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1.
Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI
ab, whereI
b=180°–I
a andI
a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature
a
semi-major axis
-
A
lk
coefficient defined in Equation (11)
-
B
lk
coefficient defined in Equation (24)
-
C
km
coefficient defined in Equation (25)
-
D, E, F
coefficients in Equations (38), (39)
-
e
eccentricity
-
H
k
expression defined in Equation (34)
-
expression defined in Equation (35)
-
I
inclination of satellite orbit on lunar (or solar) ring plane
-
J
2
coefficient of second harmonic of Earth's gravitational potential (1082.637×10–6
R
E
2
)
-
K
k, Lk, Mk
expressions in Section 4
-
expressions in Section 4
-
p=a(1–e
2)
semi-latus rectum
-
P
l
Legendre polynomial of degreel
-
q
argument of Legendre polynomial
-
radial distance of satellite
-
R
E
Earth equatorial radius (6378.16 km)
-
R, S, W
perturbing accelerations in the radial, tangential and orbit normal directions
- syn
synchronous orbit radius (42 164.2 km=6.6107R
E)
-
t
time
-
T
satellite orbital period
-
T
orbital period of perturbing body (Moon)
-
T
e
period of long periodic oscillations ine for |I|<I
a
-
T
s
synodic period
-
U
gravitational potential of lunar (or solar) ring
-
x, y, z
Cartesian coordinates of a satellite with (x, y) being the ring plane
-
coefficient defined in Equation (20)
-
average change in orbital element over one orbit (=a, e, I, , )
- 1,23
unit vectors in thex, y, z coordinate directions
-
r
,
s
,
w
unit vectors in the radial, tangential and orbit normal directions
- =+
angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite
-
angle around the ring
-
gravitational constant times mass of Earth (3.986 013×105 km s–2)
-
gravitational constant times mass of Moon (or Sun)
-
m
gravitational constant times mass of Moon (/81.301)
-
s
gravitational constant time mass of Sun (332 946 )
-
ratio of the circumference of a circle to its diameter
-
radius of lunar (or solar) ring
-
m
radius of lunar ring (60.2665R
E)
-
s
radius of solar ring (23455R
E)
-
true anomaly
-
argument of perigee
- 0
initial value of
-
i
critical value of in quadranti(i=1, 2, 3, 4)
-
longitude of ascending node on ring plane
This work was sponsored by the Department of the Air Force. 相似文献
2.
Since there are reasons for expecting supersymmetry in an underlying quantum theory of gravity, one is led to study quantum and classical cosmology with supergravity. In particular, classical solutions corresponding to these models could also be used to generate the quantization of supersymmetric minisuperspaces. In generating these solutions, the solution to the Rarita-Schwinger field in the cosmological background is also obtained. In this paper the supercosmological equations of Einstein-Rarita-Schwinger are solved for the micro-superspace sector of the Taub model, under the assumption =11*22 and
. The solution for the parameters of the metric and are proportional to each other in each order, the zeroth-order and also the second-order terms. The zeroth-order terms correspond to the solution in general relativity and are logarithmic in time, the 12 terms have an hyperbolic time-dependence. The Rarita-Schwinger field has the form cos((2/D
3)ln |t–t
0|) and oscillates an infinite number of times astt
0. This oscillating behaviour of the solution for is not only present when spinor fields are treated in a curved background, but also some cosmological wave functions behave in this manner. This solution is at the same time the supercosmological solution for the microsuperspace sector of the Taub model and also the Rarita-Schwinger field in this background.This work was supported in part by CONACYT grant P228CCOX891723, and DGICSA SEP grant C90-03-0347. 相似文献
3.
Masaya Saitou 《Astrophysics and Space Science》1989,162(1):47-56
Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values
i
=
i
+
i
,v
i
=
i
+ v
i
were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,2 =v
2 = 10–8) grow many times in marginally-stable state. 相似文献
4.
The gravity potential of an arbitrary bodyT is expanded in a series of spherical harmonics and rigorous evaluations of the general termV
n
of the expansion are obtained. It is proved thatV
n
decreases on the sphere envelopingT according to the power law if the body structure is smooth. For a body with analytic structure,V
n
decreases in geometric progression. The exactness of these evaluations is proved for bodies having irregular and analytic structures. For the terrestrial planetsV
n
=O (n
–5/2).
I I V n IV n I . . IV n I . I. IV n =O(n –5/2 )相似文献
5.
A. M. Sinzi 《Celestial Mechanics and Dynamical Astronomy》1971,4(2):273-276
Corrections to Newcomb's lunisolar precession and to motion of the equinox are evaluated from proper motions of 77 Cepheids, employing recently determined values of their distances. Results are diverse, depending on the weighting method. If the effect of the cosmic dispersion is neglected and
0 is imposed to be 25 km/s/kpc, thenp
1=1.1±0.2 and +e = 1.0 ± 0.1 per century in the FK4 system.Presented at IAU Colloquium No. 9, The IAU System of Astronomical Constants, Heidelberg, Germany, August 12–14, 1970. 相似文献
6.
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.
( ) . , , . , , , .相似文献
7.
A novel methodology for evaluating the field of anisotropically scattered radiation within a homogeneous slab atmosphere of arbitrary optical thickness is provided. It departs from the traditional radiative transfer approach in first considering that the atmosphere is illuminated by an isotropic light source. From the solution of this problem, it subsequently proceeds to that for the more conventional case of monodirectional illumination. The azimuthal dependence of the field is separated in the usual manner by an harmonic expansion, leaving a problem in four dimensions (=optical depth, 0=thickness, , =directions of incidence and scattering) which, as is well known, is numerically extremely inconvenient. Two auxiliary radiative transfer formulations of increasing dimensionality are considered: (i) a transfer equation for the newly introduced functionb
m(,,0) with Sobolev's function
m(,0) playing the role of a source-function. Because the incident direction does not intervene,
m is simply expressed as a single integral term involvingb
m. For bottom illumination, an analogous equation holds for the other new functionh
m(,,0). However, simple reciprocity relations link the two functions so that it is only necessary to considerb
m; (ii) a transfer equation for the other new functiona
m(,,,0) with a source-function provided by Sobolev's functionD
m(,,0). For bottom illumination, another functionf
m(,,,0) is introduced; by a similar argument using reciprocity relations,f
m is reduced toa
m rendering necessary only the consideration ofa
m. However, a fundamental decomposition formula is obtained which shows thata
m is expressible algebraically in terms of functions of a single angular variable. The functions
m andD
m are shown to be the values in the horizontal plane ofb
m anda
m, respectively. The other auxiliary functionsX
m andY
m are also expressed algebraically in terms ofb
m. These results enable one to proceed to the final step of evaluating the radiation field for monodirectional illumination. The above reductions toalgebraic relations involving only the functionb
m appear to be more advantageous than Sobolev's (1972) recent approach; they also circumvent some basic numerical difficulties in it. We believe the present approach may likewise prove to be superior to most (if not all) other methods of solution known heretofore.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory under Contract No. NAS-7-100 sponsored by the National Aeronautics and Space Administration. 相似文献
8.
L. K. Babadzanjanz 《Celestial Mechanics and Dynamical Astronomy》1979,20(1):43-57
The method of obtaining the estimates of the maximalt-interval (
–,
+) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g.
12) exceeds some fixed non-negative lower bound, for allt contained in (
–,
+), is considered. For given masses and initial data, the increasing sequences of the numbers
k
, each of which provides the estimate
+ >
k
, are constructed. It appears that if
+ = +, then
. 相似文献
9.
Г. А. Гусзадян 《Astrophysics and Space Science》1979,62(1):35-44
(Kilyachkoet al., 1978) , . l ( I II). (Kilyachkoet al., 1978) : (1) 800 Å , , UV Cet. EV Lac; (2) UV Cet EV Lac 8000 Å , ; (3) 8000 Å . — MO-KS; (4) 1–3 m. 相似文献
10.
, , , , . , , . , , - - ( , ..). - . 相似文献
11.
V. I. Ferronsky S. A. Denisik S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1979,20(1):69-81
The applicability of the properties of central configurations proceeding from the many-body problem to study of gaseous sphere cloud evolution during its gravitational contraction is justified. It is shown that the product runs to a constant value in the asymptotic time limit of simultaneous collision of all the particles of the cloud where is a form-factor of the potential energy and is a form-factor of the moment of inertia.The spherical bodies as well as ellipsoids of rotation and general ellipsoids with a one-dimensional mass distribution (k),k[0, 1] are found to possess the property =const.
. , - , , ., , - =const., , (k),k[0, 1].相似文献
12.
P. D. Singh A. M. Gomez Balboa J. A. De Freitas Pacheco 《Astrophysics and Space Science》1985,108(1):153-160
Spontaneous emission rates and absorption oscillator strengths for prominent V4 sequence bands of theB
2+-A
2i transition of the CN molecule are estimated. The wavelengths of some lines observed in the coma spectrum of the comet Bradfield 1980t as well as in several comets coincide with these V4 sequence LeBlanc bands of the CN radical. Formation and destruction of the CN radical in the coma of a comet are discussed in the framework of gas phase reactions.Work supported by CNPq, Brasília, under contract numbers: Processos 401236-83 and 4076/77-FA01. 相似文献
13.
, . , , . . . . . , , . 相似文献
14.
, (DM) (RM). , DM RM N
e
= n
e
ds. M
e
= n
e
H cos ds ; . Lerche (1970a, b) , DM RM N
e
M
e
. . 相似文献
15.
The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than p, again in broad agreement with Stenflo's power spectrum. 相似文献
16.
The most characteristic features of H-R diagrams of blobular clusters are summarized with particular regard to the position and the extension of the horizontal branch. A comparison of observations with theory in the two cases of evolution with and without mass loss is then shortly given.A preliminary approach to the evolution of models with large mass fractions (q
0) in the helium cores is presented. Inhomogeneous equilibrium models with double energy sources have been computed in a range of values ofq
0 and of the total mass referring to possible horizontal-branch stars.
Riassunto Sono indicate le principali caratteristiche dei diagrammi H-R degli ammassi globulari con particolare riferimento alla posizione ed alla estensione del ramo orizzontale. Sono esaminate relazioni tra la teoria ed i parametri indicati nei due casi di evoluzione con e senza perdita di massa.E' presentata infine una analisi di modelli con un'alta frazione di massa nel nucleo di elio (q 0). I modelli di equilibrio, non omogenei ed a doppia sorgente di energia, sono stati calcolati in un intervallo di valori diq 0 e della massa totale che sono in relazione alla regione delle stelle del ramo orizzontale.
- . . . q 0 . q 0 .相似文献
17.
Jiann-Tsorng Horng 《Astrophysics and Space Science》1975,34(2):L1-L5
Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for
p
< 0, where
p
1 –T
p/T
p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range
r
|
p
|
p
for
p
< 0, where
p
is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range |
p
|
p
>
r
> |
p
|
p
/(1–
r
) for
p
< 0. The marginal state is at
r
=|
p
|
p
.Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974 相似文献
18.
With the help of a model atmosphere of the Sun we evaluate the pole-equator difference in flux (as measured by Dicke and Goldenberg) assuming the following type of pole-equator temperature difference (T=T
e
–T
p
): (a) T 2K for > 0 (0 0.05); (b) T 10K for < 0.The small T at all optical depths given by (a) could, for example, be due to a pole-equator difference in effective temperatures. At small optical depths a difference in mechanical heating could give rise to the larger temperature difference given by (b). We compare the results of our calculations with Dicke and Goldenberg's observations.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
19.
Explosions of quasars and young galaxies at large redshifts must cause propagation of blast waves in the metagalactic medium. The shock waves formed can, during the radiative cooling stage, produce dense cold spherical shells around the epicentres of explosions. But, even before that, at the stage of adiabatic expansion, each spherical shock-wave front, if it lies on one line-of-sight with a more distant quasar, can imprint into the quasar spectrum a specific absorption doublet with a distance between the components (in the rest frame) 0 3 Å. The L doublet components have a small but the same equivalent widthW
0 0.3 Å, the ratioW
0/0 weakly depending onW
0 ifW
0 is small. We demonstrate here that such absorption L doublets are really present among the L forest in the absorption spectra of distant quasars which are, according to Sargentet al. (1980), of mostly intervening (and not intrinsic) origin. Further accumulation of data on absorption doublets, which can serve as direct indicators of metagalactic shock-waves, may provide valuable information about the physical conditions in the metagalactic gas at large redshifts. 相似文献
20.
Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT
eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT
eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT
eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB
with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk. 相似文献