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.     

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.     

Spacecraft Equipped with a Space Debris Removal System (Aerothermodynamics,Bulk–Mass Characteristics and Trajectories of Spacecraft Descent from Near-Earth Orbits)

The processes of space debris formation are described; the urgency of the problem of its removal from near-Earth space is noted. A method to prevent the clogging of space by equipping a spacecraft to be launched into orbit with additional devices, simple in design and mode of operation, is presented. The results of the estimation of aerothermodynamics, bulk–mass characteristics and trajectories of low-orbit spacecraft equipped with a space debris disposal system are presented.     

High resolution imaging of the Hubble Deep and Flanking Fields

42 hours of A-array VLA data and 18 days MERLIN data at 1.4 GHz have been combined to image a 10 arcminute field centred on the Hubble Deep Field (HDF). This area encloses both the Hubble Deep and Flanking Fields. A complete sample of 87 sources have been detected with flux densities above 40 μJy. All these have been imaged with the MERLIN+VLA combination to produce images with 0.2, 0.3 and 0.5 arcsecond resolution. These are the most sensitive 1.4 GHz images yet made with rms noise levels of 3.3 μJy/beam in the 0.2 arcsecond images. About 70% of the microJy sources are found to be starburst type systems associated with major disk galaxies in the redshift range 0.4–1. Some 20% are found to be low-luminosity AGN systems identified with field ellipticals at redshifts close to 1. The remaining 10% are associated with optically faint systems close to or beyond the HDF limit; many of these may be dust-shrouded starbursts at high redshift. We propose to extend this study to include VLBI data of comparable sensitivity to investigate the compact radio structures found in the microJy source population.     

Updated version of the ‘homogeneous catalog of open cluster parameters’

We report a new version of the “Homogeneous catalog of open cluster parameters” maintained by our team over the last decades. The catalog is based on redetermination of the main parameters of clusters (color excesses, heliocentric distances, and ages) based on published photometric measurements, in particular, those provided by the 2MASS point-source catalog. Currently, our catalog provides the parameters for 959 clusters. It also gives the estimates of cluster radial velocities for 496 clusters partly based on the data fromRAVE catalog. Estimates of proper-motion components are provided for all clusters included into the catalog. We analyze the distributions of the errors of the main cluster parameters and compare the distribution of cluster positions projected onto the Galactic plane with the distribution of cosmic masers thereby validating the distance scale of open clusters.     

Simulating flash heating in a muffle tube furnace

Abstract— Very rapid heating is an important chondrule-formation process, and it has not been clear whether conventional equipment, such as a muffle tube furnace, is adequate for the simulation of heating on a timescale of seconds. We present a method for measuring the internal temperature reached by a charge during rapid heating when the thermocouple response lags. We have constrained charge temperatures by monitoring the time required to melt metal wires of various compositions and melting points placed inside charges with furnace temperature at 1400, 1500, and 1600 °C. The times required for melting of the metal wires define the temperature paths inside the charges. At 1400 °C, a charge takes 31 s to reach 1399 °C; at 1500 °C, a charge takes 10 s to reach 1495 °C; and at 1600 °C, a charge takes 6 s to reach 1538 °C. Heating rates in vertical muffle tube furnaces are adequate for studying flash melting processes (i.e., of «1 min duration) invoked, for example, in the formation of chondrules.     

Adiabatic indices in a convecting anisotropic plasma

Adiabatic indices for a non-dissipative anisotropic convecting plasma are analyzed, and general expressions for the effective adiabatic index and the partial adiabatic indices parallel (γ_∥) and perpendicular (γ_⟂) to the magnetic field are obtained. It is shown that, in the general case, the value of the effective adiabatic index is not an universal constant and depends on the plasma temperature anisotropy and on the properties of the plasma motion. The values of γ_⟂ and γ_∥ are shown to be independent of the plasma parameters being completely determined by the characteristics of the plasma flow.     

Dependence of the solar wind speed on the coronal magnetic field in cycle 23

The dependence of the position of the solar wind sonic point on the magnetic field in the solar corona during cycle 23 is studied. This dependence is shown to be rather strong in the rising phase and at the cycle maximum. As the coronal magnetic field grows, the distance to the sonic point decreases. Since the distance to the sonic point has been shown previously to anticorrelate with the solar wind speed, the result obtained suggests a strong positive correlation between the later and the coronal magnetic field. The situation changed dramatically two years after the calendar date of the cycle maximum. Beginning in 2004 the solar wind speed ceased to depend on the magnetic field up until the cycle minimum in December 2008. In 2009 a strong dependence of the wind speed on the coronal magnetic field was restored. It is hypothesized that this effect is associated with two different coronal heating mechanisms whose relative efficiency, in turn, depends on the contribution from magnetic fields of different scales.