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1.
This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable. 相似文献
2.
Jagadish Singh 《Astrophysics and Space Science》2013,346(1):41-50
This study explores the effects of small perturbations in the Coriolis and centrifugal forces, radiation pressures and triaxiality of the two stars (primaries) on the position and stability of an infinitesimal mass (third body) in the framework of the planar circular restricted three-body problem (R3BP). it is observed that the positions of the usual five (three collinear and two triangular) equilibrium points are affected by the radiation, triaxiality and a small perturbation in the centrifugal force, but are unaffected by that of the Coriolis force. The collinear points are found to remain unstable, while the triangular points are seen to be stable for 0<μ<μ c and unstable for $\mu_{c} \le\mu\le\frac{1}{2}$ , where μ c is the critical mass ratio influenced by the small perturbations in the Coriolis and centrifugal forces, radiation and triaxiality. It is also noticed that the former one and all the latter three posses stabilizing and destabilizing behavior respectively. Therefore, the overall effect is that the size of the region of stability decreases with increase in the values of the parameters involved. 相似文献
3.
The existence and stability of a test particle around the equilibrium points in the restricted three-body problem is generalized
to include the effect of variations in oblateness of the first primary, small perturbations ϵ and ϵ′ given in the Coriolis and centrifugal forces α and β respectively, and radiation pressure of the second primary; in the case when the primaries vary their masses with time in
accordance with the combined Meshcherskii law. For the autonomized system, we use a numerical evidence to compute the positions
of the collinear points L
2κ
, which exist for 0<κ<∞, where κ is a constant of a particular integral of the Gylden-Meshcherskii problem; oblateness of the first primary; radiation pressure
of the second primary; the mass parameter ν and small perturbation in the centrifugal force. Real out of plane equilibrium points exist only for κ>1, provided the abscissae
x < \fracn(k-1)b\xi<\frac{\nu(\kappa-1)}{\beta}. In the case of the triangular points, it is seen that these points exist for ϵ′<κ<∞ and are affected by the oblateness term, radiation pressure and the mass parameter. The linear stability of these equilibrium
points is examined. It is seen that the collinear points L
2κ
are stable for very small κ and the involved parameters, while the out of plane equilibrium points are unstable. The conditional stability of the triangular
points depends on all the system parameters. Further, it is seen in the case of the triangular points, that the stabilizing
or destabilizing behavior of the oblateness coefficient is controlled by κ, while those of the small perturbations depends on κ and whether these perturbations are positive or negative. However, the destabilizing behavior of the radiation pressure remains
unaltered but grows weak or strong with increase or decrease in κ. This study reveals that oblateness coefficient can exhibit a stabilizing tendency in a certain range of κ, as against the findings of the RTBP with constant masses. Interestingly, in the region of stable motion, these parameters
are void for
k = \frac43\kappa=\frac{4}{3}. The decrease, increase or non existence in the region of stability of the triangular points depends on κ, oblateness of the first primary, small perturbations and the radiation pressure of the second body, as it is seen that the
increasing region of stability becomes decreasing, while the decreasing region becomes increasing due to the inclusion of
oblateness of the first primary. 相似文献
4.
Clovis Jacinto de Matos 《Astrophysics and Space Science》2012,337(1):353-354
The phenomenological nature of a new gravitational type interaction between two different bodies derived from Verlinde’s entropic
approach to gravitation in combination with Sorkin’s definition of Universe’s quantum information content, is investigated.
Assuming that the energy stored in this entropic gravitational field is dissipated under the form of gravitational waves and
that the Heisenberg principle holds for this system, one calculates a possible value for an absolute minimum time scale in
nature
t = \frac1516 \fracL1/2(h/2p) Gc4 ~ 9.27×10-105\tau=\frac{15}{16} \frac{\Lambda^{1/2}\hbar G}{c^{4}}\sim9.27\times10^{-105} seconds, which is much smaller than the Planck time t
P
=(ħG/c
5)1/2∼5.38×10−44 seconds. This appears together with an absolute possible maximum value for Newtonian gravitational forces generated by matter
Fg=\frac3230\fracc7L (h/2p) G2 ~ 3.84×10165F_{g}=\frac{32}{30}\frac{c^{7}}{\Lambda \hbar G^{2}}\sim 3.84\times 10^{165} Newtons, which is much higher than the gravitational field between two Planck masses separated by the Planck length F
gP
=c
4/G∼1.21×1044 Newtons. 相似文献
5.
We have examined the effects of oblateness up to J 4 of the less massive primary and gravitational potential from a circum-binary belt on the linear stability of triangular equilibrium points in the circular restricted three-body problem, when the more massive primary emits electromagnetic radiation impinging on the other bodies of the system. Using analytical and numerical methods, we have found the triangular equilibrium points and examined their linear stability. The triangular equilibrium points move towards the line joining the primaries in the presence of any of these perturbations, except in the presence of oblateness up to J 4 where the points move away from the line joining the primaries. It is observed that the triangular points are stable for 0 < μ < μ c and unstable for \(\mu_{\mathrm{c}} \le \mu \le \frac {1}{2},\) where μ c is the critical mass ratio affected by the oblateness up to J 4 of the less massive primary, electromagnetic radiation of the more massive primary and potential from the belt, all of which have destabilizing tendencies, except the coefficient J4 and the potential from the belt. A practical application of this model could be the study of motion of a dust particle near a radiating star and an oblate body surrounded by a belt. 相似文献
6.
This paper studies the motion of an infinitesimal mass in the framework of the restricted three-body problem (R3BP) under the assumption that the primaries of the system are radiating-oblate spheroids, enclosed by a circular cluster of material points. It examines the effects of radiation and oblateness up to J 4 of the primaries and the potential created by the circular cluster, on the linear stability of the liberation locations of the infinitesimal mass. The liberation points are found to be stable for 0<μ<μ c and unstable for $\mu_{c}\le\mu\le\frac{1}{2}$ , where μ c is the critical mass value depending on terms which involve parameters that characterize the oblateness, radiation forces and the circular cluster of material points. The oblateness up to J 4 of the primaries and the gravitational potential from the circular cluster of material points have stabilizing propensities, while the radiation of the primaries and the oblateness up to J 2 of the primaries have destabilizing tendencies. The combined effect of these perturbations on the stability of the triangular liberation points is that, it has stabilizing propensity. 相似文献
7.
We have studied a modified version of the classical restricted three-body problem (CR3BP) where both primaries are considered as oblate spheroids and are surrounded by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effects of oblateness of both primaries up to zonal harmonic J 4; together with gravitational potential from the circular cluster of material points on the existence and linear stability of the triangular equilibrium points. It is found that, the triangular points are stable for 0<μ<μ c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$ , where μ c is the critical mass ratio affected by the oblateness up to J 4 of the primaries and potential from the circular cluster of material points. The coefficient J 4 has stabilizing tendency, while J 2 and the potential from the circular cluster of material points have destabilizing tendency. A practical application of this model could be the study of the motion of a dust particle near oblate bodies surrounded by a circular cluster of material points. 相似文献
8.
In this paper, we study the existence of libration points and their linear stability when the three participating bodies are axisymmetric and the primaries are radiating, we found that the collinear points remain unstable, it is further seen that the triangular points are stable for 0<μ<μ c , and unstable for where , it is also observed that for these points the range of stability will decrease. In addition to this we have studied periodic orbits around these points in the range 0<μ<μ c , we found that these orbits are elliptical; the frequencies of long and short orbits of the periodic motion are affected by the terms which involve parameters that characterize the oblateness and radiation repulsive forces. The implication is that the period of long periodic orbits adjusts with the change in its frequency while the period of short periodic orbit will decrease. 相似文献
9.
This paper investigates the motion of an infinitesimal body in the generalized restricted three-body problem. It is generalized in the sense that both primaries are radiating, oblate bodies, together with the effect of gravitational potential from a belt. It derives equations of the motion, locates positions of the equilibrium points and examines their linear stability. It has been found that, in addition to the usual five equilibrium points, there appear two new collinear points L n1, L n2 due to the potential from the belt, and in the presence of all these perturbations, the equilibrium points L 1, L 3 come nearer to the primaries; while L 2, L 4, L 5, L n1 move towards the less massive primary and L n2 moves away from it. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ c and unstable for $\mu_{c} \le\mu\le\frac{1}{2}$ , where μ c is the critical mass ratio influenced by the oblateness and radiation of the primaries and potential from the belt, all of which have destabilizing tendency. A practical application of this model could be the study of the motion of a dust particle near the oblate, radiating binary stars systems surrounded by a belt. 相似文献
10.
It is surprising that we hardly know only 4% of the universe. Rest of the universe is made up of 73% of dark-energy and 23%
of dark-matter. Dark-energy is responsible for acceleration of the expanding universe; whereas dark-matter is said to be necessary
as extra-mass of bizarre-properties to explain the anomalous rotational-velocity of galaxy. Though the existence of dark-energy
has gradually been accepted in scientific community, but the candidates for dark-matter have not been found as yet and are
too crazy to be accepted. Thus, it is obvious to look for an alternative theory in place of dark-matter. Milgrom (Astrophys.
J. 270:365, 1983a; 270:371, 1983b) has suggested a ‘Modified Newtonian Dynamics (MOND)’ which appears to be highly successful for explaining the anomalous
rotational-velocity. But unfortunately MOND lacks theoretical support. The MOND, in-fact, is (empirical) modification of Newtonian-Dynamics
through modification in the kinematical acceleration term ‘a’ (which is normally taken as
a=\fracv2ra=\frac{v^{2}}{r}) as effective kinematic acceleration
aeffective = a m(\fracaa0)a_{\mathit{effective}} = a \mu(\frac{a}{a_{0}}), wherein the μ-function is 1 for usual-values of accelerations but equals to
\fracaa0 ( << 1)\frac{a}{a_{0}} (\ll1) if the acceleration ‘a’ is extremely-low lower than a critical value a
0(10−10 m/s2). In the present paper, a novel variant of MOND is proposed with theoretical backing; wherein with the consideration of universe’s
acceleration a
d
due to dark-energy, a new type of μ-function on theoretical-basis emerges out leading to
aeffective = a(1 -K \fraca0a)a_{\mathit{effective}} = a(1 -K \frac{a_{0}}{a}). The proposed theoretical-MOND model too is able to fairly explain ‘qualitatively’ the more-or-less ‘flat’ velocity-curve
of galaxy-rotation, and is also able to predict a dip (minimum) on the curve. 相似文献
11.
We have investigated an improved version of the classic restricted three-body problem where both primaries are considered oblate and are enclosed by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effect on the number and on the linear stability of the equilibrium locations of the small particle due to both, the primaries’ oblateness and the potential created by the circular cluster. We have drawn the zero-velocity surfaces and we have found that in addition to the usual five Lagrangian equilibrium points of the classic restricted three-body problem, there exist two new collinear points L n1,L n2 due to the potential from the circular cluster of material points. Numerical investigations reveal that with the increase in the mass of the circular cluster of material points, L n2 comes nearer to the more massive primary, while L n1 moves away from it. Owing to oblateness of the bodies, L n1 comes nearer to the more massive primary, while L n2 moves towards the less massive primary. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$ , where μ c is the critical mass ratio influenced by oblateness of the primaries and the potential from the circular cluster of material points. The oblateness and the circular cluster of material points have destabilizing tendency. 相似文献
12.
Naveen Bijalwan 《Astrophysics and Space Science》2011,336(2):413-418
Recently, Bijalwan (Astrophys. Space Sci., doi:, 2011a) discussed charged fluid spheres with pressure while Bijalwan and Gupta (Astrophys. Space Sci. 317, 251–260, 2008) suggested using a monotonically decreasing function f to generate all possible physically viable charged analogues of Schwarzschild interior solutions analytically. They discussed
some previously known and new solutions for Schwarzschild parameter
u( = \fracGMc2a ) £ 0.142u( =\frac{GM}{c^{2}a} ) \le 0.142, a being radius of star. In this paper we investigate wide range of u by generating a class of solutions that are well behaved and suitable for modeling Neutron star charge matter. We have exploited
the range u≤0.142 by considering pressure p=p(ω) and
f = ( f0(1 - \fracR2(1 - w)a2) +fa\fracR2(1 - w)a2 )f = ( f_{0}(1 - \frac{R^{2}(1 - \omega )}{a^{2}}) +f_{a}\frac{R^{2}(1 - \omega )}{a^{2}} ), where
w = 1 -\fracr2R2\omega = 1 -\frac{r^{2}}{R^{2}} to explore new class of solutions. Hence, class of charged analogues of Schwarzschild interior is found for barotropic equation
of state relating the radial pressure to the energy density. The analytical models thus found are well behaved with surface
red shift z
s
≤0.181, central red shift z
c
≤0.282, mass to radius ratio M/a≤0.149, total charge to total mass ratio e/M≤0.807 and satisfy Andreasson’s (Commun. Math. Phys. 288, 715–730, 2009) stability condition. Red-shift, velocity of sound and p/c
2
ρ are monotonically decreasing towards the surface while adiabatic index is monotonically increasing. The maximum mass found
to be 1.512 M
Θ with linear dimension 14.964 km. Class of charged analogues of Schwarzschild interior discussed in this paper doesn’t have
neutral counter part. These solutions completely describe interior of a stable Neutron star charge matter since at centre
the charge distribution is zero, e/M≤0.807 and a typical neutral Neutron star has mass between 1.35 and about 2.1 solar mass, with a corresponding radius of about
12 km (Kiziltan et al., [astro-ph.GA], 2010). 相似文献
13.
The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) gives us a chance to investigate the theoretical Neupert effect using the correlation between the thermal-energy
derivative and the nonthermal energy, or the thermal energy and the integral nonthermal energy. Based on this concept, we
analyze four M-class RHESSI flares on 13 November 2003, 4 November 2004, 3 and 25 August 2005. According to the evolution
of the temperature [T], emission measure [EM], and thermal energy [E
th], each event is divided into three phases during the nonthermal-energy input [
\frac dEnthdt\frac {\mathrm{d}E_{\mathrm{nth}}}{\mathrm{d}t} in the units of erg s−1]. Phase 1 is identified as the interval before the temperature maximum, while after the thermal-energy maximum is phase 3,
between them is phase 2. We find that these four flares show the Neupert effect in phase 1, but not in phase 3. The Neupert
effect still works well in the second phase, although the cooling becomes slightly important. We define the parameter μ in the relation of
\fracdEthdt=m\fracdEnth(t)dt\frac{\mathrm {d}E_{\mathrm{th}}}{\mathrm{d}t}=\mu\frac{\mathrm{d}E_{\mathrm {nth}}(t)}{\mathrm{d}t} or
Eth(t0)=mò0t0\fracdEnth(t)dt dtE_{\mathrm{th}}(t_{0})=\mu\int_{0}^{t_{0}}\frac{\mathrm{d}E_{\mathrm{nth}}(t)}{\mathrm{d}t}\,\mathrm{d}t when the cooling is ignored in phase 1. Considering the uncertainties in estimating the energy from the observations, it
is not possible to precisely determine the fraction of the known energy in the nonthermal electrons transformed into the thermal
energy of the hottest plasma observed by RHESSI. After a rough estimate of the flare volume and the assumption of the filling
factor, we investigate the parameter μ in these four events. Its value ranges from 0.02 to 0.20, indicating that a small fraction (2% – 20%) of the nonthermal energy
can be efficiently transformed into thermal energy, which is traced by the soft X-ray emission, and the bulk of the energy
is lost possibly due to cooling. 相似文献
14.
This paper deals with the existence of libration points and their linear stability when the more massive primary is radiating and the smaller is an oblate spheroid. Our study includes the effects of oblateness of $\bar{J}_{2i}$ (i=1,2) with respect to the smaller primary in the restricted three-body problem. Under combining the perturbed forces that were mentioned before, the collinear points remain unstable and the triangular points are stable for 0<μ<μ c , and unstable in the range $\mu_{c} \le\mu\le\frac{1}{2}$ , where $\mu_{c} \in(0,\frac{1}{2})$ , it is also observed that for these points the range of stability will decrease. The relations for periodic orbits around five libration points with their semimajor, semiminor axes, eccentricities, the frequencies of orbits and periods are found, furthermore for the orbits around the triangular points the orientation and the coefficients of long and short periodic terms also are found in the range 0<μ<μ c . 相似文献
15.
The aim of this paper is to determine the flux emergence rate due to small-scale magnetic features in the quiet Sun using
high-resolution Hinode SOT NFI data. Small-scale magnetic features are identified in the data using two different feature identification methods
(clumping and downhill); then three methods are applied to detect flux emergence events. The distribution of the intranetwork
peak emerged fluxes is determined. When combined with previous emergence results, from ephemeral regions to sunspots, the
distribution of all fluxes are found to follow a power-law distribution which spans nearly seven orders of magnitude in flux
(1016 – 1023 Mx) and 18 orders of magnitude in frequency. The power-law fit to all these data is of the form
\fracdNdY = \fracn0Y0\fracYY0-2.7,\frac{\mathrm{d}N}{\mathrm{d}\Psi} = \frac{n_0}{\Psi_0}\frac{\Psi}{\Psi _0}^{-2.7}, 相似文献
16.
Arthur C. Reardon 《Astrophysics and Space Science》2011,336(2):369-377
Detailed analyses by independent research groups over several decades reveal a significant discrepancy between the observed
rate of periastron advance in the detached eclipsing binary star systems DI Herculis and V541 Cygni and the values theoretically
predicted from the combined classical and general relativistic effects. A modification to Newton’s gravitational theory is
proposed in this investigation to account for these discrepancies, and is represented by
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