Friedman’s equations of cosmic dynamics. Having demonstrated the fallacy of this ‘specific time’ hypothesis, the positive conclusion is that there is no need to postulate a universal time. Once one is defined, its uniqueness or universality can be demonstrated (within the limits of the adopted models). To complement the study, possible causes of the redshift, alternative to the standard cosmological model, were analyzed. It has been taken in consideration the hypothesis that the same universe behaves like a black body, emitting a radiation (the cosmic microwave radiation) that can interact with the observed photons coming from remote sources, attenuating their energy and determining their redshift. A cross section for photons, and a model for photon-photon interactions that respects the law of conservation of energy have therefore been hypothesized. As a basis for the conjectures, direct observational evidence was considered, not interpreted by means of theories, obtaining (from the comparison with other standard candles) better distance estimates than the official ones based on Hubble’s law. This addendum is included as an Annex, believing that the same conjectures and some original models can represent a reference for future in-depth studies.

The work is written in Italian (1.8 MB):

pdf_ita  Brussi 2025_Epistemologia del tempo e interpretazioni cosmologiche

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Estimation of the masses of NGC7217 and NGC658

This is a report developed for the Astronomy Laboratory exam. It is educational in nature and written in Italian. There are a few minor errors and some assessments based on unproven models, but I am leaving it as it is (or as it was) in case any of the details might be useful to someone.

pdf_ita  Brussi 2021_Valutazione delle masse di NGC7217 e NGC658

 

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