scholarly journals A study of the gravitational wave pulsar signal with orbital and spindown effects

2006 ◽  
Vol 84 (6-7) ◽  
pp. 607-613
Author(s):  
S R Valluri ◽  
K M Rao ◽  
P Wiegert ◽  
F A Chishtie
Keyword(s):  
Fourier Transform ◽  
Gravitational Wave ◽  
Orbital Motion ◽  
Special Functions ◽  
The Moon ◽  
The Earth ◽  
Source Signal ◽  
Phase Corrections ◽  
The Fourier Transform ◽  
Monochromatic Source

In this work, we present an analytic and a preliminary numerical analysis of the gravitational wave signal from a pulsar that includes simple spindown effects. We estimate the phase corrections to a monochromatic source signal due to rotational and elliptical orbital motion of the Earth, and perturbations due to Jupiter and the Moon. We briefly discuss the Fourier transform of such a signal, expressed in terms of well-known special functions, and its applications. PACKS Nos.: 04.30.-w

scholarly journals A first analysis of the mean motion of CHAMP

2003 ◽  
Vol 1 ◽  
pp. 95-101
Author(s):  
F. Deleflie ◽  
P. Exertier ◽  
P. Berio ◽  
G. Metris ◽  
O. Laurain ◽  
...  
Keyword(s):  
Orbital Motion ◽  
Surface Forces ◽  
The Moon ◽  
Orbital Elements ◽  
Champ Satellite ◽  
Mean Motion ◽  
The Earth ◽  
The Mean ◽  
Low Altitude

Abstract. The present study consists in studying the mean orbital motion of the CHAMP satellite, through a single long arc on a period of time of 200 days in 2001. We actually investigate the sensibility of its mean motion to its accelerometric data, as measures of the surface forces, over that period. In order to accurately determine the mean motion of CHAMP, we use “observed" mean orbital elements computed, by filtering, from 1-day GPS orbits. On the other hand, we use a semi-analytical model to compute the arc. It consists in numerically integrating the effects of the mean potentials (due to the Earth and the Moon and Sun), and the effects of mean surfaces forces acting on the satellite. These later are, in case of CHAMP, provided by an averaging of the Gauss system of equations. Results of the fit of the long arc give a relative sensibility of about 10-3, although our gravitational mean model is not well suited to describe very low altitude orbits. This technique, which is purely dynamical, enables us to control the decreasing of the trajectory altitude, as a possibility to validate accelerometric data on a long term basis.Key words. Mean orbital motion, accelerometric data

Chebyshev-derived spindown parameters for gravitational wave signals from pulsars

2008 ◽  
Vol 86 (4) ◽  
pp. 597-600 ◽  
Author(s):  
S R Valluri ◽  
M D Fried
Keyword(s):  
Fourier Transform ◽  
Gravitational Wave ◽  
Master Equation ◽  
Chebyshev Polynomial ◽  
Polynomial Method ◽  
Frequency Pattern ◽  
Time Frequency ◽  
The Fourier Transform

The master equation described by Badri Krishnan et al. (Phys Rev. D, 70, 082001 (2004)) for the time-frequency pattern using the F-statistic is studied in the context of Chebyshev-polynomial modified spindown parameters for the case of gravitational wave pulsar signals. The Chebyshev-polynomial method enables an analytic and numeric evaluation of the Fourier transform (FT) for both the non-demodulated and F-statistic demodulated FT.PACS Nos.: 04.30.Tv, 95.85.sz, 02.30.Gp, 02.40.Re

Index to Volume 277

1975 ◽  
Vol 277 (1274) ◽  
pp. 649-649
Keyword(s):  
Orbital Motion ◽  
Lunar Orbit ◽  
Artificial Satellites ◽  
Time Interval ◽  
The Sun ◽  
The Moon ◽  
Slight Effect ◽  
The Earth ◽  
Westerly Direction ◽  
Complete Revolution

Dr R. R. Newton has notified the following correction to his contribution. The paragraph at the bottom of page 16 and the top of page 17 should read: The node of the lunar orbit rotates in a westerly direction around the plane of the ecliptic, making a complete revolution in about 18.61 years. This motion, and this time interval, are important in eclipse theory, as we shall discuss in the next section. This motion results almost entirely from the perturbation of the Sun’s gravitation on the Moon’s orbital motion. The Earth’s equatorial bulge, which is almost entirely responsible for the motion of the nodes of artificial satellites near the Earth, has only a slight effect on a satellite as distant as the Moon.

scholarly journals Theory of the Libration of the Moon

1983 ◽  
Vol 74 ◽  
pp. 37-37
Author(s):  
M. Dubois-Moons
Keyword(s):  
Gravity Field ◽  
Orbital Motion ◽  
Lunar Theory ◽  
The Sun ◽  
Lunar Gravity ◽  
The Moon ◽  
Fourth Degree ◽  
Lunar Gravity Field ◽  
The Earth ◽  
Second Degree

AbstractThe paper presents a new theory of the libration of the Moon, completely analytical with respect to the harmonic coefficients of the lunar gravity field. This field is represented through its fourth degree harmonics for the torque due to the Earth (the second degree for the torque due to the Sun). The Moon is assumed to be rigid and its orbital motion is described by the ELP 2000 solution (Chapront and Chapront-Touzé 1981) for the main problem of lunar theory with planetary perturbations and influence of the non-sphericity of the Earth. Comparisons with other theories (Migus 1980 and Eckhardt 1981) are also presented.

scholarly journals Is there any connection between solar activity and earthquakes?

2020 ◽  
Vol 26 (5) ◽  
pp. 90-102
Author(s):  
I.E. Vasylieva ◽  
Keyword(s):  
Fourier Transform ◽  
Solar Activity ◽  
Seismic Activity ◽  
Frequency Of Occurrence ◽  
Direct Connection ◽  
Time Intervals ◽  
The Earth ◽  
The Fourier Transform ◽  
Overlapping Method ◽  
Local Noon

A possible relationship between solar activity and the seismic activity of the Earth is considered. We analyzed the frequency of occurrence of earthquakes of various magnitudes with the Fourier transform: for M ≥ 7 over the period 1900—2019 and for 2.5 ≤ M ≤ 7 over the period 1973–2019. The average annual, monthly, and daily values of the solar-terrestrial variables, the number of earthquakes with intensities that fall within the specified boundaries are calculated. The epoch overlapping method was used to analyze the possible relationship between the Wolf numbers and the number of earthquakes at the corresponding moment in the cycle. 4 periods of each solar cycle were identified: the phase of ascending, maximum, descending, and minimum. Earthquakes over the entire globe and in the regions of extension and compression of the earth's crust were analyzed for each phase. No statistically significant dependencies between solar-terrestrial variables and earthquake initiation were found for all time intervals and all selected earthquake magnitudes. An interesting fact was established concerning the change in the number of earthquakes at different periods of the day. The number of earthquakes in the nighttime appreciably increases (by ~ 10 %) compared to the daytime. A slight increase in the number of earthquakes after local noon was also detected. We could not confirm the existence of a direct connection between solar activity and the seismic activity of the Earth, but we cannot also claim that such a connection does not exist.

scholarly journals WILL IT BE POSSIBLE TO MEASURE INTRINSIC GRAVITOMAGNETISM WITH LUNAR LASER RANGING?

2009 ◽  
Vol 18 (08) ◽  
pp. 1319-1326 ◽  
Author(s):  
LORENZO IORIO
Keyword(s):  
Orbital Motion ◽  
Radial Component ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Gravitomagnetic Field ◽  
Lunar Laser ◽  
Short Period ◽  
Orbital Revolution

In this paper we mainly explore the possibility of measuring the action of the intrinsic gravitomagnetic field of the rotating Earth on the orbital motion of the Moon with the lunar laser ranging (LLR) technique. Expected improvements in it should push the precision in measuring the Earth–Moon range to the mm level; the present-day root mean square (RMS) accuracy in reconstructing the radial component of the lunar orbit is about 2 cm; its harmonic terms can be determined at the mm level. The current uncertainty in measuring the lunar precession rates is about 10-1 milliarcseconds per year. The Lense–Thirring secular — i.e. averaged over one orbital period — precessions of the node and the perigee of the Moon induced by the Earth's spin angular momentum amount to 10-3 milliarcseconds per year, yielding transverse and normal shifts of 10-1-10-2 cm yr-1. In the radial direction there is only a short-period — i.e. nonaveraged over one orbital revolution — oscillation with an amplitude of 10-5 m. Major limitations come also from some systematic errors induced by orbital perturbations of classical origin, such as the secular precessions induced by the Sun and the oblateness of the Moon, whose mismodeled parts are several times larger than the Lense–Thirring signal. The present analysis holds also for the Lue–Starkman perigee precession due to the multidimensional braneworld model by Dvali, Gabadadze and Porrati (DGP); indeed, it amounts to about 5 × 10-3 milliarcseconds per year.

II. Early history of the Moon - Dynamical capture of the Moon by the Earth

1967 ◽  
Vol 296 (1446) ◽  
pp. 285-292 ◽  
Keyword(s):  
Orbital Motion ◽  
The Body ◽  
Rotational Instability ◽  
The Moon ◽  
Body System ◽  
The Earth ◽  
Geometrical Features ◽  
Planetary Orbits ◽  
History Of ◽  
Three Body

The process of extracting the Moon from the Earth through some mechanism of rotational instability, and one that can also set it into orbital motion round the Earth, has nowadays come to be widely recognized as almost certainly dynamically impossible. Accordingly ideas have turned towards the notion that the Moon originated as a separate planet and was later captured by the Earth. It is reasonable to conjecture beforehand that this could happen in a three-body system consisting of the Sun, Earth, and Moon, but nevertheless it is of interest and importance to establish that such a capture is possible within the laws of dynamics, and moreover we should like to have some numerical indications of the initial dimensions that the lunar orbit would have on the basis of such an origin. Dissipative action may well be operative upon the planetary orbits to a minute extent, and there may have been eras in the history of the solar system when such dissipation was greater than average, but it seems certain that the main geometrical features of the process of capture of a satellite must in the final stages be governed purely by dynamical forces arising only from the mutual attractions of the bodies. Thus the first stage towards demonstrating the possibility of capture will be to study motions under purely conservative dynamical forces. Considerations of a phase-space or ergodic nature suggest that if the moon were captured in such a way it would eventually escape again, but we cannot on such a basis form any notion of the period of time for which the body might remain a satellite before escaping again. Actual numerical instances are needed to determine this.

scholarly journals Fourier transform of hydrogen-type atomic orbitals

2018 ◽  
Vol 96 (7) ◽  
pp. 724-726 ◽  
Author(s):  
N. Yükçü ◽  
S.A. Yükçü
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Transform Method ◽  
Atomic Orbitals ◽  
Mathematical Properties ◽  
The Fourier Transform ◽  
Exponential Type Orbital ◽  
Analytical Expressions

Hydrogen-type atomic orbitals (HTOs) are an important type of exponential-type orbital. These orbitals have some mathematical properties and they are used usually in the theoretical atomic and molecular investigations as special functions to figure out analytical expressions. The Fourier transform method is a great way to convert basis functions into the momentum space, because their Fourier transforms are easier to use in mathematical calculations. In this paper, we obtain new and useful mathematical representations for the Fourier transform of HTOs related with Gegenbauer polynomials and hypergeometric functions, by using recurrence relations of Laguerre polynomials, Rayleigh expansion and some properties of normalized HTOs.

scholarly journals Remarks on the Restoration of Occultation Observations

1971 ◽  
Vol 2 ◽  
pp. 662-667 ◽  
Author(s):  
Terence J. Deeming
Keyword(s):  
Point Source ◽  
Diffraction Pattern ◽  
Orbital Motion ◽  
Monochromatic Light ◽  
Fresnel Diffraction ◽  
Straight Edge ◽  
The Moon ◽  
Linear Scale ◽  
The Earth ◽  
Rotation Of The Earth

If the limb of the Moon can be regarded as a straight edge, then the diffraction pattern of a point source which it produces at the distance of the Earth is the well known Fresnel diffraction pattern. Observations of stellar occultations reveal the variation of intensity with time as the diffraction pattern passes across the detector due to the orbital motion of the Moon and the rotation of the Earth. The linear scale of the diffraction pattern in monochromatic light depends on both the wavelength of observation, λ, and on the distance of the Moon, D, so that the scale is proportional to (λD)1/2.

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