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1.
We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational
few-body problems. These algorithms have only positive time steps, but require computing the force gradient in addition to
the force. We demonstrate the efficiency of these Forward Symplectic Integrators by solving the circular restricted three-body
problem in the space-fixed frame where the force on the third body is explicitly time-dependent. These algorithms can achieve
accuracy of Runge–Kutta, conventional negative time step symplectic and corrector symplectic algorithms at step sizes five
to ten times as large. 相似文献
2.
The cometary meteoroid ejection model of Jones and Brown [Physics, Chemistry, and Dynamics of Interplanetary Dust, ASP Conference Series
104 (1996b) 137] was used to simulate ejection from comets 55P/Tempel-Tuttle during the last 12 revolutions, and the last 9 apparitions
of 109P/Swift-Tuttle. Using cometary ephemerides generated by the Jet Propulsion Laboratory’s (JPL) HORIZONS Solar System
Data and Ephemeris Computation Service, two independent ejection schemes were simulated. In the first case, ejection was simulated
in 1 h time steps along the comet’s orbit while it was within 2.5 AU of the Sun. In the second case, ejection was simulated
to occur at the hour the comet reached perihelion. A 4th order variable step-size Runge–Kutta integrator was then used to
integrate meteoroid position and velocity forward in time, accounting for the effects of radiation pressure, Poynting–Robertson
drag, and the gravitational forces of the planets, which were computed using JPL’s DE406 planetary ephemerides. An impact
parameter (IP) was computed for each particle approaching the Earth to create a flux profile, and the results compared to
observations of the 1998 and 1999 Leonid showers, and the 1993 and 2004 Perseids. 相似文献
3.
Alejandro M. Leiva Carlos Bruno Briozzo 《Celestial Mechanics and Dynamical Astronomy》2008,101(3):225-245
Starting from 80 families of low-energy fast periodic transfer orbits in the Earth–Moon planar circular Restricted Three Body
Problem (RTBP), we obtain by analytical continuation 11 periodic orbits and 25 periodic arcs with similar properties in the
Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at
which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their
stability parameters and minimal distances to the Earth and Moon. The periods of these orbits are between 2.5 and 5 synodic
months, their energies are among the lowest possible to achieve an Earth–Moon transfer, and they show a diversity of circumlunar
trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close
approaches to the last. 相似文献
4.
Peter S. Gural 《Earth, Moon, and Planets》2008,102(1-4):183-189
Recent work on the gravitational focusing of meteoroid streams and their threat to satellites and astronauts in the near-Earth
environment has concentrated on Earth acting as the gravitational attractor, totally ignoring the Moon. Though the Moon is
twelve-thousandths the mass of the Earth, it too can focus meteors, albeit at a much greater distance downstream from its
orbital position in space. At the Earth–Moon distance during particular phases of the Moon, slower speed meteoroid streams
with very compact radiant diameters can show meteoroid flux enhancements in Earth’s immediate neighborhood. When the right
geometric alignment occurs, this arises as a narrowed beam of particles of approximately 1,000 km width. For a narrow radiant
of one-tenth degree diameter there is a 10-fold increase in the level of flux passing through the near-Earth environment.
Meteoroid streams with more typical radiant sizes of 1° show at most two times enhancement. For sporadic sources, the enhancement
is found to be insignificant due to the wide angular spread of the diffuse radiant and thus may be considered of little importance. 相似文献
5.
Ana B. González Pablo Martín David J. López 《Celestial Mechanics and Dynamical Astronomy》1999,75(1):29-38
Recently, González, Martín and Farto have developed new numerical methods (RKGM methods) of Runge–Kutta type and fixed step
size for the numerical integration of perturbed oscillators. Moreover, it seems natural to study the behaviour of these new
methods for the accurate integration of orbital problems after the application of linearizing transformation, such us KS or
BF due to the fact that in these variables, the structure of the problem is of the form of perturbed oscillators, for which
the methods constructed are indicated. In this paper, we check the efficiency of these new methods when integrating the satellite
problem. The RKGM methods show a very good behaviour when they compete with other, classical and special, methods.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
Position and velocity perturbations for the determination of geopotential from space geodetic measurements 总被引:10,自引:0,他引:10
Peiliang Xu 《Celestial Mechanics and Dynamical Astronomy》2008,100(3):231-249
Although space geodetic observing systems have been advanced recently to such a revolutionary level that low Earth Orbiting
(LEO) satellites can now be tracked almost continuously and at the unprecedented high accuracy, none of the three basic methods
for mapping the Earth’s gravity field, namely, Kaula linear perturbation, the numerical integration method and the orbit energy-based
method, could meet the demand of these challenging data. Some theoretical effort has been made in order to establish comparable
mathematical modellings for these measurements, notably by Mayer-Gürr et al. (J Geod 78:462–480, 2005). Although the numerical
integration method has been routinely used to produce models of the Earth’s gravity field, for example, from recent satellite
gravity missions CHAMP and GRACE, the modelling error of the method increases with the increase of the length of an arc. In
order to best exploit the almost continuity and unprecedented high accuracy provided by modern space observing technology
for the determination of the Earth’s gravity field, we propose using measured orbits as approximate values and derive the
corresponding coordinate and velocity perturbations. The perturbations derived are quasi-linear, linear and of second-order
approximation. Unlike conventional perturbation techniques which are only valid in the vicinity of reference mean values,
our coordinate and velocity perturbations are mathematically valid uniformly through a whole orbital arc of any length. In
particular, the derived coordinate and velocity perturbations are free of singularity due to the critical inclination and
resonance inherent in the solution of artificial satellite motion by using various types of orbital elements. We then transform
the coordinate and velocity perturbations into those of the six Keplerian orbital elements. For completeness, we also briefly
outline how to use the derived coordinate and velocity perturbations to establish observation equations of space geodetic
measurements for the determination of geopotential. 相似文献
7.
The possibility of using a trap with ultracold neutrons as a detector of dark matter particles with long-range forces is considered.
The main advantage of the proposed method lies in the possibility of detecting a recoil energy of ∼10−7 eV. Constraints on the parameters of an interaction potential of the form φ (r) = ae
−r/b
/r between dark matter particles and a neutron are presented at various dark matter densities on Earth. The assumption about
the long-range interaction of dark matter particles and ordinary matter is shown to lead to a significant increase in the
elastic scattering cross section at low energies. As a consequence, it becomes possible to capture and accumulate dark matter
in the Earth’s gravitational field. The accumulated dark matter in the Earth’s gravitational field is roughly estimated. The
first experimental constraints on the existence of dark matter with long-range forces on Earth are presented. 相似文献
8.
R.D. Schuiling 《Earth, Moon, and Planets》2006,99(1-4):33-49
In this paper we discuss the Herndon hypothesis that a nuclear reactor is operating at the center of the Earth. Recent experimental
evidence shows that some uranium can have partitioned into the core. There is no viable mechanism for the small amount of
uranium that is dissolved in the molten metal to crystallize as a separate uranium phase (uranium metal or uranium sulfide)
and migrate to the center of the core.
There is no need for an extra heat source, as the total heat leaving the core can be easily provided by “classical” heat sources,
which are also more than adequate to maintain the Earth’s magnetic field. It is unlikely that nuclear georeactors (fast breeder
reactors) are operating at the Earth’s center. 相似文献
9.
Yuan Ren Pierpaolo Pergola Elena Fantino Bianca Thiere 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):1-21
Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon
system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular
restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific
transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issue mainly considered
the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive ΔV’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use
of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body
model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute
the invariant tori and their manifolds in this dynamical model. 相似文献
10.
S. Schiller G. M. Tino P. Gill C. Salomon U. Sterr E. Peik A. Nevsky A. Görlitz D. Svehla G. Ferrari N. Poli L. Lusanna H. Klein H. Margolis P. Lemonde P. Laurent G. Santarelli A. Clairon W. Ertmer E. Rasel J. Müller L. Iorio C. Lämmerzahl H. Dittus E. Gill M. Rothacher F. Flechner U. Schreiber V. Flambaum Wei-Tou Ni Liang Liu Xuzong Chen Jingbiao Chen Kelin Gao L. Cacciapuoti R. Holzwarth M. P. Heß W. Schäfer 《Experimental Astronomy》2009,23(2):573-610
The Einstein Gravity Explorer mission (EGE) is devoted to a precise measurement of the properties of space-time using atomic
clocks. It tests one of the most fundamental predictions of Einstein’s Theory of General Relativity, the gravitational redshift,
and thereby searches for hints of quantum effects in gravity, exploring one of the most important and challenging frontiers
in fundamental physics. The primary mission goal is the measurement of the gravitational redshift with an accuracy up to a
factor 104 higher than the best current result. The mission is based on a satellite carrying cold atom-based clocks. The payload includes
a cesium microwave clock (PHARAO), an optical clock, a femtosecond frequency comb, as well as precise microwave time transfer
systems between space and ground. The tick rates of the clocks are continuously compared with each other, and nearly continuously
with clocks on earth, during the course of the 3-year mission. The highly elliptic orbit of the satellite is optimized for
the scientific goals, providing a large variation in the gravitational potential between perigee and apogee. Besides the fundamental
physics results, as secondary goals EGE will establish a global reference frame for the Earth’s gravitational potential and
will allow a new approach to mapping Earth’s gravity field with very high spatial resolution. The mission was proposed as
a class-M mission to ESA’s Cosmic Vision Program 2015–2025.
相似文献
S. SchillerEmail: |
11.
The first aim of the present work is to compute a more accurate and recent model for the Earth’s magnetic field. The second
aim is to determine the effects of the Earth’s magnetic field on the motion of a charged artificial satellite to evaluate
the variations of the orbital elements of the satellite due to these effects. The magnetic field and its variation with time
have been studied at different heights, longitudes and latitudes. The geomagnetic field is considered as a multiple potential
field and the electrical charge of the satellite is assumed to be constant. A new computer code has been constructed to follow
the components of the magnetic field in spherical harmonic models. The Gauss equations are solved numerically. The results
concentrate on the computation of the numerical values of orbital perturbation for the case of a low Earth satellite. RS-1
satellite and space craft gravity probe B (GPB) are chosen as cases of studies for a detailed numerical analysis. 相似文献
12.
Csilla Szasz Johan Kero Asta Pellinen-Wannberg David D. Meisel Gudmund Wannberg Assar Westman 《Earth, Moon, and Planets》2008,102(1-4):373-378
We have investigated the conditions for simultaneous meteor observations with the EISCAT UHF radar system and telescopic optical
devices. The observed characteristics of 410 meteors detected by all three UHF receivers are compared with model simulations
and their luminosity is calculated as a part of a meteoroid ablation model using a fifth order Runge–Kutta numerical integration
technique. The estimated absolute visual magnitudes are in the range of +9 to +5. The meteors should therefore be observable
using intensified CCD or EMCCD (Electron Multiplying CCD) cameras with telephoto lenses. A possible setup of a coordinated
radar and optical campaign is suggested. 相似文献
13.
Yu. D. Kotov A. V. Kochemasov A. S. Glyanenko V. N. Yurov A. I. Arkhangelsky 《Solar System Research》2011,45(2):153-161
The CORONAS-PHOTON Russian satellite intended to study the Sun was successfully launched into orbit on January 30, 2009. Scientific equipment
of the satellite includes the PHOKA radiometer of soft X-ray and extreme UV radiation. The PHOKA instrument is intended to
measure the absolute flux of solar electromagnetic radiation in the spectral windows of 0.5–7 nm, 0.5–11 nm, 27–37 nm, and
116–125 nm. When leaving and entering the Earth’s shadow, the instrument aboard the spacecraft measures absorption of radiation
by various layers of the Earth’s atmosphere. Before the launch, photodiodes of the instrument had been calibrated using a
synchrotron radiation source. In-flight stability of sensitivity of main channels is controlled using calibration channels.
The paper describes the PHOKA instrument and presents its capabilities and main characteristics, as well as some results of
its operation in orbit. 相似文献
14.
Doreen M.C. Walker 《Planetary and Space Science》1977,25(4):337-342
In analysing the orbit of Ariel 1 to determine upper-atmosphere winds, it was observed that the orbital inclination underwent a noticeable perturbation in November 1969 at the 29:2 resonance with the Earth's gravitational field, when the satellite track over the Earth repeats every 2 days after 29 revolutions. The variations in the inclination and eccentricity of the orbit between July 1969 and February 1970 have now been analysed, using 35 US Navy orbits, and fitted with theoretical curves to obtain lumped values of 29th-order harmonic coefficients in the geopotential. 相似文献
15.
K. G. Hadjifotinou M. Gousidou-Koutita 《Celestial Mechanics and Dynamical Astronomy》1998,70(2):99-113
We present a new implementation of the recurrent power series (RPS) method which we have developed for the integration of
the system of N satellites orbiting a point-mass planet. This implementation is proved to be more efficient than previously
developed implementations of the same method. Furthermore, its comparison with two of the most popular numerical integration
methods: the 10th-order Gauss–Jackson backward difference method and the Runge–Kutta–NystrRKN12(10)17M shows that the RPS
method is more than one order of magnitude better in accuracy than the other two. Various test problems with one up to four
satellites are used, with initial conditions obtained from ephemerides of the saturnian satellite system. For each of the
three methods we find the values of the user-specified parameters (such as the method's step-size (h or tolerance (TOL)) that
minimize the global error in the satellites' coordinates while keeping the computer time within reasonable limits. While the
optimal values of the step-sizes for the methods GJ and RKN are all very small (less than T/100, the ones that are suitable
for the RPS method are within the range: T/13<h<T/6 (T being the period of the innermost satellite of the problem). Comparing
the results obtained by the three methods for these step-sizes and for the various test problems we observe the superiority
of the RPS method over GJ in terms of accuracy and over RKN both in accuracy and in speed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
A method is suggested for enhancing the on-board forecasting accuracy of the COG motion of a GEO SC with a long time of independent
operation. The suggested method consists of introducing so-called compensative transversal acceleration (CTA), along with
zonal harmonics into the right sides of the differential equations of SC motion among other disturbances due to the Earth’s
gravitational field eccentricity. The CTA compensates the integral effect of the sectoral and tesseral harmonics; its value
is constant for a specified point of GEO SC location (standing point) and is calculated on the Earth from numerical integration
of differential equations of motion taking into account the complete set of gravitational field harmonics. The CTA value is
transmitted on-board of an SC as program command data. The method is implemented in algorithms of on-board forecasting of
Electro-L SC motion and can be used to enhance the on-board forecasting accuracy of the COG motion of GEO SCs with a long
time of independent operation. 相似文献
17.
This paper investigates the orbit radial stabilization of a two-craft virtual Coulomb structure about circular orbits and
at Earth–Moon libration points. A generic Lyapunov feedback controller is designed for asymptotically stabilizing an orbit
radial configuration about circular orbits and collinear libration points. The new feedback controller at the libration points
is provided as a generic control law in which circular Earth orbit control form a special case. This control law can withstand
differential solar perturbation effects on the two-craft formation. Electrostatic Coulomb forces acting in the longitudinal
direction control the relative distance between the two satellites and inertial electric propulsion thrusting acting in the
transverse directions control the in-plane and out-of-plane attitude motions. The electrostatic virtual tether between the
two craft is capable of both tensile and compressive forces. Using the Lyapunov’s second method the feedback control law guarantees
closed loop stability. Numerical simulations using the non-linear control law are presented for circular orbits and at an
Earth–Moon collinear libration point. 相似文献
18.
Michael C. Denlinger 《Earth, Moon, and Planets》2005,96(1-2):59-80
The chemical compositions of the primordial atmospheres of Venus, Earth and Mars have long been a topic of debate between
the experts. Some believe that the original atmospheres were a product of outgassed volatiles from the newly accreted terrestrial
planets and that these atmospheres consisted primarily of carbon dioxide, nitrogen, water vapor and residual hydrogen and
helium (e.g., Lewis and Prinn, <it>Planets and their Atmospheres,</it> Academic Press, Orlando, FL, 1984, pp. 62–63, 81–84,
228–231, 383). Still others think the earliest atmospheres were composed of the gas components of the solar nebula from which
the solar system formed (i.e., hydrogen, helium, methane, ammonia and water). I consider the latter to be the correct scenario.
Presented herein is a proposed mechanism by which the original atmospheres of Venus, Earth and Mars were transformed to atmospheres
rich in carbon dioxide and nitrogen. An explanation is proposed for why water is so common on the surface of Earth and so
scarce on the surfaces of Venus and Mars. Also presented are the effects the “great impact” (single cataclysmic event that
was responsible for producing the Earth–Moon system) had upon the early atmosphere of Earth. The origin, structure and composition
of the impacting object are determined through deductive analyses. 相似文献
19.
This paper presents a Hamiltonian approach to modelling spacecraft motion relative to a circular reference orbit based on
a derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling
of high-order terms and orbital perturbations within the context of the Clohessy–Wiltshire solution. First, the Hamiltonian
is partitioned into a linear term and a high-order term. The Hamilton–Jacobi equations are solved for the linear part by separation,
and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and
perturbations, such as Earth’s oblateness, are incorporated into the analysis by a variation of parameters procedure. As an
example, closed-form solutions for J2-invariant orbits are obtained. 相似文献
20.
Marco Tantardini Elena Fantino Yuan Ren Pierpaolo Pergola Gerard Gómez Josep J. Masdemont 《Celestial Mechanics and Dynamical Astronomy》2010,108(3):215-232
Of the three collinear libration points of the Sun–Earth Circular Restricted Three-Body Problem (CR3BP), L3 is that located opposite to the Earth with respect to the Sun and approximately at the same heliocentric distance. Whereas
several space missions have been launched to the other two collinear equilibrium points, i.e., L1 and L2, taking advantage of their dynamical and geometrical characteristics, the region around L3 is so far unexploited. This is essentially due to the severe communication limitations caused by the distant and permanent
opposition to the Earth, and by the gravitational perturbations mainly induced by Jupiter and the close passages of Venus,
whose effects are more important than those due to the Earth. However, the adoption of a suitable periodic orbit around L3 to ensure the necessary communication links with the Earth, or the connection with one or more relay satellites located at
L4 or L5, and the simultaneous design of an appropriate station keeping-strategy, would make it possible to perform valuable fundamental
physics and astrophysics investigations from this location. Such an opportunity leads to the need of studying the ways to
transfer a spacecraft (s/c) from the Earth’s vicinity to L3. In this contribution, we investigate several trajectory design methods to accomplish such a transfer, i.e., various types
of two-burn impulsive trajectories in a Sun-s/c two-body model, a patched conics strategy exploiting the gravity assist of
the nearby planets, an approach based on traveling on invariant manifolds of periodic orbits in the Sun–Earth CR3BP, and finally
a low-thrust transfer. We examine advantages and drawbacks, and we estimate the propellant budget and time of flight requirements
of each. 相似文献