A Study of the Elliptic Restricted Three-Body Problem with Triaxial and Radiating Primaries Surrounded by a Belt
Jagadish Singh,
Ndaman Isah
Issue:
Volume 9, Issue 1, March 2021
Pages:
1-16
Received:
28 September 2020
Accepted:
30 November 2020
Published:
22 January 2021
Abstract: This paper examines the effects of radiation pressure and triaxiality of two stars (primaries) surrounded by a belt (circumbinarydisc)onthepositionsandstabilityofathirdbodyofaninfinitesimalmassintheframeworkoftheEllipticrestricted three body problem (ER3BP). We have obtained analytical solutions to the triangular equilibrium points and their stability and have also investigated these solutions numerically and graphically using radiating binary system (Xi- Bootis and Kruger 60). It is observed that their positions and stability are affected by semi-major axis, eccentricity of the orbit, triaxiality, radiation pressure of the primaries and potential from the belt. The perturbed parameters show the destabilizing tendency by decreasing the range of stability. The triangular points are found to bestable for 0 < µ < µc where µc is the critical mass parameter. The stability analysis for the binary system yielded a stable outcome when we consider the range of mass parameterµ in the region of the Routhonian critical mass ratio (0.03852) when the effect of circumbinary disc is dominant. We found triaxiality and radition factors inducing instability even within this range.
Abstract: This paper examines the effects of radiation pressure and triaxiality of two stars (primaries) surrounded by a belt (circumbinarydisc)onthepositionsandstabilityofathirdbodyofaninfinitesimalmassintheframeworkoftheEllipticrestricted three body problem (ER3BP). We have obtained analytical solutions to the triangular equilibrium points and their stabil...
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On the Linearized Dynamics of the Neutral Cells at High Latitudes in the Earth’s Thermosphere and Exosphere
Issue:
Volume 9, Issue 1, March 2021
Pages:
17-20
Received:
27 May 2021
Accepted:
18 June 2021
Published:
25 June 2021
Abstract: The linearized dynamics of the idealized narrow neutral cells at high latitudes in the absence or presence of auroral energy impulse of the type q0 e-at is discussed in the upper atmosphere. The general expression for the oscillation amplitude ∆z of the cells is given by ∆ z=q0 [e-at – cos (ω t) + a sin (ω t)/ω)]/(a2 + ω2) + ν0 sin (ω t)/ω Here ν0 is the cell’s initial velocity, ω is its Brunt - Vaisala frequency which varies from about 1.7x10-2 at 200 km to 1.3x10-2 radians/s at 300 km for an exospheric temperature of 1000 K. The maximum ∆z varies from a few km at 200 km for 1000 K to about 25 km at 300 km for 2000 K. For the observed high- and low-density cells, ω is less and high respectively by around 15% than those in the ambient atmosphere at 200 km in the temperature range of 1000-2000K. In absence of ν0 and q0, the cells are stable in the thermosphere. The oscillations during disturbed conditions, should eventually cease in the presence of existing nonlinear forces like collision frequencies, emission from atomic constituents, heat conduction and losses, which should be further incorporated to provide a framework for their theoretical interpretation and implications for the high latitudinal thermospheric as well for the ionospheric morphology.
Abstract: The linearized dynamics of the idealized narrow neutral cells at high latitudes in the absence or presence of auroral energy impulse of the type q0 e-at is discussed in the upper atmosphere. The general expression for the oscillation amplitude ∆z of the cells is given by ∆ z=q0 [e-at – cos (ω t) + a sin (ω t)/ω)]/(a2 + ω2) + ν0 sin (ω t)/ω Here ν0 ...
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