First-order theory of weakly eccentric orbital motion

Starting from the analytical theory of perturbed circular motions presented in Celestial Mechanics (Bois, 1994), this paper presents an extended resolution valid also for small eccentricity orbits. The solution is of the first order of a small parameter characterizing the magnitude of disturbing forces. The solution has the form of Fourier series with the coefficients given by iterative formation laws. The solution is free from singularities due to small eccentricity or inclination. As an example of numerical application the equatorial artificial satellite orbits are analyzed. For some high satellite orbits with small eccentricity the difference between the numerical integration and the analytical model does not exceed few centimeters per one revolution.On leave from Astronomical Observatory of A. Mickiewicz University, Soneczna 36, PL60-286 Pozna, Poland.     

Short-Term Periodicities in the Time Series of Solar Radio Emissions at Different Solar Altitudes

A spectral analysis of the time series of daily values of 12 parameters, namely, ten solar radio emissions in the range 275–1755 MHz, 2800 MHz solar radio flux, and sunspot numbers for six continuous intervals of 132 values each during June 1997–July 1999 showed considerable differences from one interval to the next, indicating a nonstationary nature. A 27-day periodicity was noticed in Interval 2 (26.8 days), 3 (27.0 days), 5 (25.5 days), 6 (27.0 days). Other periodicities were near 11.4, 12.3, 13.3, 14.5, 15.5, 16.5, 35, 40, 50–70 days. Periodicities were very similar in a large vertical span of the coronal region corresponding to 670–1755 MHz. Above this region, the homogeneity disappeared. Below this region, there were complications and distortions due to localized solar surface phenomena.     

The stability parameters of three-body periodic orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear iso-energetic stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of horizontally critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These critical-critical orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination.     

Сопоставление модели карлсона с моделью сплошной среды

, (1962, 1963) . , (1) (2) .     

Diffuse cosmic gamma rays observed at an equatorial balloon altitude

A 3×3 NaI(T1) crystal-photomultiplier assembly with a 4 charged particle anticoincidence shield is used to determine the gamma ray spectrum in the energy region of about 100 keV to 8.5 MeV at a balloon altitude of 4.7 g cm^–2 over Hyderabad, India (geomagnetic latitude 8°N). The atmospheric growth curves are used to obtain the contribution of the diffuse cosmic gamma ray flux in the above energy range. The cosmic photon flux thus deduced up to about 8.5 MeV is consistent with a continuation of the power law spectrum observed at energies between 20 and 200 keV with an index of –2.3, and hence contradicts the flattening trend observed in ERS-18 at an energy of a few MeV.Results presented at the IAU/COSPAR symposium No. 55 on X-and Gamma-Ray Astronomy Madrid, 11–13th May, 1972.     

О природе всплесков γ-излучения

- . , - . -.     

Expansions of the derivatives of the disturbing function in planetary problems

A method is suggested to develop literal expansions of derivatives of the disturbing function especially for the case of large values of the major axis ratio . The series remain convergent as well if =1, unless the eccentricities vanish at the same time. The treatment holds true in the case when usual analytical expansions are not valid, that is if the orbits have points equidistant from the primary. The general case is considered too, the intersecting orbits being included.     

ОJ 287: Поляризационное и фотометрическое поведение В 1971–1976 гг

J 287 1972–1976. , . . J ( ), () . (₀=80°) . J 287 ¶ . p=42.8%, ₀=101°. (50%).     

Оь излучении звезд типа Т Тельца в далеком ельтрафиоле те

, oqn ANS (1500–3300 Å) , I , 3–15 . , <2000 Å nepexo , 1.5 MB . ₀ , . .     

Имп␣льсное γ-излучение нейтронных, коллапсирующих qiх qi qsверхновых qzвезд

qp qz : (1) -, qi , (2) - (R=0.01–0.1R ) (3) - . qs. (1) - 0.1 10^–4 cm ^–2, . - . (2) 10⁸ . . 10^42–43 , (25 ). 10% - (0.1 ). , , , , , . . (3) , , - . . (2×10⁴¹ ) (10²¹ ). - 10³⁸–10³⁹ , 0.25 . , , qq . - , , .

---

The following three mechanisms of generation of gamma-ray bursts at advanced phases of stellar evolution are considered; (1) gamma-ray bursts as a result of absorption of neutrino propagating through the envelope of a collapsing star, (2) gamma-ray burst due to thermal radiation of external layers of a compact star (R=0.01–0.1R ) heated by powerful shock wave, and (3) gamma-ray burst as a consequence of possible ejection of matter from neutron star at some active phases of its evolution. In the case (1) the gamma-ray flux at the top of the Earth's atmosphere is about 10^–4 (0.1 MeV photons) cm^–2, if a collapsing star is at Galactic distance (10 kpc). It is considerably less than observed one. The observations of such gamma-bursts however would be an important supplement to the direct detection of neutrino radiation from collapsing stars. In the case (2) external layers of a star are heated up to 10⁸ K. As a result we have a short pulse of thermal radiation with total energy of the order of 10^42–43 erg. The main fraction of the radiation is in the X-ray ( 25 keV), about 10% of total energy being radiated in gamma-ray ( 0.1 MeV). The energy of such a burst is sufficient for explaining observed gamma-bursts provided the supernova outburst probably takes place in our Galaxy and as a result we have some trouble with explanation of observed frequency and spectra of gammabursts. In the case (3) ejection from neutron star of chemically nonequilibrium matter results in the intensive gamma-radiation in consequence of superheavy nuclei fission followed by beta-decays and radiative captures of free neutrons. The ejection of matter from neutron stars may be connected with observed jumps of pulsar's periods. The total ejected mass ( 10²¹ g) can be evaluated from increase of kinetic energy ( 2×10⁴¹ erg.) of Crab nebula filaments. The resulting theoretical energy of gammabursts is of the order of 10^38–39 erg. It is in accordance with observations provided the mean distance of gamma-ray sources is about 0.25 kpc. Contrary to the supernova-outburst mechanism in this case we have probably no troubles with frequency and spectra of gamma-bursts. Among the three mechanisms considered above ejection of matter from neutron stars seems to be a more suitable one for explanation of observations.

     

Радиоизлучение Быстрых космических ионов

, . () . , , , . ( ), , , . . (2.7). ( ₁ k ₁ ,V — , — .) (k ₁) (k) §2 ( (2.14)). , (3.6) (3.4), (3.8) . (3.9)–(3.13) ( (3.9), (3.10) (3.11) , (3.12)–(3.13) ). (3.14), (3.16)–(3.19). - . (3.15). ( (4.14)–(4.15)). (4.23)–(4.25). (4.26)–(4.28). §5. , . ((5.5)–(5.6)). , . (5.10) .     

Le développement du potentiel dans le cas d'une densité analytique

The potential of a body of revolution is expanded in a series of spherical functions. It is proved that, for a body with analytical density limited by an analytical surface the coefficients of expansion decrease in geometrical progression.

---

. , , , .

     

Спектр и поляризация источника синхротронного излучения при релятивистском разлете его компонент

, , , . () , . , .     

Stability of the libration points of a rotating triaxial ellipsoid

The problem of stability of the equilibrium points (the libration points) in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid is investigated in the strict sense.In the plane of parameters, depending on the form and dynamical characteristics of the ellipsoids, the regions of stability and instability of the libration points are obtained.It is shown that the libration points of the ellipsoids, the form and dynamical characteristics of which are close to the planets of the solar system, are stable.

---

( ) . , , . , , , .

     

Индуцированное комптоновское рассеяние изотропного излучения релятивистскими электронами

, kT _b mc ² . . , , . E ^–5, - E ², mc ²(kT /mc ²)^1/7. , (>2.10⁵ cm ^–3) . , -, , .     

Об устойчивости лагранжевых решений пространственной эллиптической задачи трех тел

. . ,e, , . . e, . , .

---

Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.

     

Orientation of interstellar and interplanetary grains

The explicit expressions for the orientation distribution function of interstellar and interplanetary dust grains in the anisotropic corpuscular or radiation fluxes, with consideration for the magnetic field influence, are obtained. An orientation is shown to be possible in a medium having an anisotropic temperature, which is usually the case for a non-equilibrium plasma in a magnetic field. It is noted that the small inhomogeneous dust grains should possess a specific rotation of polarization. The orientation of these dust grains is considered. The time required for the orientation is estimated. A possibility of explaining the interstellar polarization and polarization of the cometary radiation is discussed.

---

. , . , . . .

     

Космические лучи В крупномасштаБном сильнотурБу лентном магнитном поде

. .     

Моду ляционная неустойчивость нелинейньiх волн в релятявистской плазме с учетом нелинейного затухания ландау

i , i i , , . i . : (T _e 0,5MeV) (T _e 0,5 MeV) . - i 2.3 keV i , i : . i , , 2c/ _pi . , . - .     

Pitch angle scattering of solar particles: Comparison of ‘particle’ and ‘field’ approach

In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(), the absolute value of the mean free path , and the rigidity dependence of the mean free path (R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the layer model in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D() and based on the trajectory simulation for 100 MeV protons (field approach) are compared with results obtained from solar proton data (particle approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (QLT approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the field and particle approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the field and QLT approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfvén-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.