The construction of gravitational field models on the basis of satellite measurements of gravitational potential derivatives

In [1] expressions were constructed for the derivatives of all the orders of a planet’s gravitational potential with respect to the rectangular coordinates related to the gravity center of a planet. These expressions are series of spherical functions. The coefficients of the series of first-order derivatives depend on two Stokes constants, whereas the coefficients of next-order derivatives are linear combinations of the coefficients of preceding-order derivatives. In the present paper the derived expressions for the first and second potential derivatives are transformed into the form that is most convenient for solving the inverse problem, i.e., evaluating Stokes constants from satellite measurements of these derivatives. Each term of the new series for a derivative depends on a sum of two Stokes constants multiplied by linear combinations of several spherical functions. The new form of the expansions for the potential derivatives makes it possible to calculate Stokes constants by simultaneously applying satellite data either for all three first-order potential derivatives, or for all six second-order derivatives. The constructed series may be applied for modeling the Earth’s gravitational field from the satellite data obtained in the international CHAMP, GRACE, and GOCE missions.     

Homologous flare–CME events and their metric type II radio burst association

Active region NOAA 11158 produced many flares during its disk passage. At least two of these flares can be considered as homologous: the C6.6 flare at 06:51 UT and C9.4 flare at 12:41 UT on February 14, 2011. Both flares occurred at the same location (eastern edge of the active region) and have a similar decay of the GOES soft X-ray light curve. The associated coronal mass ejections (CMEs) were slow (334 and 337 km/s) and of similar apparent widths (43° and 44°), but they had different radio signatures. The second event was associated with a metric type II burst while the first one was not. The COR1 coronagraphs on board the STEREO spacecraft clearly show that the second CME propagated into the preceding CME that occurred 50 min before. These observations suggest that CME–CME interaction might be a key process in exciting the type II radio emission by slow CMEs.     

On the large-scale structure of the tail current as measured by THEMIS

The magnetic field structure and the spatial characteristics of the large-scale currents in the magnetospheric tail were studied during quiet and moderately disturbed geomagnetic conditions in 2009. The magnetic field of the currents other than the tail current was calculated in terms of a paraboloid model of the Earth’s magnetosphere, A2000, and was subtracted from measurements. It was found on the base of obtained tail current magnetic field radial distribution that the inner edge of the tail current sheet is located in the night side magnetosphere, at distances of about 10 R_E and of about 7 R_E during quiet and disturbed periods respectively. During the disturbance of February 14, 2009 (Dst_min ∼ −35 nT), the B_x and the B_z component of the tail current magnetic field near its inner edge were about 60 nT, and −60 nT that means that strong cross-tail current have been developed. The tail current parameters at different time moments during February 14, 2009 have been estimated. Solar wind conditions during this event were consistent with those during moderate magnetic storms with minimum Dst of about −100 nT. However, the magnetospheric current systems (magnetopause and cross-tail currents) were located at larger geocentric distances than typical during the 2009 extremely quiet epoch and did not provide the expected Dst magnitude. Very small disturbance on the Earth’s surface was detected consistent with an “inflated” magnetosphere.     

Signatures of strong geomagnetic storms in the equatorial latitude

Ionosonde data from two equatorial stations in the African sector have been used to study the signatures of four strong geomagnetic storms on the height – electron density profiles of the equatorial ionosphere with the objective of investigating the effects and extent of the effects on the three layers of the equatorial ionosphere. The results showed that strong geomagnetic storms produced effects of varying degrees on the three layers of the ionosphere. Effect of strong geomagnetic storms on the lower layers of the equatorial ionosphere can be significant when compared with effect at the F2-layer. Fluctuations in the height of ionization within the E-layer were as much as 0% to +20.7% compared to −12.5% to +8.3% for the F2-layer. The 2007 version of the International Reference Ionosphere, IRI-07 storm-time model reproduced responses at the E-layer but overestimated the observed storm profiles for the F1- and F2-layers.     

Cosmic Ray Energetics And Mass for the International Space Station (ISS-CREAM)

The Cosmic Ray Energetics And Mass (CREAM) instrument is configured with a suite of particle detectors to measure TeV cosmic-ray elemental spectra from protons to iron nuclei over a wide energy range. The goal is to extend direct measurements of cosmic-ray composition to the highest energies practical, and thereby have enough overlap with ground based indirect measurements to answer questions on cosmic-ray origin, acceleration and propagation. The balloon-borne CREAM was flown successfully for about 161 days in six flights over Antarctica to measure elemental spectra of Z = 1–26 nuclei over the energy range 10¹⁰ to >10¹⁴ eV. Transforming the balloon instrument into ISS-CREAM involves identification and replacement of components that would be at risk in the International Space Station (ISS) environment, in addition to assessing safety and mission assurance concerns. The transformation process includes rigorous testing of components to reduce risks and increase survivability on the launch vehicle and operations on the ISS without negatively impacting the heritage of the successful CREAM design. The project status, including results from the ongoing analysis of existing data and, particularly, plans to increase the exposure factor by another order of magnitude utilizing the International Space Station are presented.     

Analytical-HZETRN model for rapid assessment of active magnetic radiation shielding

The use of active radiation shielding designs has the potential to reduce the radiation exposure received by astronauts on deep-space missions at a significantly lower mass penalty than designs utilizing only passive shielding. Unfortunately, the determination of the radiation exposure inside these shielded environments often involves lengthy and computationally intensive Monte Carlo analysis. In order to evaluate the large trade space of design parameters associated with a magnetic radiation shield design, an analytical model was developed for the determination of flux inside a solenoid magnetic field due to the Galactic Cosmic Radiation (GCR) radiation environment. This analytical model was then coupled with NASA’s radiation transport code, HZETRN, to account for the effects of passive/structural shielding mass. The resulting model can rapidly obtain results for a given configuration and can therefore be used to analyze an entire trade space of potential variables in less time than is required for even a single Monte Carlo run. Analyzing this trade space for a solenoid magnetic shield design indicates that active shield bending powers greater than ∼15 Tm and passive/structural shielding thicknesses greater than 40 g/cm² have a limited impact on reducing dose equivalent values. Also, it is shown that higher magnetic field strengths are more effective than thicker magnetic fields at reducing dose equivalent.     

Small amplitude ion acoustic solitons in a weakly magnetized plasma with anisotropic ion pressure and kappa distributed electrons

The Zakharov–Kuznetzov (ZK) equation is derived for nonlinear electrostatic waves in a weakly magnetized plasma in the presence of anisotropic ion pressure and superthermal electrons. The anisotropic ion pressure is defined using Chew–Goldberger–Low (CGL) while a generalized Lorentzian (kappa) distribution is assumed for the non-thermal electrons. The standard reductive perturbation method (RPM) is employed to derive the two dimensional ZK equation for the dynamics of obliquely propagating low frequency ion acoustic wave. The influence of spectral index (kappa) of non-thermal electron on the soliton is discussed in the presence of anisotropic ion pressure in plasmas. It is found that ion pressure anisotropy and superthermality of electrons affect both the width and amplitude of the solitary waves. On the other hand the magnetic field is found to alter the dispersive property of the plasma only, and hence the width of the solitons is affected while the amplitude of the solitary waves is independent of external magnetic field. The numerical results are also presented for illustrations.     

A new global version of M(3000)F2 prediction model based on artificial neural networks

A new version of global empirical model for the ionospheric propagation factor, M(3000)F2 prediction is presented. Artificial neural network (ANN) technique was employed by considering the relevant geophysical input parameters which are known to influence the M(3000)F2 parameter. This new version is an update to the previous neural network based M(3000)F2 global model developed by Oyeyemi et al. (2007), and aims to address the inadequacy of the International Reference Ionosphere (IRI) M(3000)F2 model (the International Radio Consultative Committee (CCIR) M(3000)F2 model). The M(3000)F2 has been found to be relatively inaccurate in representing the diurnal structure of the low latitude region and the equatorial ionosphere. In particular, the existing hmF2 IRI model is unable to reproduce the sharp post-sunset drop in M(3000)F2 values, which correspond to a sharp post-sunset peak in the peak height of the F2 layer, hmF2. Data from 80 ionospheric stations globally, including a good number of stations in the low latitude region were considered for this work. M(3000)F2 hourly values from 1987 to 2008, spanning all periods of low and high solar activity were used for model development and verification process. The ability of the new model to predict the M(3000)F2 parameter especially in the low latitude and equatorial regions, which is known to be problematic for the existing IRI model is demonstrated.     

An empirical approach to predicting the key parameters for a sunspot number cycle

The common methodologies used to predict the smooth sunspot number (SSN) at peak (Rmax) and the rise time (Tr) for a cycle are noted. The estimates based on geomagnetic precursors give the best prediction of Rmax for five SSN cycles (20–24). In particular, an empirical technique invoking three-cycle quasi-periodicity (TCQP) in Ap index has made accurate predictions of Rmax and Tr for two consecutive SSN cycles (23 and 24). The dynamo theories are unable to account for TCQP. If it endures in the 21st century the Sun shall enter a Dalton-like grand minimum. It was a period of global cooling. The current status of the ascending phase of cycle 24 is described and the delayed reversal of the solar polar field reversal in the southern hemisphere in September 2013 is noted.     

Alternative transfer to the Earth–Moon Lagrangian points L4 and L5 using lunar gravity assist

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth–Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon’s sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon’s gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.