Existence of homographic solutions in non-Newtonian dynamics

2011 ◽  
Author(s):  
E. A. Grebenikov ◽  
D. M. Diarova ◽  
N. I. Zemtsova
Keyword(s):  
Newtonian Dynamics ◽  
Homographic Solutions

scholarly journals Newtonian Fractional-dimension Gravity and Rotationally Supported Galaxies

2021 ◽  
Author(s):  
Gabriele U Varieschi
Keyword(s):  
Fractional Dimension ◽  
Newtonian Gravity ◽  
Axially Symmetric ◽  
Local Dimension ◽  
Radial Acceleration ◽  
Modified Newtonian Dynamics ◽  
Newtonian Dynamics ◽  
The Subject ◽  
Symmetric Structures ◽  
Natural Scale

Abstract We continue our analysis of Newtonian Fractional-Dimension Gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces including those with fractional (i.e., non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (Bulge-Dominated Spiral), NGC 6503 (Disk-Dominated Spiral), and NGC 3741 (Gas-Dominated Dwarf). As was done in the general cases of spherically-symmetric and axially-symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dynamics, a leading alternative gravity model which explains the observed properties of these galaxies without requiring the Dark Matter hypothesis. In our model, the MOND acceleration constant a0 ≃ 1.2 × 10−10m s−2 can be related to a natural scale length l0, namely $a_{0} \approx GM/l_{0}^{2}$ for a galaxy of mass M. Also, the empirical Radial Acceleration Relation, connecting the observed radial acceleration gobs with the baryonic one gbar, can be explained in terms of a variable local dimension D. As an example of this methodology, we provide detailed rotation curve fits for the three galaxies mentioned above.

scholarly journals Central Configurations and Action Minimizing Orbits in Kite Four-Body Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
B. Benhammouda ◽  
A. Mansur ◽  
M. Shoaib ◽  
I. Szücs-Csillik ◽  
D. Offin
Keyword(s):  
Cross Sections ◽  
Body Problem ◽  
Mass Parameter ◽  
Central Configurations ◽  
Continuous Family ◽  
Classical Action ◽  
Dynamical Aspect ◽  
Homographic Solutions ◽  
Four Body Problem ◽  
Current Article

In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses. We consider two different types of symmetrical configurations. In each of the two cases, the existence of a continuous family of central configurations for positive masses is shown. We address the dynamical aspect of periodic solutions in the settings considered and show that the minimizers of the classical action functional restricted to the homographic solutions are the Keplerian elliptical solutions. Finally, we provide numerical explorations via Poincaré cross-sections, to show the existence of periodic and quasiperiodic solutions within the broader dynamical context of the four-body problem.

scholarly journals Loss of Mass and Stability of Galaxies in Modified Newtonian Dynamics

2007 ◽  
Vol 665 (2) ◽  
pp. L101-L104 ◽  
Author(s):  
Xufen Wu ◽  
HongSheng Zhao ◽  
Benoit Famaey ◽  
G. Gentile ◽  
O. Tiret ◽  
...  
Keyword(s):  
Modified Newtonian Dynamics ◽  
Newtonian Dynamics ◽  
Loss Of Mass
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