My Science & Epistemology Researches
In stellar astrophysics, opacity ( k ) is a measure of a material’s resistance to the flow of radiative energy. One analytical descriptions of this phenomenon is Kramers’ opacity law, a power-law relation derived from atomic physics that characterizes how stellar matter interacts with radiation under specific thermodynamic conditions.
Brussi 2026_Brief on Kramers’ Opacity Law in Stellar Astrophysics
Brief analysis of Chandrasekhar’s formula on dynamic friction in the general case of galactic encounters in the study of Galactic Dynamics.
Spoiler: we get a result for the dynamical friction timescale which means that in a time span of a few Gyr, for instance with the values of our assumptions applied to the Milky Way, the orbit of a massive satellite has substantially reduced, while the orbit of lower mass satellites (such as globular clusters) has not been significantly affected by dynamic friction.
Brussi 2026_Chandrasekhar dynamical friction formula
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.
The first to observe that the propagation of light was not instantaneous was the astronomer Giovanni Domenico Cassini (1625-1712); the first to estimate its speed, in 1676, was the Danish astronomer Ole Christensen Rømer (1644-1710), both based their observations on the solar system.
Brussi 2026_Ole Rømer and the finite speed of light
Some personal notes on the strange relativistic rotation effect, the Penrose-Terrell rotation, of a body moving at high speed; written in italian.
Brussi 2026_The Penrose-Terrell rotation
Some personal notes on the famous relativistic garage paradox, written in italian.
Brussi 2026_The Garage Paradox
Der Wahrheit ist immer nur ein kurzes Siegesfest beschieden, zwischen den beiden langen Zeiträumen, wo sie als paradox verdammt und als trivial geringgeschätzt wird.
“Truth is always granted only a brief victory celebration, between the two long periods of time where it is condemned as paradoxical and dismissed as trivial.”
Arthur Schopenhauer, Die Welt als Wille und Vorstellung, Leipzig: F.A. Brockhaus (1819)
An expression with an epistemological, not just philosophical, flavor. Schopenhauer’s thought, in fact, is dominated by cosmic pessimism, arguing that reality is driven by a blind and irrational force, the Will to Live, a source of perpetual suffering, since to will is to desire, and to desire means to lack and suffer. For him, existence is an oscillation between pain and boredom, and the paths to liberation are temporary (art) or permanent (compassion and asceticism), and deny the will itself, transforming non-will into the ultimate goal.
A little reminder about a useful function used in Astronomy: the Abel integral equation (source: Google AI)
At school, 50 years ago, they taught me a proof of the Pythagorean theorem.
I didn’t remember it and tried to make my own.
Among the dozen I’ve made, I’ll list a couple of demonstration drafts.
Brussi 2026_Pythagorean theorem 2
Brussi 2026_Pythagorean theorem 9
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).
Brussi 2026_Pantheon+ low z issue
