Wenceslao Segura

Instituto de Estudios Campogibraltareños

We have developed a software called "Crescent Moon Visibility" which provides information on the visibility of the first lunar crescent under certain conditions. This software takes into account the physical laws and the capacity of human visual perception to determine whether the crescent can be seen or not. It calculates the probability of observ...

Among the bi-parametric empirical criteria designed to determine when we will see the lunar crescent for the first time are multi-functional criteria, characterized by using several functions or visibility curves, which provide information about the difficulty of seeing the crescent. We show in detail six of these criteria and compare them with th...

Medieval Arab astronomers must have calculated the Julian calendar date of the first day of the Islamic calendar. We repeat this calculation using the Julian day and find the desired date is July 16, 622. We use the Islamic computational calendar developed in the Middle Ages to find this result.

We examine the Meton lunisolar cycle, consisting of 19 solar years and 235 lunations. We develop the general techniques of lunisolar cycles and apply them to the various Meton cycles used in calendars: Julian, Christian ecclesiastical, Hebrew and astronomical. Although based on Meton's original idea, they are different cycles. We calculate the disp...

We have developed a software called "Crescent Moon Visibility" which provides information on the visibility of the first lunar crescent under certain conditions. This software takes into account the physical laws and the capacity of human visual perception to determine whether the crescent can be seen or not. It calculates the probability of observ...

We calculate the gravitational induction force acting on an accelerated particle to deduce Mach's principle. Assuming strong gravitational absorption in the early universe, we avoid divergent integrals.

We explain in depth the Julian and Gregorian lunisolar calendars, that is, the calendar that allow us to determine the day of Easter. We define and use the golden number, the epact, the dominical letter, the concurrent, the regular,... In the end, we expose the algorithms to find Easter Sunday,

We formulate the equivalence principle in Newtonian mechanics and General Relativity. We distinguish seven formulations of the equivalence principle, but not all are equivalent. We summarize the methods used in General Relativity to calculate the inertial mass. His examination leads us to consider two total energy-momentum tensors: calculated from...

Gravity is a long-range interaction, so the entire causally connected Universe acts gravitationally on a test body. In this investigation, we calculate the cosmic gravitational potential at a fixed location in the Universe. We verified that the most distant bodies are the ones that produce a more intense gravitational action. The Big Bang singulari...

We obtain the equation of motion of a particle as a function of distance and proper time. We are checking that it is invariant before recalibration of the gravitational potential.

We concisely expose the theory of Special Relativity. We treat its foundations, the Lagrangian and Hamiltonian formulations, and the four-dimensional formulation, and we apply the results to the relativistic dynamics of continuous media.

In the evening when we see the crescent of the Moon for the first time, sometime after its conjunction with the Sun, there is a time when we see the crescent more easily, which we call the best time for visibility of the crescent of the Moon. We present software that determines this best time, knowing the date, the geographic coordinates, and the a...

In the evening when we see the crescent of the Moon for the first time, sometime after its conjunction with the Sun, there is a time when we see the crescent more easily, which we call the best time for visibility of the crescent of the Moon. We present software that determines this best time, knowing the date, the geographic coordinates, and the a...

Software to calculate the best time for the visibility of the crescent of the Moon.

The latitude of optimum viewing of the lunar crescent is the latitude for a specific meridian where it is easiest to see the lunar crescent. We show an algorithm to determine the optimum latitude, which depends on the meridian and the depression of the Sun. We draw the line of optimum viewing or line that joins the places of optimum viewing of each...

We call Fotheringham curves of visibility of the first lunar crescent graphs of the altitude of the center of the Moon and its difference in azimuth with the center of the Sun (represented at the moment when the center of the true Sun is on the horizon), which separates the zones lunar visibility and invisibility. These are multiparameter curves, w...

We define the width of the window of visibility of the first lunar crescent as the interval of altitudes of the Moon between which we can see the crescent. We define the duration of the visibility window or time during which we see the crescent; and we also define the altitude of optimal vision of the crescent. We check the parameters on which the...

We expose and analyze the proposed models of the visual magnitude of the Moon for large phase angles (>150º). We devised a method to determine the luminance and illuminance per unit angular length of the lunar crescent as a function of position and phase angles.

We show that in high geographic latitudes (approximately > 50º north or south), the lunar months of 28 and 31 days are possible.

We describe the global view of the Moon's crescent and show the movement of the apex and the point of first visibility of the crescent.

For the central zone of the Earth (approximately 50ºN-50ºS), Islamic months have lengths of 29 and 30 days depending on the place of Earth from where we observe the first lunar crescent. We verify that all the lunar months have two durations for the central zone, one of 29 days and the other of 30 days. For higher latitudes (50º N or S to 61.5º N o...

We verify that the Islamic calendar is not exclusively lunar but is also related to the movement of the Sun; for this reason, we say that the Islamic calendar has some lunisolar aspects.

The month of the Islamic calendar begins with the first observation of the crescent of the Moon. This phenomenon is highly dependent on the geographical position of the observation site. We expose the dependency of the first sighting of the Moon on latitude and longitude. We define the concepts: terrestrial terminator, Month Change Line, zone of fi...

We calculate, as a function of latitude, the universal time when the visibility of the first lunar crescent begins. We verified that for the same meridian, the time of the first visibility of the crescent depends on the latitude and that the atmospheric absorption that attenuates the moonlight has little influence.

Bruin (1977) devised a procedure to find out the visibility of the first crescent Moon. He applied various simplifications to his theory, not all of them acceptable. We rethink Bruin's method by making some corrections: we take into account the variation of the luminance of the Moon with the phase, we use the experimental results of Knoll et al. (1...

Schaefer (1991) determined the Danjon limit or minimum angle between the Sun and the Moon from which the Moon can be seen shortly after the conjunction. Schaefer's method uses Hapke's (1984) lunar photometric theory and considers a fixed value for the threshold illuminance. We show Schaefer's method and its shortcomings, and we expose a modified th...

Brief report on how to calculate the first visibility of the Moon crescent. We warn against the misinterpretation of Blackwell's threshold visibility experiment. We state that the width of the first lunar crescent is less than the resolving power of the human eye, so the determining factor for visibility is the illuminance of the Moon and not its b...

We formulate Mach's principle and show that the inertial force is the gravitational induction force the Universe exerts on an accelerated body. We show that inertial mass depends on cosmic time, which has measurable consequences.

We analyze some of the periodic parameters that characterize the Moon: latitude, inclination of the orbit, tropic velocity, synodic velocity, lunation, distance from Earth, as well as the periodicities of other phenomena that have some relationship with calendars: lunar day, the interval between consecutive moonsets, synodic and ecliptic movement,...

We show techniques for finding the arc-light, or angle between the centers of the Sun and the Moon. We describe the periodicity of the Moon's ecliptic latitude and its effect on the arc-light. We verify that the arc-light at the New Moon time has a periodicity of approximately 173.5 days. We define the topocentric New Moon, which occurs when there...

When observing the first Moon crescent, it is necessary to gather information about the Moon: site in the sky where it is at sunset, luminosity, width, and orientation of its horns. We calculate the angles that the midpoint of the crescent forms with the vertical and the hour circle, data that allows us to know the orientation of the Moon's horns.

We expose the techniques to find computational lunar calendars. We distinguish between regular and semi-regular calendars. We study the Islamic calendar proposed by Rashed, Moklof, and Hamza, and we use the chronological Julian day to do the conversion to other calendars.

We calculate the Danjon limit or the smallest angular distance between the Moon and the Sun with which we can see the lunar crescent, using the model developed by astronomers at the Helwan Observatory. We found that the Moon could be seen with the naked eye at 5.6º away from the Sun in exceptional conditions. With a more realistic calculation, we f...

We calculate in detail the maximum width of the illuminated part of the Moon and the phase, or proportion of the illuminated area to the total surface. We do the calculations from the geocentric and topocentric points of view.

The Arab astronomer and mathematician al-Battani (858-929) developed a theory to determine when the Moon would first be visible after it was new. In this paper, we study this criterion with current astronomical knowledge.

We show that the criteria of lunar crescent visibility of al-Khwarizmi (9th century) and al-Qallas (10th century) is not the Indian criterion, according to which the Moon will be visible if between the moonset and sunset there are more than 48 minutes. Therefore, we distinguished two new visibility criteria: al-Khwarizmi and al-Qallas, which we ana...

We describe the arithmetic or computational Islamic calendar of medieval Muslim astronomers. We classify the different calendars of this type, also called tabular, finding the possible intercalation criteria. With the chronological Julian day, we obtain precise rules to convert this tabular calendar to the Julian or Gregorian calendar and vice vers...

This paper develops the uniqueness theorem of the curvature tensor, which states that the Riemann-Christoffel tensor (and its linear combinations) is the only tensor that depends on the connection and is linear with respect to the second derivatives of the metric tensor. From this result, Cartan's theorem is obtained, according to which Einstein's...

According to the principle dynamic equilibrium, we understand the force of inertia is a force that acts on whatever body that accelerated with respect to an inertial frame. It is, therefore, a real force, observed in whatever reference frame. We identify this force with force gravitational induction produced by the whole of the Universe. Therefore,...

We study the application of the laws of mechanics in inertial and non-inertial reference frames. We verify that in the usual formulation of mechanics, there are no centrifugal forces. We understand the force of inertia as a force that acts on everybody that is accelerated with respect to an inertial reference frame. The so-called fictitious forces...

We find that the force of inertia acting on an accelerated body is the result of the action of the gravitational induction force produced by the relative movement of the Universe as a whole, which fully confirms the Mach's Principle. The calculations are developed with the linearized theory of General Relativity.

We show that the forces of inertia acting on the accelerated bodies are forces of gravitational induction exerted by the whole of the Universe. Therefore, the phenomenon of inertia and the inertial mass of a body have a cosmic origin, as demanded by the Mach's principle. The calculations will be applied to a vector gravitational field theory. In a...

We will deduce the induction forces obtained from the field equation of Nordstrom's scalar gravitational theory and investigate whether they can explain the origin of the forces of inertia acting on a body when it is accelerated.

We will deduce the inductive forces of a vectorial gravitational theory and we will study whether these forces can be identified with the forces of inertia that act on a body when it is accelerated.

In the same publication in which Hermann Weyl in 1918 published his unified field theory, Albert Einstein raised sharp criticism to the new theory. He argued that if true would not exist defined spectral lines. Later Wolfgang Pauli developed this review in more detail, which was accepted by other physicists of the time, including to Weyl. The resul...

In 1945, Einstein began a new investigation into the unified field theory, which we call the Hermitian theory. A metric tensor and a connection whose components are complex numbers and have the Hermitian property. In essence it is an asymmetric metric-affine theory. In three studies, one conducted jointly with Straus, Einstein formulated the equati...

Sinopsis. En el año 1919 Einstein publicó un artículo donde expuso que las partículas cargadas eran estables por efecto de una fuerza de origen gravitatorio. Einstein modificó la ecuación de la Relatividad General, cambiando el coeficiente numérico 1/2 por el de 1/4. La nueva teoría satisface todos los resultados de la Relatividad General, e introd...

Sinopsis. En el año 1943 Erwin Schrödinger inició una serie de publicaciones de lo que llamó Teoría Unitaria de Campo, con la que pretendía unificar los campos gravitatorio, electromagnético y mesónico sobre una base geométrica. En este artículo que, es continuación de [34], [35] y [36], analizamos la cuarta y definitiva de las teorías puramente af...

Sinopsis. En el año 1943 Erwin Schrödinger inició una serie de publicaciones de lo que llamó Teoría Unitaria de Campo, con la que pretendía unificar los campos gravitatorio, electromagnético y mesónico sobre una base geométrica. En este artículo que, es continuación de [36] y [37], analizamos la tercera de las teorías puramente afín de Schrödinger...

Sinopsis. En el año 1943 Erwin Schrödinger inició una serie de publicaciones de lo que llamo Teoría Unitaria de Campo, con la que pretendía unificar los campos gravitatorio, electromagnético y mesónico sobre una base geométrica. En este artículo que, es continuación de [36], analizamos la segunda de las teorías puramen-te afín de Schrödinger (Schrö...

Sinopsis. En el año 1943 Erwin Schrödinger inició una serie de publicaciones de lo que él llamo Teoría Unitaria de Campo, con la que pretendía unificar los campos gravitatorio, electromagnético y mesónico sobre una base geométrica. El enfoque de su invetigación se basa en la teoría puramente afín, que supone a la conexión afín como el elemento geom...

Sinopsis. Durante el año de 1923 Einstein escribió tres artículos en los que desarrolló la primera teoría de campo puramente afín con la que pretendía unificar los campos gravitatorio y electromagnético. La teoría no resultó satisfactoria, pero la investigación de Einstein, primero olvidada y luego recuperada en los años cuarenta por Schrödinger, a...

The first serious attempt by Einstein to construct a unified field theory was developed during the year 1923 when he published several articles on the purely affine theory which was quickly forgotten. In the next two years, Einstein continued working in this field and the result was a metric-affine theory published in 1925 and which we present in t...

Este es un libro de Matemática para físicos. Con ello queremos decir que los conceptos y desarrollos matemáticos que exponemos se hacen con la finalidad de aplicarlos a la Física; o sea, aquí entendemos la Matemática como una herramienta, y como tal herramienta no es importante el grado de rigor con la que se aplique, sino la utilidad que se consig...

Tarifa ha dado al mundo varios apellidos relacionados con el nombre de la ciudad. Se han extendido por España y América. Curiosamente, Tarifa es un apellido en Albania, sin otra relación con la ciudad de igual nombre que su origen, que posiblemente venga de nombre árabe Tarif.

Hace muchos años que Jesús Terán Gil se convirtió en el cronista de Tarifa por excelencia. Supo continuar la labor de investigación histórica que comenzara su padre Francisco Terán Fernández. Su prodigiosa memoria, junto a un completísimo archivo personal, le permitió narrar de una forma singular la historia tarifeñas en artículos, conferencias y l...