scholarly journals A Comparison of Averaged and Full Models to Study the Third-Body Perturbation

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Carlos Renato Huaura Solórzano ◽  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Initial Conditions ◽  
Artificial Satellite ◽  
Main Body ◽  
Long Term Effects ◽  
Third Body ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Averaged Models ◽  
Averaged Model

The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made.

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

scholarly journals Third-Body Perturbation Using a Single Averaged Model: Application in Nonsingular Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Carlos Renato Huaura Solórzano ◽  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Semimajor Axis ◽  
The Moon ◽  
Orbital Elements ◽  
Third Body ◽  
Short Period ◽  
Time Histories ◽  
Physical Reasons ◽  
Averaged Model ◽  
The Mathematical Model ◽  
Third Body Perturbation

The Lagrange's planetary equations written in terms of the classical orbital elements have the disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical model used and do not have physical reasons. In this paper, we studied the third-body perturbation using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the inclination.

On the Probability Densities of the Output of Some Random Systems

1961 ◽  
Vol 28 (2) ◽  
pp. 161-164 ◽  
Author(s):  
Frank Kozin
Keyword(s):  
Probability Density ◽  
Initial Conditions ◽  
Random Systems ◽  
Mean Motion ◽  
Second Moments ◽  
Ensemble Mean ◽  
Probability Densities ◽  
Mean And Variance ◽  
The Mean ◽  
Spring Constants

The probability density, mean, and variance of the displacement of simple linear one-degree-of-freedom systems are investigated when the spring constants and the initial conditions are random variables. The ensemble mean motion is found to be considerably different from the “mean” motion obtained by first averaging over the spring constants. Furthermore, it is found that only the first and second moments of the initial conditions affect the first and second moments of the displacement.

scholarly journals Structure of Comets and the Possible Origin of Faint Asteroids

1971 ◽  
Vol 12 ◽  
pp. 465-469
Author(s):  
V. Vanýsek
Keyword(s):  
Final Stage ◽  
Heliocentric Distance ◽  
Outer Boundary ◽  
Very Old ◽  
Cometary Nuclei ◽  
Mean Motion ◽  
Short Period ◽  
Asteroidal Belt ◽  
The Mean

It is shown that very old and still active icy-conglomerate or “clathrate” cometary nuclei may exist at the outer boundary of the asteroidal belt and belong to the group of relatively stable “outer” short-period comets of which only a small fraction have been discovered or recognized as cometary objects.hich is much more convincing, it explains their brightness dependence on the heliocentric distance.The search for these comets among very faint asteroids with the mean motion μ ≤ 600”, and the study of their behavior could be very important to our knowledge about the final stage of cometary nuclei.

FROZEN ORBITS AROUND EUROPA

2012 ◽  
Vol 22 (10) ◽  
pp. 1250240 ◽  
Author(s):  
J. P. S. CARVALHO ◽  
D. C. MOURÃO ◽  
A. ELIPE ◽  
R. VILHENA DE MORAES ◽  
A. F. B. A. PRADO
Keyword(s):  
Artificial Satellite ◽  
Analytical Theory ◽  
Third Body ◽  
Planetary Satellite ◽  
Frozen Orbits ◽  
Satellites Of Jupiter ◽  
Long Lifetime ◽  
Low Altitude ◽  
Natural Satellites ◽  
Averaged Model

Low-altitude, near-polar orbits are very desirable for scientific missions to study the natural satellites of the planets of the Solar System, such as Europa, that is one of the natural satellites of Jupiter. The problem is analyzed considering that an artificial satellite is orbiting Europa and that this spacecraft is perturbed by the nonuniform distribution of mass of the planetary satellite (J2, J3, C22) and by the gravitational attraction of the third-body. We present an analytical theory using the averaged model and applications were done by performing numerical integrations of the analytical equations developed. Using the averaged method, several frozen orbits were obtained. Some of them has low inclination, low altitude and long lifetime. Numerical simulations are performed using the software Mercury, to compare the results obtained using the analytical theory.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

scholarly journals The lunar and solar diurnal variations of water-level in a well at Kew observatory, Richmond

1918 ◽  
Vol 94 (663) ◽  
pp. 476-478
Keyword(s):  
Water Level ◽  
Royal Society ◽  
Correlation Coefficients ◽  
Barometric Pressure ◽  
Diurnal Variations ◽  
Range Of Movement ◽  
Nearest Point ◽  
Similar Relation ◽  
Short Period ◽  
The Mean

In a paper communicated to the Royal Meteorological Society, it was shown that the experimental well at Kew Observatory responded to the lunar fortnightly oscillation of mean level in the River Thames, which is 300 yards from the Observatory at its nearest point. The sensitiveness of the water-level to barometric pressure has also been investigated, and the results have been given in a paper recently read before the Royal Society. The present paper deals with the effects of the short-period tides in the solar and lunar series, S 1 , S 2 , S 3 , S 4 , and M 1 , M 2 , M 3 , M 4 . Two-hourly measurements, both in lunar and solar time, were made on the traces obtained during the first two years, August, 1914-August, 1916, omitting days of very irregular movement. Monthly mean inequalities were then computed. Well marked solar and lunar diurnal variations were found in each month, taking the form of double oscillations with two maxima and two minima during the 24 hours. The range of movement was in each case found to be highly associated with the mean height of the water in the well, the correlation coefficients being 0·89 (lunar) and 0·90 (solar). A similar relation had been previously found to exist in the case of barometric pressure.

scholarly journals Dynamics of Comets

1992 ◽  
Vol 152 ◽  
pp. 255-268 ◽  
Author(s):  
A. Carusi ◽  
G.B. Valsecchi
Keyword(s):  
Molecular Clouds ◽  
Vertical Component ◽  
The Sun ◽  
Giant Molecular Clouds ◽  
Mean Motion Resonances ◽  
Galactic Field ◽  
Mean Motion ◽  
Short Period ◽  
Gravitational Processes

The gravitational processes affecting the dynamics of comets are reviewed. At great distances from the Sun the motion of comets is primarily affected by the vertical component of the galactic field, as well as by encounters with stars and giant molecular clouds. When comets move in the region of the planets, encounters with these can strongly affect their motion. A good fraction of all periodic comets spend some time in temporary libration about mean motion resonances with Jupiter; some comets can be captured by this planet as temporary satellites. Finally, there is a small number of objects with orbital characteristics quite different from those of all other short-period comets.

scholarly journals A modified fluctuation test for elucidating drug resistance in microbial and cancer cells

2020 ◽  
Author(s):  
Pavol Bokes ◽  
Abhyudai Singh
Keyword(s):  
Drug Resistance ◽  
Cancer Cells ◽  
Colony Size ◽  
Random Number ◽  
Initial Conditions ◽  
Fano Factor ◽  
Persister Cells ◽  
Efficient Treatment ◽  
Fluctuation Test ◽  
The Mean

AbstractClonal populations of microbial and cancer cells are often driven into a drug-tolerant persister state in response to drug therapy, and these persisters can subsequently adapt to the new drug environment via genetic and epigenetic mechanisms. Estimating the frequency with which drug-tolerance states arise, and its transition to drug-resistance, is critical for designing efficient treatment schedules. Here we study a stochastic model of cell proliferation where drug-tolerant persister cells transform into a drug-resistant state with a certain adaptation rate, and the resistant cells can then proliferate in the presence of the drug. Assuming a random number of persisters to begin with, we derive an exact analytical expression for the statistical moments and the distribution of the total cell count (i.e., colony size) over time. Interestingly, for Poisson initial conditions the noise in the colony size (as quantified by the Fano factor) becomes independent of the initial condition and only depends on the adaptation rate. Thus, experimentally quantifying the fluctuations in the colony sizes provides an estimate of the adaptation rate, which then can be used to infer the starting persister numbers from the mean colony size. Overall, our analysis introduces a modification of the classical Luria–Delbrück experiment, also called the “Fluctuation Test”, providing a valuable tool to quantify the emergence of drug resistance in cell populations.

scholarly journals The Polar Fields and Time Fluctuations of the General Magnetic Field of the Sun

1971 ◽  
Vol 43 ◽  
pp. 675-695 ◽  
Author(s):  
A. B. Severny
Keyword(s):  
Magnetic Field ◽  
Close Agreement ◽  
Present Knowledge ◽  
Short Time Scale ◽  
The Sun ◽  
Statistical Nature ◽  
General Magnetic Field ◽  
Short Period ◽  
The Mean ◽  
Short Time

In an attempt to summarize the present knowledge on the general magnetic field (gmf) of the Sun we pointed out the fine structure and the statistical nature of the gmf as one of its most important properties. The dipole-like behaviour of the mean polar field strengths is combined sometimes (since 1964) with a bias of the S-polarity flux for both poles. Highly uneven distribution of gmf with latitude and longitude, the disappearance of gmf at the South pole for months, and short period, almost synchronous at both poles, variations in the sign of gmf are pointed out. The fluctuations with time of the mean magnetic field of the Sun seen as a star (as well as mf at different latitudes) shows periodicity connected with the rotation of the Sun and very close agreement with the fluctuations of the interplanetary field (sector structure). The effect of faster rotation of N-polarities as compared with S-polarities as well as the bias of mean solar as well as interplanetary S-polarity fields are also pointed out. The possibility of short time-scale (hours) intrinsic changes in the local pattern of gmf is demonstrated.

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