Discussion on the Identification of Magnetic Cloud Boundaries Using Cloud Natural Coordinate System

Magnetic clouds (MCs) belong to an important subset of interplanetary coronal mass ejections. The identification of their boundaries is always a problem in the studies of MCs. This paper discusses a method to identify the boundaries of MCs by coordinate transformation. Instead of the conventional GSE (Geocentric Solar Ecliptic) coordinate system, the interplanetary magnetic field data are converted into a cloud natural coordinate system, in which the profile of the MC as a magnetic flux tube is clearly displayed. Then, combining with the plasma properties of the MC, the boundary of the cloud can be identified easily. Six observed MCs are analyzed using this method, and the results show that this method is feasible and can reduce the uncertainty in the identification of MC boundaries.     

On Re-sampling of Solar Images

Digital image data are now commonly used throughout the field of solar physics. Many steps of image data analysis, including image co-alignment, perspective reprojection of the solar surface, and compensation for solar rotation, require re-sampling original telescope image data under a distorting coordinate transformation. The most common image re-sampling methods introduce significant, unnecessary flaws into the data. More correct techniques have been known in the computer graphics community for some time but remain little known within the solar community and hence deserve further presentation. Furthermore, image distortion under specialized coordinate transformations is a powerful analysis technique with applications well beyond image resizing and perspective compensation. Here I give a brief overview of the mathematics of data re-sampling under arbitrary distortions, present a simple algorithm for optimized re-sampling, give some examples of distortion as an analysis tool, and introduce scientific image distortion software that is freely available over the Internet. ``First get your facts straight. Then you can distort them as you please.' – Mark Twain     

The Fermi coordinate system in the post-Newtonian framework

The Fermi coordinate system (or the non-rotating proper reference frame) is studied within the framework of the post-Newtonian approximation of general relativity. First its general functional form is found to consist of three parts; (1) the motion of the space origin of the Fermi coordinate system relative to the background one, (2) the Fermi-Walker tetrad transported along the world line of the space origin, and (3) the spacelike geodesic starting from the space origin. Next, the post-Newtonian expressions of the latter two are obtained under the condition that the first is given. Then the full coordinate transformation formula connecting the Fermi coordinate system to the background one is derived explicitly. The effectiveness of the Fermi coordinate system is discussed and the effective region is found to be a cylinder with the radius of about 0.5 kpc for the Fermi coordinate system comoving with the Earth. The mathematical way to derive the generalized Fermi coordinate system which Ashby and Bertotti defined is also shown.     

广义相对论在时频计量中的应用

介绍了广义相对论在时频计量中的应用的重要性和当前研究现状，评述了该领域的几个主要问题：原（固有，本征）时与坐标时的关系；不同坐标时之间的转换；各种不同方式的时间比对及各种不同方式的频率比对，给出了有关研究的最新结果。最后，简要地讨论了该领域需要关注的几个问题。     

The adiabatic cooling of the protons in the solar wind: The case where the interplanetary magnetic-field is of spiral form

This is a sequel to the paper by Eyni and Kaufman (1971) in which the coordinate systems with respect to the magnetic direction and solar radial-direction were assumed coincident. In the present account, it is shown that the theoretical expression for the proton cooling derived in that paper is still applicable in the case of the spiral magnetic-field provided the appropriate transformation of kinetic temperature from the magnetic direction to the radial direction as derived here is used. A detailed comparison is made between the present model and other models based on the spiral form of the magnetic field; the agreement is satisfactory.     

Coordinate Additional Perturbations to Mars Orbiters and Choice of Corresponding Coordinate System

Similar to the study of the related problems of Earth satellites, in the research of the motion of Mars orbiter especially for low-orbit satellites, it is more appropriate to choose an epoch Mars-centered and Mars-equator reference system, which indeed is called the Mars-centered celestial coordinate system. In this system, the xy-plane and the direction of the x-axis correspond to the mean equator and mean equinox. Similar to the precession and nutation of the Earth, the wiggling of instantaneous Mars equator causes the coordinate additional perturbations in this Mars coordinate system. The paper quotes a method which is similar to the one used in dealing with the coordinate additional perturbations of Earth. According to this method, based on the IAU2000 Mars orientation model and under the precondition of a certain accuracy, we are able to figure out the precession part of the change of Mars gravitation. This lays the foundation for further study of its influence on the Mars orbiter's orbit of precession and the solution of the corresponding coordinate additional perturbations. The obtained analytical solution is easy to use. Compared with the numerical solution with higher accuracy, the result shows that the accuracy of this analytical solution could satisfy the general requirements in use. Therefore, our result verifies that a unified coordinate system, the Mars-centered celestial system in which J2000.0 is chosen as its current initial epoch, could be applied to deal with the relative problems of Mars orbiters, especially for low-orbit satellites. It is different from the method we previously used in dealing with the corresponding problems of Earth satellites, where we adopted the instantaneous equator and epoch (J1950.0) mean equinox as xy-plane and the direction of x -axis. In contrast, the coordinate transformation brings heavy workload and certain inconvenience in relative former works in which the prior system is used. If adopting the unified coordinate system, the transformation could be simply avoided and the computation load could be decreased significantly.     

Synchronization of perturbed non-linear Hamiltonians

We propose a new method based on Lie transformations for simplifying perturbed Hamiltonians in one degree of freedom. The method is most useful when the unperturbed part has solutions in non-elementary functions. A non-canonical Lie transformation is used to eliminate terms from the perturbation that are not of the same form as those in the main part. The system is thus transformed into a modified version of the principal part. In conjunction with a time transformation, the procedure synchronizes the motions of the perturbed system onto those of the unperturbed part.A specific algorithm is given for systems whose principal part consists of a kinetic energy plus an arbitrary potential which is polynomial in the coordinate; the perturbation applied to the principal part is a polynomial in the coordinate and possibly the momentum.We demonstrate the strategy by applying it in detail to a perturbed Duffing system. Our procedure allow us to avoid treating the system as a perturbed harmonic oscillator. In contrast to a canonical simplification, our method involves only polynomial manipulations in two variables. Only after the change of time do we start manipulating elliptic functions in an exhaustive discussion of the flows.     

Model of VLBI observation within the relativistic framework

In this paper we derive the post-newtonian expressions for the VLBI time delay and gravitational delay in the barycentric coordinate system of the solar system. We discuss the effect of the various bodies and their range of action. From the transformation between the barycentric and the geocentric systems we then give the VLBI observational model in the geocentric system. Our final results are given by formula (16) for the gravitational delay and by formula (25) for the VLBI time delay.     

Measuring the plasma environment at Mercury: The fast imaging plasma spectrometer

Abstract— The plasma environment at Mercury is a rich laboratory for studying the interaction of the solar wind with a planet. Three primary populations of ions exist at Mercury: solar wind, magnetospheric, and pickup ions. These pickup ions are generated through the ionization of Mercury's exosphere or are sputtered particles from the Mercury surface. A comprehensive mission to Mercury, such as MESSENGER (MErcury: Surface, Space ENvironment, GEochemistry, Ranging), should include a sensor that is able to determine the dynamical properties and composition of all these plasma components. An instrument to measure the composition of these ion populations and their three‐dimensional velocity distribution functions must be lightweight, fast, and have a very large field of view. The fast imaging plasma spectrometer (FIPS) is an imaging mass spectrometer, part of NASA's MESSENGER mission, the first Mercury orbiter. This versatile instrument has a very small footprint, and has a mass that is ?1 order of magnitude less than other comparable systems. It maintains a nearly full‐hemisphere field of view, suitable for either spinning or three‐axis‐stabilized platforms. The major piece of innovation to enable this sensor is a new deflection system geometry that enables a large instantaneous (?1.5π) field of view. This novel electrostatic analyzer system is then combined with a position sensitive time‐of‐flight system. We discuss the design and prototype tests of the FIPS deflection system and show how this system is expected to address one key problem in Mercury science, that of the nature of the radar‐bright regions at the Hermean poles.     

Concerning the regularizing KS-transformation

In this note we give by means of quaternions in vector notation a new derivation of the KS-transformation acting from a four-dimensional parameter space into the three-dimensional physical space. Using quaternions in vector notation each step in the derivation has an immediate geometrical interpretation. In particular, the KS-transformation appears as the Levi-Civita transformation, formulated in a rotated coordinate system.Dedicated to Professor Otto Volk.     

Hawking radiation of Kerr-Newman black hole in different tortoise coordinate transformations

Hawking radiation effect of Maxwell’s electromagnetic fields in the Kerr-Newman black hole space-time is investigated using two different tortoise coordinate transformations. It has been shown that the new tortoise coordinate transformation produces constant term ξ in the expression of surface gravity and Hawking temperature. If ξ is set to zero, the surface gravity and Hawking temperature will be equal to those obtained from the old tortoise coordinate transformation. This indicates that new transformation is more reliable and accurate. The black body radiant spectrum of photon displays a new spin-rotation coupling effect.     

Elimination of the nodes in problems ofn bodies

In application of the Reduction Theorem to the general problem ofn (>-3) bodies, a Mathieu canonical transformation is proposed whereby the new variables separate naturally into (i) a coordinate system on any reduced manifold of constant angular momentum, and (ii) a quadruple made of a pair of ignorable longitudes together with their conjugate momenta. The reduction is built from a binary tree of kinetic frames Explicit transformation formulas are obtained by induction from the top of the tree down to its root at the invariable frame; they are based on the unit quaternions which represent the finite rotations mapping one vector base onto another in the chain of kinetic frames. The development scheme lends itself to automatic processing by computer in a functional language.     

Algorithmic regularization of the few-body problem

Using a modified leapfrog method as a basic mapping, we produce a new numerical integrator for the stellar dynamical few-body problem. We do not use coordinate transformation and the differential equations are not regularized, but the leapfrog algorithm gives regular results even for collision orbits. For this reason, application of extrapolation methods gives high precision. We compare the new integrator with several others and find it promising. Especially interesting is its efficiency for some potentials that differ from the Newtonian one at small distances.     

A more exact expression for the gravitational deflection of light,derived using material medium approach

The deflection of a ray of light passing close to a gravitational mass is generally calculated from the null geodesic which the light ray (photon) follows. However, there is an alternate approach, where the effect of gravitation on the ray of light is estimated by considering the ray to be passing through a material medium. Calculations have been done in this paper, following the latter approach, to estimate the amount of deflection due to a static non-rotating mass. The refractive index of such a material medium, has been calculated in a more rigorous manner in the present work, and the final expression for the amount of deflection calculated here is claimed to be more exact than all other expressions derived so far, using material medium approach. Based on this expression, the amount of deflection for a sun grazing ray has also been calculated. The exact amount of deflection can be performed in a number of ways, without the material medium approach. However, the method presented here using the material medium approach and without any weak field approximation is believed to be original.     

Self-gravitating fluid in a conformally-flat space-time

The Einstein field equations for an irrotational perfect fluid with pressurep, equal to energy density are studied when the space-time is conformally flat. The coordinate transformation to co-moving coordinates is discussed. The energy and Hawking-Penrose inequalities are studied. Static and non-static solutions of the field equations are obtained. It is interesting to note that in the static case the only spherically-symmetric conformally flat solution for self-gravitating fluid is simply the empty flat space-time of general relativity.     

Rotational dynamics of celestial bodies: Generalized rotation and considerations of angular momentum

The transformation equations under generalized rotation are obtained for an initially defined reduced velocity tensor governing the motion of a deformable finite material continuum. Then angular momentum considerations lead to relations between flow properties of the continuum and properties of a coordinate system introduced to describe generalized rotation of the continuum. Such relations could define preferable coordinate systems perceiving zero angular momentum for the continuum or referring that it moves according to linear laws.     

An observational determination of the principal nutation constants

The longitude and obliquity components of the principal nutation terms were derived from observations made in 1955–1977 of 43 star-pairs common to the ILS Programmes VI and VII. The observations were reduced to a uniform system appropriate to these 43 star-pairs. The results are 6'.'850 for the longitude component and 9'.'212 for the obliquity component.