Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories.     

Fraile Detection of Solar $$-Modes by Fossat et al.

The internal gravity modes of the Sun are notoriously difficult to detect, and the claimed detection of gravity modes presented by Fossat et al. (Astron. Astrophys.604, A40, 2017) is thus very exciting. Given the importance of these modes for understanding solar structure and dynamics, the results must be robust. While Fossat et al. described their method and parameter choices in detail, the sensitivity of their results to several parameters was not presented. Therefore, we test the sensitivity of the results to a selection of the parameters. The most concerning result is that the detection vanishes when we adjust the start time of the 16.5-year velocity time-series by a few hours. We conclude that this reported detection of gravity modes is extremely fragile and should be treated with utmost caution.     

The Problem of the Height Dependence of Magnetic Fields in Sunspots

To understand the physics of sunspots, it is important to know the properties of their magnetic field, and especially its height stratification plays a substantial role. There are mainly two methods to assess this stratification, but they yield different magnetic gradients in the photospheric layers. Determinations based on the several spectral lines of different formation heights and the slope of their profiles result in gradients of ?2 to ?3 G?km^?1, or even steeper. This is similar for the total magnetic field strength and for the vertical component of the magnetic field. The other option is to determine the horizontal partial derivatives of the magnetic field, and with the condition \(\operatorname{div} {{\boldsymbol {B}}} = 0\) also the vertical derivative is known. With this method, gradients of ?0.5 G?km^?1 and even shallower are obtained. Obviously, these results do not agree. If chromospheric spectral lines are included, only shallow gradients around ?0.5 G?km^?1 are obtained. Shallow gradients are also found from gyro-resonance measurements in the radio wave range 300?–?2000 GHz.Some indirect methods are also considered, but they cannot clarify the total picture. An analysis of a numerical simulation of a sunspot indicates a shallow gradient over a wide height range, but with slightly steeper gradients in deep layers.Several ideas to explain the discrepancy are also discussed. With no doubts cast on Maxwell’s equations, the first one is to look at the uncertainties of the formation heights of spectral lines, but a wider range of these heights would require an extension of the solar photosphere that is incompatible with observations and the theory of stellar atmospheres. Submerging and rising magnetic flux might play a role in the outer penumbra, if the resolution is too low to separate them, but it is not likely that this effect acts also in the umbra. A quick investigation assuming a spatial small scale structure of sunspots together with twist and writhe of individual flux tubes shows a reduction of the measured magnetic field strength for spectral lines sensitive to a larger height range. However, sophisticated investigations are required to prove that the explanation for the discrepancy lies here, and the problem of the height gradient of the magnetic field in sunspots is still not solved.     

Mid-term periodicities and heliospheric modulation of coronal index and solar flare index during solar cycles 22–23

We applied fast Fourier transform techniques and Morlet wavelet transform on the time series data of coronal index, solar flare index, and galactic cosmic ray, for the period 1986–2008, in order to investigate the long- and mid-term periodicities including the Rieger (\({\sim }130\) to \({\sim }190\) days), quasi-period (\({\sim }200\) to \({\sim }374\) days), and quasi-biennial periodicities (\({\sim }1.20\) to \({\sim }3.27\) years) during the combined solar cycles 22–23. We emphasize the fact that a lesser number of periodicities are found in the range of low frequencies, while the higher frequencies show a greater number of periodicities. The rotation rates at the base of convection zone have periods for coronal index of \({\sim }1.43\) years and for solar flare index of \({\sim }1.41\) year, and galactic cosmic ray, \({\sim }1.35\) year, during combined solar cycles 22–23. In relation to these two solar parameters (coronal index and solar flare index), for the solar cycles 22–23, we found that galactic cosmic ray modulation at mid cut-off rigidity (\(\hbox {Rc} = 2.43\hbox {GV}\)) is anti-correlated with time-lag of few months.     

Sodium in the atmospheres of thick-disk red giants

The atmospheric parameters and elemental abundances for ten thick-disk red giants have been determined from high-resolution spectra by the method of model stellar atmospheres. The results of a comparative analysis of the [Na/Fe] abundances in the atmospheres of the investigated stars and thin-disk red giants are presented. Sodium in the atmospheres of thick-disk red giants is shown to have no overabundances typical of thin-disk red giants.     

Effective Acceleration Model for the Arrival Time of Interplanetary Shocks driven by Coronal Mass Ejections

In a previous work (Paouris and Mavromichalaki in Solar Phys. 292, 30, 2017), we presented a total of 266 interplanetary coronal mass ejections (ICMEs) with as much information as possible. We developed a new empirical model for estimating the acceleration of these events in the interplanetary medium from this analysis. In this work, we present a new approach on the effective acceleration model (EAM) for predicting the arrival time of the shock that preceds a CME, using data of a total of 214 ICMEs. For the first time, the projection effects of the linear speed of CMEs are taken into account in this empirical model, which significantly improves the prediction of the arrival time of the shock. In particular, the mean value of the time difference between the observed time of the shock and the predicted time was equal to +3.03 hours with a mean absolute error (MAE) of 18.58 hours and a root mean squared error (RMSE) of 22.47 hours. After the improvement of this model, the mean value of the time difference is decreased to ?0.28 hours with an MAE of 17.65 hours and an RMSE of 21.55 hours. This improved version was applied to a set of three recent Earth-directed CMEs reported in May, June, and July of 2017, and we compare our results with the values predicted by other related models.     

Revisiting Field Burial by Accretion onto Neutron Stars

The surface magnetic field strength of millisecond pulsars (MSPs) is found to be about 4 orders of magnitude lower than that of garden variety radio pulsars (with a spin of \({\sim }\)0.5–5 s and \(B{\sim }10^{12}\hbox { G}\)). The exact mechanism of the apparent reduction of field strength in MSPs is still a subject of debate. One of the proposed mechanisms is burial of the surface magnetic field under matter accreted from a companion. In this article we review the recent work on magnetic confinement of accreted matter on neutron stars poles. We present the solutions of the magneto-static equations with a more accurate equation of state of the magnetically confined plasma and discuss its implications for the field burial mechanism.     

Catalog of equatorial coordinates and <Emphasis Type="Italic">B</Emphasis>-magnitudes of stars of the Kitab part of the FON project

The processing of the plates of the Kitab part of the FON project has been completed. In total, 1963 plates were processed. The catalog of equatorial coordinates α, δ, and B-magnitudes for 13 413268 stars and galaxies up to B ≤ 17.5 ^m for the epoch 1984.97 is compiled. The Epson Expression 10000XL scanner with a 1200 dpi scanning mode and a plate size of 30 × 30 cm or 13000 × 13000 pel was used to digitize astronegatives. Coordinates of stars and galaxies are obtained in the Tycho-2 catalog system and B-magnitudes are obtained in the photovoltaic system. The catalog internal accuracy for all objects is σ_α,δ = 0.23" and σ _B = 0.15 ^m (for stars in the range B = 5 ^m …14 ^m , errors are σ_α,δ = 0.085" and σ _B = 0.054 ^m ) for equatorial coordinates and stellar B-magnitudes, respectively. Convergence between the calculated and reference positions is σ_α,δ = 0.042", and convergence between photoelectric B-magnitudes is σ _B = 0.16 ^m . Coordinate errors with respect to the UCAC-4 catalog are σ_α,δ = 0.26" (9892697 or 73.75% of stars and galaxies were identified).