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1.
R. Misawa  J-Ph. Bernard  Y. Longval  I. Ristorcelli  P. Ade  D. Alina  Y. André  J. Aumont  L. Bautista  P. de Bernardis  O. Boulade  F. Bousqet  M. Bouzit  V. Buttice  A. Caillat  M. Chaigneau  M. Charra  B. Crane  F. Douchin  E. Doumayrou  J. P. Dubois  C. Engel  M. Griffin  G. Foenard  S. Grabarnik  P. Hargrave  A. Hughes  R. Laureijs  B. Leriche  S. Maestre  B. Maffei  C. Marty  W. Marty  S. Masi  J. Montel  L. Montier  B. Mot  J. Narbonne  F. Pajot  E. Pérot  J. Pimentao  G. Pisano  N. Ponthieu  L. Rodriguez  G. Roudil  M. Salatino  G. Savini  O. Simonella  M. Saccoccio  J. Tauber  C. Tucker 《Experimental Astronomy》2017,43(3):211-235
The Polarized Instrument for Long-wavelength Observation of the Tenuous interstellar medium (PILOT) is a balloon-borne astronomy experiment designed to study the linear polarization of thermal dust emission in two photometric bands centred at wavelengths 240 μm (1.2 THz) and 550 μm (545 GHz), with an angular resolution of a few arcminutes. Several end-to-end tests of the instrument were performed on the ground between 2012 and 2014, in order to prepare for the first scientific flight of the experiment that took place in September 2015 from Timmins, Ontario, Canada. This paper presents the results of those tests, focussing on an evaluation of the instrument’s optical performance. We quantify image quality across the extent of the focal plane, and describe the tests that we conducted to determine the focal plane geometry, the optimal focus position, and sources of internal straylight. We present estimates of the detector response, obtained using an internal calibration source, and estimates of the background intensity and background polarization.  相似文献   

2.
The advanced Russian project Laplace-P is aimed at developing and launching two scientific spacecraft (SC)—Laplace-P1 (LP1 SC) and Laplace-P2 (LP2 SC)—designed for remote and in-situ studies of the system of Jupiter and its moon Ganymede. The LP1 and LP2 spacecraft carry an orbiter and a lander onboard, respectively. One of the orbiter’s objectives is to map the surface of Ganymede from the artificial satellite’s orbit and to acquire the data for the landing site selection. The main objective of the lander is to carry out in-situ investigations of Ganymede’s surface. The paper describes the scientific goals and objectives of the mission, its special features, and the LP1 and LP2 mission profiles during all of the phases—from the launch to the landing on the surface of Ganymede.  相似文献   

3.
Physical conditions in the near-surface layer of the Moon are overviewed. This medium is formed in the course of the permanent micrometeoroid bombardment of the lunar regolith and due to the exposure of the regolith to solar radiation and high-energy charged particles of solar and galactic origin. During a considerable part of a lunar day (more than 20%), the Moon is passing through the Earth’s magnetosphere, where the conditions strongly differ from those in the interplanetary space. The external effects on the lunar regolith form the plasma-dusty medium above the lunar surface, the so-called lunar exosphere, whose characteristic altitude may reach several tens of kilometers. Observations of the near-surface dusty exosphere were carried out with the TV cameras onboard the landers Surveyor 5, 6, and 7 (1967–1968) and with the astrophotometer of Lunokhod-2 (1973). Their results showed that the near-surface layer glows above the sunlit surface of the Moon. This was interpreted as the scattering of solar light by dust particles. Direct detection of particles on the lunar surface was made by the Lunar Ejects and Meteorite (LEAM) instrument deployed by the Apollo 17 astronauts. Recently, the investigations of dust particles were performed by the Lunar Atmosphere and Dust Environment Explorer (LADEE) instrument at an altitude of several tens of kilometers. These observations urged forward the development of theoretical models for the lunar exosphere formation, and these models are being continuously improved. However, to date, many issues related to the dynamics of dust and the near-surface electric fields remain unresolved. Further investigations of the lunar exosphere are planned to be performed onboard the Russian landers Luna-Glob and Luna-Resurs.  相似文献   

4.
The present work discusses astronomical site survey reports on dust content, vertical distribution of atmospheric turbulence, precipitable water vapor (PWV), surface and upper-air data, and their effects on seeing over the Indian Astronomical Observatory (IAO) Hanle. Using Laser Particulate Counter, ambient dust measurements at various sizes (0.3 μm to 25 μm) were performed at various locations at the site during November 2015. Estimated volume concentration for the particle size at 0.5 μm was around 10,000 per cubic foot, which is equivalent to ten thousand class of clean room standard protocol. During the measurement, surface wind speed varied from 0-20 m s ?1, while estimated aerosol optical depth (AOD) using Sky radiometer (Prede) varied from 0.02-0.04 at 500 nm, which indicates the site is fairly clean. The two independent measurements of dust content and aerosol concentrations at the site agreed well. The turbulence or wind gust at the site was studied with wind profiles at three different heights above the ground. The strength of the wind gust varies with time and altitude. Nocturnal temperature across seasons varied with a moderate at summer (6?8 °C) and lower in winter (4?5 °C). However, the contrast between the two is significantly small due to cold and extremely dry typical climatic conditions of the site. The present study also examined the effects of surface and upper-air data along with Planetary Boundary Layer (PBL) dynamics with seeing measurement over the site. Further, a comparative study of such observed parameters was conducted with other high altitude astronomical observatories across the globe.  相似文献   

5.
The Cadmium Zinc Telluride Imager (CZTI) is a high energy, wide-field imaging instrument on AstroSat. CZTI’s namesake Cadmium Zinc Telluride detectors cover an energy range from 20 keV to \(>200\) keV, with 11% energy resolution at 60 keV. The coded aperture mask attains an angular resolution of 17\(^\prime \) over a 4.6\(^\circ \) \(\times \) 4.6\(^\circ \)  (FWHM) field-of-view. CZTI functions as an open detector above 100 keV, continuously sensitive to GRBs and other transients in about 30% of the sky. The pixellated detectors are sensitive to polarization above \(\sim \)100 keV, with exciting possibilities for polarization studies of transients and bright persistent sources. In this paper, we provide details of the complete CZTI instrument, detectors, coded aperture mask, mechanical and electronic configuration, as well as data and products.  相似文献   

6.
To identify temporal variations of the characteristics of Jupiter’s cloud layer, we take into account the geometric modulation caused by the rotation of the planet and planetary orbital motion. Inclination of the rotation axis to the orbital plane of Jupiter is 3.13°, and the angle between the magnetic axis and the rotation axis is β ≈ 10°. Therefore, over a Jovian year, the jovicentric magnetic declination of the Earth φ m varies from–13.13° to +13.13°, and the subsolar point on Jupiter’s magnetosphere is shifted by 26.26° per orbital period. In this connection, variations of the Earth’s jovimagnetic latitude on Jupiter will have a prevailing influence in the solar-driven changes of reflective properties of the cloud cover and overcloud haze on Jupiter. Because of the orbit eccentricity (e = 0.048450), the northern hemisphere receives 21% greater solar energy inflow to the atmosphere, because Jupiter is at perihelion near the time of the summer solstice. The results of our studies have shown that the brightness ratio A j of northern to southern tropical and temperate regions is an evident factor of photometric activity of Jupiter’s atmospheric processes. The analysis of observational data for the period from 1962 to 2015 reveals the existence of cyclic variations of the activity factor A j of the planetary hemispheres with a period of 11.86 years, which allows us to talk about the seasonal rearrangement of Jupiter’s atmosphere.  相似文献   

7.
A Multi-Application Solar Telescope (MAST) is proposed to be installed at the lake site (Lake Fatehsagar) of Udaipur Solar Observatory (USO) in India. The lake site Observatory of USO is located on a small island in the middle of the lake. To determine the optimum size of the MAST (for use with an adaptive optics system), it was decided to quantify the seeing conditions prevailing at the lake site during the different months of the year. For this purpose, we have used short-exposure (3 ms) high-resolution Hα (6563 Å) images (spatial scale of ~0.55 arc sec per pixel) of the Sun taken in burst mode with the 15-cm refractor Spar telescope located at the lake site of USO. Spectral ratio technique as reported by von der Lühe (1984, J. Opt. Soc. Am. A1, 510) has been used to estimate the Fried’s parameter (r 0) at this site, which gives the quantitative measure of astronomical seeing. This study has been carried out daily on an hourly basis during 4:30?–?10:30 UT over the months January?–?June of the years 2005 and 2006 to understand the diurnal and seasonal variations in r 0 at this site. It is noteworthy that the lake was almost dry during the observing period in 2005, while it overflowed during our observations in 2006 because of abundant monsoon rains. The seeing in the presence of water shows improvement in r 0 by about 1.0 cm with respect to the previous year’s dry condition and mean r 0 varies between 4.0 and 4.5 cm as evident from the data obtained between January and June, 2006.  相似文献   

8.
In this paper, the initial value problem of space dynamics in universal Stumpff anomaly \(\psi\) is set up and developed in analytical and computational approach.For the analytical expansions, the linear independence of the functions \(\mathrm{U}_{{ j}} { (\psi;\varsigma)}\); \({j=0,1,2,3}\) are proved. The differential and recurrence equations satisfied by them and their relations with the elementary functions are given. The universal Kepler equation and its validations for different conic orbits are established together with the Lagrangian coefficients. Efficient representations of these functions are developed in terms of the continued fractions.
For the computational developments we consider the following items:
  1. 1.
    Top-down algorithm for continued fraction evaluation.
     
  2. 2.
    One-point iteration formulae.
     
  3. 3.
    Determination of the coefficients of Kepler’s equation.
     
  4. 4.
    Derivatives of Kepler’s equation of any integer order.
     
  5. 5.
    Determination of the initial guess for the solution of the universal Kepler equation.
     
Finally we give summary on the computational design for the initial value problem of space dynamics in universal Stumpff anomaly. This design based on the solution of the universal Kepler’s equation by an iterative schemes of quadratic up to any desired order \(\ell\).  相似文献   

9.
Long-slit grating spectrometers in scanning mode and Fabry–Perot interferometers as tunable filters are commonly used to perform integral wide-field spectroscopy on extended astrophysical objects as HII regions and nearby galaxies. The goal of this paper is to demonstrate, by comparison, through a thorough review of the imaging Fourier transform spectrometer (IFTS) properties, that this instrument represents another interesting solution. After a brief recall of the performances, regarding FOV and spectral resolution, of the grating spectrometer, without and with integral field units (IFU), and of the imaging Fabry–Perot, it is demonstrated that for an IFTS the product of the maximum resolution R by the entrance beam étendue U is equal to $2.6\,N\times S_I$ with $N\,\times \,N$ the number of pixels of the detector array and S $_I$ the area of the interferometer beamsplitter. As a consequence, the IFTS offers the most flexible choice of field size and spectral resolution, up to high values for both parameters. It also presents on a wide field an important multichannel advantage in comparison to integral field grating spectrometers, even with multiple IFUs. To complete, the few astronomical IFTSs, built behind ground-based telescopes and in space, for the visible range up to the sub-millimetric domain, are presented. Through two wide-field IFTS projects, one in the visible, the other one in the mid-infrared, the question is addressed of the practical FOV and resolution limits, set by the optical design of the instrument, which can be achieved. Within the 0.3 to $\sim $ 2.5 $\upmu$ m domain, a Michelson interferometer with wide-field diopric collimators provides the easiest solution. This design is illustrated by a $11^{\prime}\times 11^{\prime}$ -field IFTS in the 0.35–0.90 $\upmu$ m range around an off-axis interferometer, called SITELLE, proposed for the 3.6-m CFH Telescope. At longer wavelengths, an all-mirror optics is required, as studied for a spaceborne IFTS, H2EX, for the 8–29 $\upmu$ m range, a $20^{\prime} \times 20^{\prime}$ field, and a high resolution of $\simeq 3\times 10^4$ at 10 $\upmu$ m. To comply with these characteristics, the interferometer is designed with cat’s eye retroreflectors. In the same domain and up to the far infrared, if the instrument aims only at a low spectral resolution (few thousands) and a smaller field (few arcmins $^2$ ), roof-top or corner cube mirrors, as for the IFTS SPIRE on the Herschel space telescope, are usable. At last, perspectives are opened, behind an ELT in the visible and the near infrared with the SITELLE optical combination, in the 2–5 $\upmu$ m on the Antarctic plateau or in space up to longer wavelengths, with the H2EX design, to provide the missing capability of global high spectral resolution studies of extended sources, from comets to distant galaxy clusters.  相似文献   

10.
The processes of ion acceleration and Alfvén wave generation by accelerated particles at the Earth’s bow shock are studied within a quasi-linear approach. Steady-state ion and wave spectra are shown to be established in a time of 0.3–4 h, depending on the background level of Alfvénic turbulence in the solar wind. The Alfvén waves produced by accelerated ions are confined within the frequency range 10?2–1 Hz and their spectral peak with a wave amplitude βBB comparable to the interplanetary magnetic field strength B corresponds to the frequency v = (2–3) × 10?2 Hz. The high-frequency part of the wave spectrum (v > 0.2 Hz) undergoes damping by thermal ions. The calculated spectra of the accelerated ions and the Alfvén waves generated by them reproduce the main features observed in experiments.  相似文献   

11.
We describe the modifications made in the design of the Kyiv meridian axial circle (MAC) and in the observation technique after the instrument was equipped with a CCD camera with an array of 1040×1160 pixels. The observations are performed in the drift-scan mode (time-delay imaging) with an effective exposure time of 108 s for equatorial stars. The MAC photometric system reproduces the standard V system; the limiting magnitude is V = 17 m . The observations made with the modified MAC in 2001–2003 served as the basis for the KMAC1 catalog which contains positions, proper motions, and magnitudes B, V, R, r′, J for 100 000 stars in the sky areas with the ICRF objects. The errors of positions and V magnitudes in the catalog are 50–90 mas and 0.1 m , respectively, for stars with V = 15 m . Stars in the equatorial sky areas and radio stars are presently observed with the aim to determine their exact positions, proper motions, and magnitudes. The catalogs are available in the data base of the Centre de Données Astronomiques de Strasbourg (ftp.cdsarc.u-strasbg.fr) and on the site of the Main Astronomical Observatory (http://www.mao.kiev.ua).  相似文献   

12.
As a coronal mass ejection (CME) passes, the flank and wake regions are typically strongly disturbed. Various instruments, including the Large Angle and Spectroscopic Coronagraph (LASCO), the Atmospheric Imaging Assembly (AIA), and the Coronal Multi-channel Polarimeter (CoMP), observed a CME close to the east limb on 26 October 2013. A hot (\({\approx}\,10~\mbox{MK}\)) rising blob was detected on the east limb, with an initial ejection flow speed of \({\approx}\, 330~\mbox{km}\,\mbox{s}^{-1}\). The magnetic structures on both sides and in the wake of the CME were strongly distorted, showing initiation of turbulent motions with Doppler-shift oscillations enhanced from \({\approx}\, \pm 3~\mbox{km}\,\mbox{s}^{-1}\) to \({\approx}\, \pm 15~\mbox{km}\,\mbox{s}^{-1}\) and effective thermal velocities from \({\approx}\,30~\mbox{km}\,\mbox{s}^{-1}\) to \({\approx}\,60~\mbox{km}\,\mbox{s}^{-1}\), according to the CoMP observations at the Fe?xiii line. The CoMP Doppler-shift maps suggest that the turbulence behaved differently at various heights; it showed clear wave-like torsional oscillations at lower altitudes, which are interpreted as the antiphase oscillation of an alternating red/blue Doppler shift across the strands at the flank. The turbulence seems to appear differently in the channels of different temperatures. Its turnover time was \({\approx}\,1000\) seconds for the Fe 171 Å channel, while it was \({\approx}\,500\) seconds for the Fe 193 Å channel. Mainly horizontal swaying rotations were observed in the Fe 171 Å channel, while more vertical vortices were seen in the Fe 193 Å channel. The differential-emission-measure profiles in the flank and wake regions have two components that evolve differently: the cool component decreased over time, evidently indicating a drop-out of cool materials due to ejection, while the hot component increased dramatically, probably because of the heating process, which is suspected to be a result of magnetic reconnection and turbulence dissipation. These results suggest a new turbulence-heating scenario of the solar corona and solar wind.  相似文献   

13.
In this note a study of the convergence properties of some starters \( E_0 = E_0(e,M)\) in the eccentricity–mean anomaly variables for solving the elliptic Kepler’s equation (KE) by Newton’s method is presented. By using a Wang Xinghua’s theorem (Xinghua in Math Comput 68(225):169–186, 1999) on best possible error bounds in the solution of nonlinear equations by Newton’s method, we obtain for each starter \( E_0(e,M)\) a set of values \( (e,M) \in [0, 1) \times [0, \pi ]\) that lead to the q-convergence in the sense that Newton’s sequence \( (E_n)_{n \ge 0}\) generated from \( E_0 = E_0(e,M)\) is well defined, converges to the exact solution \(E^* = E^*(e,M)\) of KE and further \( \vert E_n - E^* \vert \le q^{2^n -1}\; \vert E_0 - E^* \vert \) holds for all \( n \ge 0\). This study completes in some sense the results derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014) by using Smale’s \(\alpha \)-test with \(q=1/2\). Also since in KE the convergence rate of Newton’s method tends to zero as \( e \rightarrow 0\), we show that the error estimates given in the Wang Xinghua’s theorem for KE can also be used to determine sets of q-convergence with \( q = e^k \; \widetilde{q} \) for all \( e \in [0,1)\) and a fixed \( \widetilde{q} \le 1\). Some remarks on the use of this theorem to derive a priori estimates of the error \( \vert E_n - E^* \vert \) after n Kepler’s iterations are given. Finally, a posteriori bounds of this error that can be used to a dynamical estimation of the error are also obtained.  相似文献   

14.
Jupiter’s satellites are subject to strong tidal forces which result in variations of the gravitational potential and deformations of the satellites’ surfaces on the diurnal tidal cycle. Such variations are described by the Love numbers \(k_2\) and \(h_2\) for the tide-induced potential variation due to internal mass redistribution and the radial surface displacement, respectively. The phase-lags \( \phi _{k_2}\) and \( \phi _{h_2}\) of these complex numbers contain information about the rheological and dissipative states of the satellites. Starting from interior structure models and assuming a Maxwell rheology to compute the tidal deformation, we calculate the phase-lags in application to Ganymede and Europa. For both satellites we assume a decoupling of the outer ice-shell from the deep interior by a liquid subsurface water ocean. We show that, in this case, the phase-lag difference \(\varDelta \phi = \phi _{k_2}- \phi _{h_2}\) can provide information on the rheological and thermal state of the deep interiors if the viscosities of the deeper layers are small. In case of Ganymede, phase-lag differences can reach values of a few degrees for high-pressure ice viscosities \({<}10^{14}\) Pa s and would indicate a highly dissipative state of the deep interior. In this case \(\varDelta \phi \) is dominated by dissipation in the high-pressure ice layer rather than dissipation within the ice-I shell. These phase lags would be detectable from spacecraft in orbit around the satellite. For Europa \(\varDelta \phi \) could reach values exceeding \(20^\circ \) and phase-lag measurements could help distinguish between (1) a hot dissipative silicate mantle which would in thermal equilibrium correspond to a very thin outer ice-I shell and (2) a cold deep interior implying that dissipation would mainly occur in a thick (several tens of km) outer ice-I shell. These measurements are highly relevant for ESA’s Jupiter Icy Moons Explorer (JUICE) and NASA’s Europa Multiple Flyby Mission, both targeted for the Jupiter system.  相似文献   

15.
On 27 June 2012, an eruptive solar prominence was observed in the extreme ultraviolet (EUV) and radio wavebands. At the Aalto University Metsähovi Radio Observatory (MRO) it was observed at 37 GHz. It was the first time that the MRO followed a radio prominence with dense sampling in the millimetre wavelengths. This prompted us to study the connection of the 37 GHz event with other wavelength domains. At 37 GHz, the prominence was tracked to a height of around \(1.6~\mathrm{R}_{\odot}\), at which the loop structure collapsed. The average velocity of the radio prominence was \(55 \pm 6~\mbox{km}\,\mbox{s}^{-1}\). The brightness temperature of the prominence varied between \(800 \pm 100\) K and \(3200 \pm 100\) K. We compared our data with the Solar Dynamic Observatory (SDO)/Atmospheric Imaging Assembly (AIA) instrument’s 304 Å EUV data, and found that the prominence behaves very similarly in both wavelengths. The EUV data also reveal flaring activity nearby the prominence. We present a scenario in which this flare works as a trigger that causes the prominence to move from a stable stage to an acceleration stage.  相似文献   

16.
17.
The quest for other habitable worlds and the search for life among them are major goals of modern astronomy. One way to make progress towards these goals is to obtain high-quality spectra of a large number of exoplanets over a broad range of wavelengths. While concepts currently investigated in the United States are focused on visible/NIR wavelengths, where the planets are probed in reflected light, a compelling alternative to characterize planetary atmospheres is the mid-infrared waveband (5–20 μm). Indeed, mid-infrared observations provide key information on the presence of an atmosphere, the surface conditions (e.g., temperature, pressure, habitability), and the atmospheric composition in important species such as H2O, CO2, O3, CH4, and N2O. This information is essential to investigate the potential habitability of exoplanets and to make progress towards the search for life in the Universe. Obtaining high-quality mid-infrared spectra of exoplanets from the ground is however extremely challenging due to the overwhelming brightness and turbulence of the Earth’s atmosphere. In this paper, we present a concept of space-based mid-infrared interferometer that can tackle this observing challenge and discuss the main technological developments required to launch such a sophisticated instrument.  相似文献   

18.
J-Ph. Bernard  P. Ade  Y. André  J. Aumont  L. Bautista  N. Bray  P. de Bernardis  O. Boulade  F. Bousquet  M. Bouzit  V. Buttice  A. Caillat  M. Charra  M. Chaigneau  B. Crane  J.-P. Crussaire  F. Douchin  E. Doumayrou  J.-P. Dubois  C. Engel  P. Etcheto  P. Gélot  M. Griffin  G. Foenard  S. Grabarnik  P. Hargrave  A. Hughes  R. Laureijs  Y. Lepennec  B. Leriche  Y. Longval  S. Maestre  B. Maffei  J. Martignac  C. Marty  W. Marty  S. Masi  F. Mirc  R. Misawa  J. Montel  L. Montier  B. Mot  J. Narbonne  J-M. Nicot  F. Pajot  G. Parot  E. Pérot  J. Pimentao  G. Pisano  N. Ponthieu  I. Ristorcelli  L. Rodriguez  G. Roudil  M. Salatino  G. Savini  O. Simonella  M. Saccoccio  P. Tapie  J. Tauber  J.-P. Torre  C. Tucker 《Experimental Astronomy》2016,42(2):199-227
Future cosmology space missions will concentrate on measuring the polarization of the Cosmic Microwave Background, which potentially carries invaluable information about the earliest phases of the evolution of our universe. Such ambitious projects will ultimately be limited by the sensitivity of the instrument and by the accuracy at which polarized foreground emission from our own Galaxy can be subtracted out. We present the PILOT balloon project, which aims at characterizing one of these foreground sources, the polarized continuum emission by dust in the diffuse interstellar medium. The PILOT experiment also constitutes a test-bed for using multiplexed bolometer arrays for polarization measurements. This paper presents the instrument and its expected performances. Performance measured during ground calibrations of the instrument and in flight will be described in a forthcoming paper.  相似文献   

19.
This paper describes a new reference solar spectrum retrieved from measurements of the satellite instrument SCIAMACHY in the wavelength region from \(0.24~\upmu\mbox{m}\) to \(2.4~\upmu\mbox{m}\) and its comparison with several other established solar reference spectra. The SCIAMACHY reference spectrum was recorded early in the mission before substantial optical degradation due to the harsh space environment sets in. The radiometric calibration of SCIAMACHY, applied in this study, includes a physical model of the scanner unit. Furthermore, SCIAMACHY’s internal white light source (WLS) is used to correct for on-ground to in-flight changes. The resultant calibrated solar spectrum from SCIAMACHY is in good agreement with several available solar spectral irradiance (SSI) references in the visible spectral range. Strong throughput losses due to detector icing in the near infrared (NIR) are now adequately accounted for. Nevertheless, a deficit with respect to the ATLAS-3 composite and SORCE/SIM SSI is observed in the NIR. However, the SCIAMACHY solar reference spectrum agrees well with the recently re-evaluated SOLAR/SOLSPEC-ISS and recent ground measurements taken at Mauna Loa in the NIR.  相似文献   

20.
In this note, by using Smale’s \(\alpha \)-theorem on the convergence of Newton’s method, the \(\alpha \)-sets of convergence of some starters of solving the elliptic Kepler’s equation are derived. For each starter we compute the exact \(\alpha \)-set in the eccentricity-main anomaly \((e,M)\in [0,1)\times [0,\pi ]\), showing that these sets are larger than those derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014). Further, new convergence tests based on the Newton–Kantorowitch theorem are given comparing with the derived from Smale’s \(\alpha \)-test.  相似文献   

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