Main braking phase for a soft moon landing as a form of trajectory correction

Rationale is given for the braking profile of a spacecraft making a soft landing on the Moon’s surface, including the following four phases: main braking, free fall, repeated braking, and descent at a constant speed. Due to the large altitude differential over the braking path in near-polar regions of the Moon, main braking is proposed as a type of trajectory correction impulse using no altimeter. The boundary problem solution and statistical calculations are used to give the potential energy costs and characteristics of the dispersion characteristics for this phase and choose an optimal thrust-to-weight ratio for the phase.     

On Choosing a Rational Flight Trajectory to the Moon

The algorithm for choosing a trajectory of spacecraft flight to the Moon is discussed. The characteristic velocity values needed for correcting the flight trajectory and a braking maneuver are estimated using the Monte Carlo method. The profile of insertion and flight to a near-circular polar orbit with an altitude of ~100 km of an artificial lunar satellite (ALS) is given. The case of two corrections applied during the flight and braking phases is considered. The flight to an ALS orbit is modeled in the geocentric geoequatorial nonrotating coordinate system with the influence of perturbations from the Earth, the Sun, and the Moon factored in. The characteristic correction costs corresponding to corrections performed at different time points are examined. Insertion phase errors, the errors of performing the needed corrections, and the errors of determining the flight trajectory parameters are taken into account.     

Will the lunar renaissance come forth?

The article gives a brief review of the scientific program of the unmanned studies of the Moon performed in the USSR in 1960s–1970s, most notably by the “Luna” Spacecraft. The main results obtained during this period are considered, in particular photographing of the far side of the Moon, mapping of the far side of the Moon, soft landing, remote (from the orbit of an artificial lunar satellite) and in situ (on the surface) studies of the lunar surface composition and circumlunar space, automated soil sampling, and delivery of surface samples to the Earth. Various institutes of the Russian Academy of Sciences played important role in the studies, including the Vernadskii Institute of Geochemistry and Analytical Chemistry and the Space Research Institute, established in 1965, where the Moon and Planets Department was established under the leadership of K.P. Florenskii. In the conclusion, the article considers some further issues of lunar studies and possibilities for lunar exploration. The challenging Moon exploration mission “Luna-Glob”, currently under development in Russia, is a potentially important step in the beginning of the process.     

满足一定约束条件的登月飞行轨道的设计

讨论满足约束条件的登月飞行轨道的设计问题，将约束条件分类为只与太阳，月球，地球，飞行器和观测站之间的相对位置有关的运动学约束条件以及小及到飞行器轨道云动的动力学约束条件，在考虑登月飞行轨道的特征后，给出一种设计满足约束条件的标准飞行轨道的方法，并将方法应用于不同约束条件下的我国登月飞行以及月球卫星的轨道预测计。     

The lunar gravity mission MAGIA: preliminary design and performances

The importance of an accurate model of the Moon gravity field has been assessed for future navigation missions orbiting and/or landing on the Moon, in order to use our natural satellite as an intermediate base for next solar system observations and exploration as well as for lunar resources mapping and exploitation. One of the main scientific goals of MAGIA mission, whose Phase A study has been recently funded by the Italian Space Agency (ASI), is the mapping of lunar gravitational anomalies, and in particular those on the hidden side of the Moon, with an accuracy of 1 mGal RMS at lunar surface in the global solution of the gravitational field up to degree and order 80. MAGIA gravimetric experiment is performed into two phases: the first one, along which the main satellite shall perform remote sensing of the Moon surface, foresees the use of Precise Orbit Determination (POD) data available from ground tracking of the main satellite for the determination of the long wavelength components of gravitational field. Improvement in the accuracy of POD results are expected by the use of ISA, the Italian accelerometer on board the main satellite. Additional gravitational data from recent missions, like Kaguya/Selene, could be used in order to enhance the accuracy of such results. In the second phase the medium/short wavelength components of gravitational field shall be obtained through a low-to-low (GRACE-like) Satellite-to-Satellite Tracking (SST) experiment. POD data shall be acquired during the whole mission duration, while the SST data shall be available after the remote sensing phase, when the sub-satellite shall be released from the main one and both satellites shall be left in a free-fall dynamics in the gravity field of the Moon. SST range-rate data between the two satellites shall be measured through an inter-satellite link with accuracy compliant with current state of art space qualified technology. SST processing and gravitational anomalies retrieval shall benefit from a second ISA accelerometer on the sub-satellite in order to decouple lunar gravitational signal from other accelerations. Experiment performance analysis shows that the stated scientific requirements can be achieved with a low mass and low cost sub-satellite, with a SST gravimetric mission of just few months.     

Capability of the penetrator seismometer system for lunar seismic event observation

We developed a seismometer system for a hard landing “penetrator” probe in the course of the former Japanese LUNAR-A project to deploy new seismic stations on the Moon. The penetrator seismometer system (PSS) consists of two short-period sensor components, a two-axis gimbal mechanism for orientation, and measurement electronics. To carry out seismic observations on the Moon using the penetrator, the seismometer system has to function properly in a lunar environment after a hard landing (impact acceleration of about 8000 G), and requires a signal-to-noise ratio to detect lunar seismic events. We evaluated whether the PSS could satisfactorily observe seismic events on the Moon by investigating the frequency response, noise level, and response to ground motion of our instrument in a simulated lunar environment after a simulated impact test. Our results indicate that the newly developed seismometer system can function properly after impact and is sensitive enough to detect seismic events on the Moon. Using this PSS, new seismic data from the Moon can be obtained during future lunar missions.     

Comparison of low-energy lunar transfer trajectories to invariant manifolds

In this study, transfer trajectories from the Earth to the Moon that encounter the Moon at various flight path angles are examined, and lunar approach trajectories are compared to the invariant manifolds of selected unstable orbits in the circular restricted three-body problem. Previous work focused on lunar impact and landing trajectories encountering the Moon normal to the surface, and this research extends the problem with different flight path angles in three dimensions. The lunar landing geometry for a range of Jacobi constants is computed, and approaches to the Moon via invariant manifolds from unstable orbits are analyzed for different energy levels.     

Control of chaos in the vicinity of the Earth‐Moon L5 Lagrangian point to keep a spacecraft in orbit

The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi, and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L₅ of the Earth‐Moon system. We have determined the escape rate of the trajectories in the general three‐ and four‐body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L₅ point of the Earth‐Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L₅. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit‐keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time, and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L₅. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The INPOP10a planetary ephemeris and its applications in fundamental physics

Compared to the previous INPOP versions, the INPOP10a planetary and lunar ephemeris has several improvements. For the planets of our Solar System, no big change was brought in the dynamics but improvements were implemented in the fitting process, the data sets used in the fit and in the selection of fitted parameters. We report here the main characteristics of the planetary part of INPOP10a like the fit of the product of the solar mass with the gravitational constant ( GM_\odot{{\rm GM}_{\odot}}) instead of the astronomical unit. Determinations of PPN parameters as well as adjustments of the Sun J2 and of asteroid masses are also presented. New advances of nodes and perihelia of planets were also estimated and are given here. As for INPOP08, INPOP10a provides to the user, positions and velocities of the planets, the Moon, the rotation angles of the Earth and the Moon as well as TT-TDB Chebyshev polynomials at .     

Measurements of the Quiet-Sun Level Brightness Temperature at 8 mm

Defining the solar brightness temperature accurately at millimeter wavelengths has always been challenging. One of the main reasons has been the lack of a proper calibration source. New Moon was used earlier as a calibration source. We carried out a new extensive set of observations at 8 mm using the New Moon for calibration. The solar and Moon observations were made using the 14-meter radiotelescope operated by the Aalto University Metsähovi Radio Observatory in Finland. In this article, we present our method for defining the brightness temperature of the quiet-Sun level (QSL). Based on these observations, we found \(8100~\mbox{K} \pm 300~\mbox{K}\) to be the mean value for the QSL temperature. This value is between the values that were reported in earlier studies.     

Investigating the crystallization history of Apollo 15 mare basalts using quantitative textural analysis

Mare basalts collected at the Apollo 15 landing site are classified as belonging to either the quartz-normative suite or the olivine-normative suite, based on differences in whole-rock major element chemistry. A wide range of textures are displayed within samples from both suites, which provide insight into eruption processes on the Moon. Here we use crystal size distribution (CSD) analysis and spatial distribution pattern (SDP) analysis of pyroxene, olivine, and plagioclase crystals in eight Apollo 15 mare basalt samples to investigate the crystallization and emplacement of the quartz-normative and olivine-normative suites. In general, our results show similarities between the CSDs and SDPs for both mare basalt suites. However, we also report two distinct groups of pyroxene CSD trends that likely represent samples with common cooling histories, originating from comparable depths within respective olivine-normative and quartz-normative lava flows. We use our results to determine the relative depths of samples within the lava flows at the Apollo 15 landing site.     

On the chronology of lunar origin and evolution

An origin of the Moon by a Giant Impact is presently the most widely accepted theory of lunar origin. It is consistent with the major lunar observations: its exceptionally large size relative to the host planet, the high angular momentum of the Earth–Moon system, the extreme depletion of volatile elements, and the delayed accretion, quickly followed by the formation of a global crust and mantle.According to this theory, an impact on Earth of a Mars-sized body set the initial conditions for the formation and evolution of the Moon. The impact produced a protolunar cloud. Fast accretion of the Moon from the dense cloud ensured an effective transformation of gravitational energy into heat and widespread melting. A “Magma Ocean” of global dimensions formed, and upon cooling, an anorthositic crust and a mafic mantle were created by gravitational separation.Several 100 million years after lunar accretion, long-lived isotopes of K, U and Th had produced enough additional heat for inducing partial melting in the mantle; lava extruded into large basins and solidified as titanium-rich mare basalt. This delayed era of extrusive rock formation began about 3.9 Ga ago and may have lasted nearly 3 Ga.A relative crater count timescale was established and calibrated by radiometric dating (i.e., dating by use of radioactive decay) of rocks returned from six Apollo landing regions and three Luna landing spots. Fairly well calibrated are the periods ≈4 Ga to ≈3 Ga BP (before present) and ≈0.8 Ga BP to the present. Crater counting and orbital chemistry (derived from remote sensing in spectral domains ranging from γ- and x-rays to the infrared) have identified mare basalt surfaces in the Oceanus Procellarum that appear to be nearly as young as 1 Ga. Samples returned from this area are needed for narrowing the gap of 2 Ga in the calibrated timescale. The lunar timescale is not only used for reconstructing lunar evolution, but it serves also as a standard for chronologies of the terrestrial planets, including Mars and possibly early Earth.The Moon holds a historic record of Galactic cosmic-ray intensity, solar wind composition and fluxes and composition of solids of any size in the region of the terrestrial planets. Some of this record has been deciphered. Secular mixing of the Sun was constrained by determining ³He/⁴He of solar wind helium stored in lunar fines and ancient breccias. For checking the presumed constancy of the impact rate over the past ≈3.1 Ga, samples of the youngest mare basalts would be needed for determining their radiometric ages.Radiometric dating and stratigraphy has revealed that many of the large basins on the near side of the Moon were created by impacts about 4.1 to 3.8 Ga ago. The apparent clustering of ages called “Late Heavy Bombardment (LHB)” is thought to result from migration of planets several 100 million years after their accretion.The bombardment, unexpectedly late in solar system history, must have had a devastating effect on the atmosphere, hydrosphere and habitability on Earth during and following this epoch, but direct traces of this bombardment have been eradicated on our planet by plate tectonics. Indirect evidence about the course of bombardment during this epoch on Earth must therefore come from the lunar record, especially from additional data on the terminal phase of the LHB. For this purpose, documented samples are required for measuring precise radiometric ages of the Orientale Basin and the Nectaris and/or Fecunditatis Basins in order to compare these ages with the time of the earliest traces of life on Earth.A crater count chronology is presently being built up for planet Mars and its surface features. The chronology is based on the established lunar chronology whereby differences between the impact rates for Moon and Mars are derived from local fluxes and impact energies of projectiles. Direct calibration of the Martian chronology will have to come from radiometric ages and cosmic-ray exposure ages measured in samples returned from the planet.     

A new lunar absolute control point: established by images from the landing camera on Chang'e-3

The establishment of a lunar control network is one of the core tasks in selenodesy, in which defining an absolute control point on the Moon is the most important step. However, up to now, the number of absolute control points has been very sparse. These absolute control points have mainly been lunar laser ranging retroreflectors, whose geographical location can be observed by observations on Earth and also identified in high resolution lunar satellite images. The Chang'e-3(CE-3) probe successfully landed on the Moon, and its geographical location has been monitored by an observing station on Earth. Since its positional accuracy is expected to reach the meter level, the CE-3 landing site can become a new high precision absolute control point. We use a sequence of images taken from the landing camera, as well as satellite images taken by CE-1 and CE-2, to identify the location of the CE-3 lander. With its geographical location known, the CE-3 landing site can be established as a new absolute control point, which will effectively expand the current area of the lunar absolute control network by 22%, and can greatly facilitate future research in the field of lunar surveying and mapping, as well as selenodesy.     

Properties of the Hermean regolith: IV. Photometric parameters of Mercury and the Moon contrasted with Hapke modelling

A comparison of the photometric properties of Mercury and the Moon is performed, based on their integral phase curves and disk-resolved image data of Mercury obtained with the Swedish Vacuum Solar Telescope. Proper absolute calibration of integral V-band magnitude observations reveals that the near-side of the Moon is 10-15% brighter than average Mercury, and 0-5% brighter for the “bolometric” wavelength range 400-1000 nm. As shown, this is supported by recent estimates of their geometric albedos. Hapke photometric parameters of their surfaces are derived from identical approaches, allowing a contrasting study between their surface properties to be performed. Compared to the average near-side Moon, Mercury has a slightly lower single-scattering albedo, an opposition surge with smaller width and of marginally smaller amplitude, and a somewhat smoother surface with similar porosity. The width of the lobes of the single-particle scattering function are smaller for Mercury, and the backward scattering anisotropy is stronger. In terms of the double Henyey-Greenstein b-c parameter plot, the scattering properties of an average particle on Mercury is closer to the properties of lunar maria than highlands, indicating a higher density of internal scatterers than that of lunar particles. The photometric roughness of Mercury is well constrained by the recent study of Mallama et al. (2002, Icarus 155, 253-264) to a value of about 8°, suggesting that the surfaces sampled by the highest phase angle observations (Borealis, Susei, and Sobkou Planitia) are lunar mare-like in their textural properties. However, Mariner 10 disk brightness profiles obtained at intermediate phase angles indicate a surface roughness of about twice this value. The photometric parameters of the Moon are more difficult to constrain due to limited phase angle coverage, but the best Hapke fits are provided by rather small surface roughnesses. Better-calibrated, multiple-wavelength observations of the integral and disk-resolved brightnesses of both bodies, and obtained at higher phase angle values in the case of the Moon, are urgently needed to arrive at a more consistent picture of the contrasting light scattering properties of their surfaces.     

Creating an isotopically similar Earth–Moon system with correct angular momentum from a giant impact

The giant impact hypothesis is the dominant theory explaining the formation of our Moon. However, the inability to produce an isotopically similar Earth–Moon system with correct angular momentum has cast a shadow on its validity. Computer-generated impacts have been successful in producing virtual systems that possess many of the observed physical properties. However, addressing the isotopic similarities between the Earth and Moon coupled with correct angular momentum has proven to be challenging. Equilibration and evection resonance have been proposed as means of reconciling the models. In the summer of 2013, the Royal Society called a meeting solely to discuss the formation of the Moon. In this meeting, evection resonance and equilibration were both questioned as viable means of removing the deficiencies from giant impact models. The main concerns were that models were multi-staged and too complex. We present here initial impact conditions that produce an isotopically similar Earth–Moon system with correct angular momentum. This is done in a single-staged simulation. The initial parameters are straightforward and the results evolve solely from the impact. This was accomplished by colliding two roughly half-Earth-sized impactors, rotating in approximately the same plane in a high-energy, off-centered impact, where both impactors spin into the collision.     

Implementation of the First Asteroid Landing

Spacecraft have successfully landed on the Moon, Venus, and Mars, and have penetrated the atmosphere of Jupiter. On 2001 February 12, the Near-Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft landed on the surface of the asteroid (433) Eros after a year of observations in orbit about the asteroid. NEAR Shoemaker was not designed to land on an asteroid, complicating the design of operations needed to accomplish this feat. However, the NEAR Shoemaker team wanted to attempt a landing after the year of orbital operations that consumed most of the remaining spacecraft fuel, operations funding, and planned Deep Space Network tracking. This would be a fitting end to the mission, and it would be possible to obtain images at much greater resolution during the descent than could be obtained from orbit. The operations were more successful than the NEAR Shoemaker team had hoped, obtaining 70 high-resolution images during the descent and two weeks of gamma-ray spectrometer data from the surface after the successful soft landing.     

Polarimetric mapping of the Moon at a phase angle near the polarization minimum

At small phase angles the light scattered by the Moon reveals a negative polarization branch whose average amplitude is 1%. We present results of polarimetric mappings of the Moon in Pmin at a phase angle near 11°. The observations were carried out with the Kharkov 50-cm telescope at the Maidanak Observatory (Middle Asia) using a polarizing filter. A thorough calibration of the camera array allows for the reliable detection of significant variations of |Pmin| over the lunar surface, from 0.2 to 1.6%, at a wavelength of 0.52 μm. The smallest |Pmin| are characteristic of young bright craters, while the |Pmin| are the highest for the lunar highland and bright mare areas. The horse-shoe shape of the correlation dependence Pmin (albedo) is treated with data of our laboratory measurements of powdered surfaces and computer modeling of light scattering by small particles with the DDA (discrete dipole approximation) technique.     

Magnetization of celestial bodies with special application to the primeval Earth and Moon

The magnetic fields of celestial bodies are usually supposed to be due to a ‘hydromagnetic dynamo’. This term refers to a number of rather speculative processes which are supposed to take place in the liquid core of a celestial body. In this paper we shall follow another approach which is more closely connected with hydromagnetic processes well-known from the laboratory, and hence basically less speculative. The paper should be regarded as part of a general program to connect cosmical phenomena with phenomena studied in the laboratory. As has been demonstrated by laboratory experiments, a poloidal magnetic field may be increased by the transfer of energy from a toroidal magnetic field through kink instability of the current system. This mechanism can be applied to the fluid core of a celestial body. Any differential rotation will produce a toroidal field from an existing poloidal field, and the kink instability will feed toroidal energy back to the poloidal field, and hence amplify it. In the Earth-Moon system the tidal braking of the Earth's mantle acts to produce a differential angular velocity between core and mantle. The braking will be transferred to the core by hydromagnetic forces which at the same time give rise to a strong magnetic field. The strength of the field will be determined by the rate of tidal braking. It is suggested that the magnetization of lunar rocks from the period ?4 to ?3 Gyears derives from the Earth's magnetic field. As the interior of the Moon immediately after accretion probably was too cool to be melted, the Moon could not produce a magnetic field by hydromagnetic effects in its core. The observed lunar magnetization could be produced by such an amplified Earth field even if the Moon never came closer than 10 or 20 Earth's radii. This hypothesis might be checked by magnetic measurements on the Earth during the same period.