Semi-analytical theory of motion for the PSR B1257+12 planetary system

A planetary system around the pulsar B1257+12 has three planets A, B and C with the orbital periods of 25, 66 and 98 days, respectively (Wolszczan 1994). Dynamical properties of the system have been thoroughly studied by Rasioet al. (1993) and Malhotra (1993). They demonstrated that the gravitational interactions between planets B and C are significant enough to be detected. In such case, the motion of the system is no longer Keplerian and it is necessary to use a more precise description of motion in order to model the data properly. In this paper we derive a semi-analytical theory of motion assuming that the relative inclination of the orbits is small. We perform numerical simulations to show that our theory sucessfully predicts times of arrival of pulsar pulses and allows a determination of orbital inclinations and hence the masses of planets B and C.

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Mass determination of the 1:3:5 near-resonant planets transiting GJ 9827 (K2-135)

Astronomy and Astrophysics ◽

10.1051/0004-6361/201832872 ◽

2018 ◽

Vol 618 ◽

pp. A116 ◽

Cited By ~ 13

Author(s):

J. Prieto-Arranz ◽

E. Palle ◽

D. Gandolfi ◽

O. Barragán ◽

E. W. Guenther ◽

...

Keyword(s):

Planetary System ◽

Initial Conditions ◽

Dynamical Evolution ◽

Space Mission ◽

Mass Determination ◽

Velocity Measurements ◽

Orbital Periods ◽

The Masses ◽

Better Than

Context. Multiplanet systems are excellent laboratories to test planet formation models as all planets are formed under the same initial conditions. In this context, systems transiting bright stars can play a key role, since planetary masses, radii, and bulk densities can be measured. Aims. GJ 9827 (K2-135) has recently been found to host a tightly packed system consisting of three transiting small planets whose orbital periods of 1.2, 3.6, and 6.2 days are near the 1:3:5 ratio. GJ 9827 hosts the nearest planetary system (~30 pc) detected by NASA’s Kepler or K2 space mission. Its brightness (V = 10.35 mag) makes the star an ideal target for detailed studies of the properties of its planets. Methods. Combining the K2 photometry with high-precision radial-velocity measurements gathered with the FIES, HARPS, and HARPS-N spectrographs we revised the system parameters and derive the masses of the three planets. Results. We find that GJ 9827 b has a mass of Mb = 3.69−0.46+0.48 M⊕ and a radius of Rb = 1.58−0.13+0.14 R⊕, yielding a mean density of ρb = 5.11−1.27+1.74 g cm−3. GJ 9827 c has a mass of Mc = 1.45−0.57+0.58 M⊕, radius of Rc = 1.24−0.11+0.11 R⊕, and a mean density of ρc = 4.13−1.77+2.31 g cm−3. For GJ 9827 d, we derive Md = 1.45−0.57+0.58 M⊕, Rd = 1.24−0.11+0.11 R⊕, and ρd = 1.51−0.53+0.71 g cm−3. Conclusions. GJ 9827 is one of the few known transiting planetary systems for which the masses of all planets have been determined with a precision better than 30%. This system is particularly interesting because all three planets are close to the limit between super-Earths and sub-Neptunes. The planetary bulk compositions are compatible with a scenario where all three planets formed with similar core and atmosphere compositions, and we speculate that while GJ 9827 b and GJ 9827 c lost their atmospheric envelopes, GJ 9827 d maintained its primordial atmosphere, owing to the much lower stellarirradiation. This makes GJ 9827 one of the very few systems where the dynamical evolution and the atmosphericescape can be studied in detail for all planets, helping us to understand how compact systems form and evolve.

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Determination of the masses of Jupiter and Saturn from the motion of Trojans

International Astronomical Union Colloquium ◽

10.1017/s0252921100033789 ◽

1974 ◽

Vol 22 ◽

pp. 93-96

Author(s):

H. Scholl

Keyword(s):

Minor Planets ◽

Planetary Mass ◽

Orbital Periods ◽

The Masses ◽

Two Bodies

The mass of a planet can be determined by the motion of its satellites or by perturbational effects on nearby bodies, such as comets, planets, minor planets. It is well known, for instance, that a body on a nearby orbit which is in close resonance with a planet is suitable for the determination of the planetary mass. In this case the orbital periods of the two bodies are equal or nearly equal to the ratio of small integers (i.e. 1: 1, 2: 1, 3:2).

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From the Oort cloud to Halley-type comets

International Astronomical Union Colloquium ◽

10.1017/s0252921100031638 ◽

1999 ◽

Vol 173 ◽

pp. 327-338 ◽

Cited By ~ 5

Author(s):

J.A. Fernández ◽

T. Gallardo

Keyword(s):

Total Population ◽

Complex Function ◽

Dynamical Evolution ◽

Oort Cloud ◽

Capture Process ◽

Influx Rate ◽

Short Period ◽

Dynamical Properties ◽

Orbital Periods ◽

Probability Of Capture

AbstractThe Oort cloud probably is the source of Halley-type (HT) comets and perhaps of some Jupiter-family (JF) comets. The process of capture of Oort cloud comets into HT comets by planetary perturbations and its efficiency are very important problems in comet ary dynamics. A small fraction of comets coming from the Oort cloud − of about 10−2− are found to become HT comets (orbital periods < 200 yr). The steady-state population of HT comets is a complex function of the influx rate of new comets, the probability of capture and their physical lifetimes. From the discovery rate of active HT comets, their total population can be estimated to be of a few hundreds for perihelion distancesq <2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods < 20 yr) show dynamical properties that do not match the observed properties of JF comets, in particular the distribution of their orbital inclinations, so Oort cloud comets can be ruled out as a suitable source for most JF comets. The scope of this presentation is to review the capture process of new comets into HT and short-period orbits, including the possibility that some of them may become sungrazers during their dynamical evolution.

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Determination of bimodal molar mass distribution functions of polystyrene by photon correlation spectroscopy: numerical simulations and experimental realization in comparison with gel permeation chromatography data

Macromolecules ◽

10.1021/ma00180a022 ◽

1988 ◽

Vol 21 (2) ◽

pp. 415-420 ◽

Cited By ~ 13

Author(s):

Gyula Vancso ◽

Ivan Tomka ◽

Klara Vancso-Polacsek

Keyword(s):

Numerical Simulations ◽

Molar Mass ◽

Photon Correlation Spectroscopy ◽

Gel Permeation Chromatography ◽

Distribution Functions ◽

Correlation Spectroscopy ◽

Photon Correlation ◽

Experimental Realization ◽

Gel Permeation

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Optimal Synchronization of a Memristive Chaotic Circuit

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416500930 ◽

2016 ◽

Vol 26 (06) ◽

pp. 1650093 ◽

Cited By ~ 7

Author(s):

Michaux Kountchou ◽

Patrick Louodop ◽

Samuel Bowong ◽

Hilaire Fotsin ◽

Jurgen Kurths

Keyword(s):

Numerical Simulations ◽

Chaos Synchronization ◽

Chaotic Systems ◽

Analog Circuit ◽

Electronic Circuit ◽

Dynamical Behavior ◽

Circuit Implementation ◽

Chaotic Circuit ◽

Dynamical Properties ◽

Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

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A NUCLEAR MANY-BODY THEORY AT FINITE TEMPERATURE APPLIED TO A PROTONEUTRON STAR

International Journal of Modern Physics E ◽

10.1142/s0218301302000727 ◽

2002 ◽

Vol 11 (02) ◽

pp. 83-104 ◽

Cited By ~ 16

Author(s):

GUILHERME F. MARRANGHELLO ◽

CESAR A. Z. VASCONCELLOS ◽

MANFRED DILLIG ◽

J. A. DE FREITAS PACHECO

Keyword(s):

Phase Transition ◽

Nuclear Matter ◽

Finite Temperature ◽

Degrees Of Freedom ◽

Many Body ◽

Many Body Theory ◽

The Masses ◽

Protoneutron Stars ◽

Protoneutron Star

Thermodynamical properties of nuclear matter are studied in the framework of an effective many-body field theory at finite temperature, considering the Sommerfeld approximation. We perform the calculations by using the nonlinear Boguta and Bodmer model, extended by the inclusion of the fundamental baryon octet and leptonic degrees of freedom. Trapped neutrinos are also included in order to describe protoneutron star properties through the integration of the Tolman–Oppenheimer–Volkoff equations, from which we obtain, beyond the standard relations for the masses and radii of protoneutron stars as functions of the central density, new results of these quantities as functions of temperature. Our predictions include: the determination of an absolute value for the limiting mass of protoneutron stars; new structural aspects on the nuclear matter phase transition via the behavior of the specific heat and, through the inclusion of quark degrees of freedom, the properties of a hadron-quark phase transition and hybrid protoneutron stars

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Numerical simulations of the soft X-ray signals for determination of radial locations of the magnetic islands in the STOR-M tokamak

Radiation Effects and Defects in Solids ◽

10.1080/10420150.2011.615315 ◽

2011 ◽

Vol 166 (10) ◽

pp. 765-773 ◽

Cited By ~ 1

Author(s):

M. Dreval ◽

C. Xiao ◽

A. Hirose

Keyword(s):

Numerical Simulations ◽

Magnetic Islands ◽

X Ray

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A tale of two periods: determination of the orbital ephemeris of the super-Eddington pulsar NGC 7793 P13

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833292 ◽

2018 ◽

Vol 616 ◽

pp. A186 ◽

Cited By ~ 19

Author(s):

F. Fürst ◽

D. J. Walton ◽

M. Heida ◽

F. A. Harrison ◽

D. Barret ◽

...

Keyword(s):

Accretion Disk ◽

Orbital Period ◽

Timing Analysis ◽

X Ray ◽

System Parameters ◽

Orbital Resonance ◽

Photometric Period ◽

Orbital Periods ◽

Analyze Data

We present a timing analysis of multiple XMM-Newton and NuSTAR observations of the ultra-luminous pulsar NGC 7793 P13 spread over its 65 d variability period. We use the measured pulse periods to determine the orbital ephemeris, confirm a long orbital period with Porb = 63.9+0.5−0.6 d, and find an eccentricity of e ≤ 0.15. The orbital signature is imprinted on top of a secular spin-up, which seems to get faster as the source becomes brighter. We also analyze data from dense monitoring of the source with Swift and find an optical photometric period of 63.9 ± 0.5 d and an X-ray flux period of 66.8 ± 0.4 d. The optical period is consistent with the orbital period, while the X-ray flux period is significantly longer. We discuss possible reasons for this discrepancy, which could be due to a super-orbital period caused by a precessing accretion disk or an orbital resonance. We put the orbital period of P13 into context with the orbital periods implied for two other ultra-luminous pulsars, M82 X-2 and NGC 5907 ULX, and discuss possible implications for the system parameters.

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More Dynamical Properties Revealed from a 3D Lorenz-like System

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414501338 ◽

2014 ◽

Vol 24 (10) ◽

pp. 1450133 ◽

Cited By ~ 9

Author(s):

Haijun Wang ◽

Xianyi Li

Keyword(s):

Numerical Simulations ◽

Local Stability ◽

Equilibrium Points ◽

Heteroclinic Orbits ◽

Mathematical Work ◽

Chaotic Attractors ◽

Heteroclinic Cycles ◽

Homoclinic And Heteroclinic Orbits ◽

Dynamical Properties ◽

Theoretical Results

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both "locally" and "globally" and both "finitely" and "infinitely" — to comprehensively explore a given system.

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