Effect of oblateness and viscous force in the Robe’s circular restricted three-body problem

The magnetosphere and ionosphere have a crucial interaction during severe geomagnetic storms. The Global Navigation Satellite System (GNSS) provides high-quality ionospheric observations with high temporal and spatial resolution, is generally preferred to investigate the ionospheric variation. In this study, the storm-time ionospheric response of the June 2015 severe storm (Dstmin = −208 nT) was investigated by the Total Electron Content (TEC) data of the Global Ionosphere Maps (GIMs), COSMIC radio occultation (RO) and a chain of International GNSS Service (IGS) stations. GIMs were used to show the global TEC variation during the storm. COSMIC RO data were also utilized to investigate the TEC variation and electron density profiles in an anomaly area with a limited time interval. GNSS TEC data of the 16 IGS stations were utilized to investigate the ionospheric variability on different latitudes of hemispheres. The results showed that intense positive phases formed in high latitudes of the Southern Hemisphere (SH) and the western longitudes of the Northern Hemisphere (NH), especially over the North Atlantic Ocean until the main phase of the storm. Besides, negative phases were observed in high latitudes and eastern longitudes of the NH. During the recovery phase of the storm, positive phases were seen in the low latitudes of the SH and the ionospheric conditions calmed down in the entire SH after the depletion of these phases. Negative phases were also observed almost wholly covered in the NH, which denser in the European-African sector. As a particular result, the electron density profiles of COSMIC RO showed that the ionospheric phases of the June 2015 storm not only related to TEC values but also the altitude of maximum electron density.

Investigation of global ionospheric response of the severe geomagnetic storm on June 22-23, 2015 by GNSS-based TEC observations

Effect of perturbations in the Coriolis and centrifugal forces in the Robe‐finite straight segment model with arbitrary density parameter

Kind of Robe’s restricted problem with heterogeneous irregular primary of N-layers when outer most layer has viscous fluid

We analyze the existence of equilibrium points for a particle or dust grain in the framework of unperturbed and perturbed Robe’s motion. This particle is moving in a spherical nebula consisting of ...

On Robe’s restricted problem with a modified Newtonian potential

In this paper we study the existence and linear stability of the equilibrium points in the Robe’s restricted three-body problem when one of the primaries is a finite straight segment. We observe that the center of the first primary is always an equilibrium point for all values of the density parameter k , mass parameter μ and length parameter l . There is an additional equilibrium point lying on the line joining the center of the first primary and the second primary, provided k > 1 + l 2 . When k + μ = 1 + l 2 ( 1 − μ ) , there are infinite number of equilibrium points lying on a circle with radius 1 − 2 3 l 2 and center as the second primary, provided they lie within the spherical shell. When k 0 and k + μ + 2 μ l 2 > 0 , there are two more equilibrium points lying in the x z -plane forming triangles with the center of the shell and the second primary. We analyze the linear stability of the equilibrium points.

Robe's restricted three-body problem when one of the primaries is a finite straight segment

This paper deals with the photogravitational circular restricted three-body problem, including the effect of circular cluster of material points. The parametric evolution of the position of equilibrium points and the existence of a different number of equilibrium points are illustrated using graphs. A detailed investigation to find out the influence of the radiation pressure $q$
 , mass ratio $\mu $
 and the circular cluster of material points $M_{b}$
 on the geometry of basins of attraction is carried out. Further, the number of iterations required to obtain the desired level of accuracy is recorded and presented using probability distribution diagram. The correlations between the domain of convergence of equilibrium points and the corresponding number of the iterations required to obtain the desired level of accuracy are explained. We monitor the parametric evolution of the basin entropy to reveal the unpredictability in the basins of attractions. It is found that unpredictable (fractal) regions exist in the vicinity of boundaries of the basins of attraction.

Vinay Kumar

Papers

Robe's restricted three-body problem when one of the primaries is a finite straight segment

The unpredictability of the basins of attraction in photogravitational Chermnykh’s problem

Elliptic restricted synchronous three-body problem (ERS3BP) with a mass dipole model

Unpredictable basin boundaries in restricted six-body problem with square configuration

Capricious basins of attraction in photogravitational magnetic binary problem