Research Article
Equilibrium Positions in a Gravitational Field Generated by an Elongated Asteroid with Density of Order 4
El Haj El Ourabi*
,
Mohammed Bennai
Issue:
Volume 12, Issue 1, March 2025
Pages:
1-8
Received:
26 November 2024
Accepted:
10 December 2024
Published:
7 January 2025
DOI:
10.11648/j.ajaa.20251201.11
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Abstract: Calculating the gravitational potential generated by non-spherical mass distributions is an old problem that has been tackled by astronomical researchers. The majority of small celestial objects have an elongated shape with a non-uniform mass distribution. Early work in this field modelled these elongated bodies as segments with a uniform mass distribution. In a previous work, we established the analytical form of the potential generated by an asteroid modelled by a linear and inhomogeneous repair whose mass density is a polynomial of order four. We have studied the dynamic behavior of a test particle in the vicinity of this asteroid, which is assumed to be at rest, and have extracted periodic orbits under certain conditions. Every celestial object has an angular momentum due to its own rotation. This result in competition between gravitational attraction and centrifugal repulsion in the synodic reference frame linked to the object. This led us to focus our research on the existence of relative equilibrium positions. We calculated the Jacobi integral analytically and used the zero velocity curves numerically to extract four equilibrium positions, two isosceles and two equilateral.
Abstract: Calculating the gravitational potential generated by non-spherical mass distributions is an old problem that has been tackled by astronomical researchers. The majority of small celestial objects have an elongated shape with a non-uniform mass distribution. Early work in this field modelled these elongated bodies as segments with a uniform mass dist...
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Research Article
Description of Lorentz Transformations, the Doppler Effect, Hubble's Law, and Related Phenomena in Curvilinear Coordinates by Generalized Biquaternions
Alimzhan Kholmuratovich Babaev*
Issue:
Volume 12, Issue 1, March 2025
Pages:
9-20
Received:
11 December 2024
Accepted:
27 December 2024
Published:
22 January 2025
Abstract: This paper presents the derivation of Lorentz transformations in curvilinear coordinates utilizing generalized biquaternions. Generalized biquaternions are rotations in curvilinear coordinates, including on the tx, ty, and tz planes. These space-time rotations are precisely the Lorentz transformations in curvilinear coordinates. The orbital rotation of the source and/or receiver, which mathematically represents the Lorentz transformation in spherical coordinates, is identified as the cause of the transverse Doppler effect. The change in wave frequency, specifically the "redshift," results in nonlinearities of Hubble's law manifesting as phenomena such as accelerated and anisotropic expansion of the universe, aberration, and wave polarization. Apparently, redshift exists even without radial expansion of the universe, i.e., without the "Big Bang". The reasons for the accelerated expansion of the universe, the anisotropic (angular) distribution of relic radiation, and the polarization of light from distant stars become clear in this approach. This greatly simplifies the mathematical description and understanding of the supposedly complex processes occurring in the universe.
Abstract: This paper presents the derivation of Lorentz transformations in curvilinear coordinates utilizing generalized biquaternions. Generalized biquaternions are rotations in curvilinear coordinates, including on the tx, ty, and tz planes. These space-time rotations are precisely the Lorentz transformations in curvilinear coordinates. The orbital rotatio...
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Research Article
Exoplanets and Their Characterization in the Environment of Galaxy Formation
Diriba Gonfa Tolasa*,
Adugna Terecha Furi
Issue:
Volume 12, Issue 1, March 2025
Pages:
21-27
Received:
24 December 2024
Accepted:
8 January 2025
Published:
23 January 2025
Abstract: The exploration of exoplanets has become a crucial domain in astrophysics, particularly in understanding their formation and evolution within the broader framework of galaxy formation. This paper offers a comprehensive analysis of the current methodologies employed for exoplanet detection and characterization, highlighting the intricate relationships between galactic dynamics and planetary systems. We introduce an innovative approach that integrates numerical simulations with analytical models to investigate how various galactic environments influence the properties of exoplanets. Our findings reveal significant correlations between the attributes of exoplanets and their host galaxies, suggesting that the conditions conducive to planetary formation are deeply interconnected with the galactic context. In particular, we examine how factors such as the density of surrounding gas and dust, the presence of nearby stars, and the gravitational effects of dark matter shape the characteristics of emerging planetary systems. Our analysis demonstrates that understanding these interactions is essential for developing comprehensive models of planetary formation and evolution. The results indicate that exoplanets do not form in isolation but are significantly influenced by the dynamics of their host galaxies. Additionally, our study underscores the importance of advanced observational techniques, including those enabled by the James Webb Space Telescope (JWST), which are poised to revolutionize the field of exoplanet research. By combining theoretical frameworks, numerical simulations, and observational data, this research contributes to the ongoing discourse on exoplanet characterization and the broader implications for galaxy formation. Ultimately, we aim to enhance our understanding of exoplanets, providing insights that could inform future studies on the potential for habitability and the existence of life beyond Earth.
Abstract: The exploration of exoplanets has become a crucial domain in astrophysics, particularly in understanding their formation and evolution within the broader framework of galaxy formation. This paper offers a comprehensive analysis of the current methodologies employed for exoplanet detection and characterization, highlighting the intricate relationshi...
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