In this comment on the article“Locating the source field lines of Jovian decametric radio emissions”by Wang YM et al.,2020,we discuss the assumptions used by the authors to compute the beaming angle of Jupiter’s de...In this comment on the article“Locating the source field lines of Jovian decametric radio emissions”by Wang YM et al.,2020,we discuss the assumptions used by the authors to compute the beaming angle of Jupiter’s decametric emissions induced by the moon Io.Their method,relying on multi-point radio observations,was applied to a single event observed on 14th March 2014 by Wind and both STEREO A/B spacecraft from~5 to~16 MHz.They have erroneously identified the emission as a northern(Io-B type)instead of a southern one(Io-D type).We encourage the authors to update their results with the correct hemisphere of origin and to test their method on a larger sample of Jupiter-Io emissions.展开更多
To better understand Earth's present tectonic style-plate tectonics—and how it may have evolved from single plate(stagnant lid) tectonics, it is instructive to consider how common it is among similar bodies in th...To better understand Earth's present tectonic style-plate tectonics—and how it may have evolved from single plate(stagnant lid) tectonics, it is instructive to consider how common it is among similar bodies in the Solar System. Plate tectonics is a style of convection for an active planetoid where lid fragment(plate) motions reflect sinking of dense lithosphere in subduction zones, causing upwelling of asthenosphere at divergent plate boundaries and accompanied by focused upwellings, or mantle plumes;any other tectonic style is usefully called "stagnant lid" or "fragmented lid". In 2015 humanity completed a 50+ year effort to survey the 30 largest planets, asteroids, satellites, and inner Kuiper Belt objects,which we informally call "planetoids" and use especially images of these bodies to infer their tectonic activity. The four largest planetoids are enveloped in gas and ice(Jupiter, Saturn, Uranus, and Neptune)and are not considered. The other 26 planetoids range in mass over 5 orders of magnitude and in diameter over 2 orders of magnitude, from massive Earth down to tiny Proteus; these bodies also range widely in density, from 1000 to 5500 kg/m^3. A gap separates 8 silicate planetoids with ρ = 3000 kg/m^3 or greater from 20 icy planetoids(including the gaseous and icy giant planets) with ρ = 2200 kg/m^3 or less. We define the "Tectonic Activity Index"(TAI), scoring each body from 0 to 3 based on evidence for recent volcanism, deformation, and resurfacing(inferred from impact crater density). Nine planetoids with TAI = 2 or greater are interpreted to be tectonically and convectively active whereas 17 with TAI <2 are inferred to be tectonically dead. We further infer that active planetoids have lithospheres or icy shells overlying asthenosphere or water/weak ice. TAI of silicate(rocky) planetoids positively correlates with their inferred Rayleigh number. We conclude that some type of stagnant lid tectonics is the dominant mode of heat loss and that plate tectonics is unusual. To make progress understanding Earth's tectonic history and the tectonic style of active exoplanets, we need to better understand the range and controls of active stagnant lid tectonics.展开更多
We review previously published and newly obtained crater size-frequency distributions in the inner solar system. These data indicate that the Moon and the ter- restrial planets have been bombarded by two populations o...We review previously published and newly obtained crater size-frequency distributions in the inner solar system. These data indicate that the Moon and the ter- restrial planets have been bombarded by two populations of objects. Population 1, dominating at early times, had nearly the same size distribution as the present-day asteroid belt, and produced heavily cratered surfaces with a complex, multi-sloped crater size-frequency distribution. Population 2, dominating since about 3.8-3.7 Gyr, had the same size distribution as near-Earth objects （NEOs） and a much lower im- pact flux, and produced a crater size distribution characterized by a differential -3 single-slope power law in the crater diameter range 0.02 km to 100 km. Taken to- gether with the results from a large body of work on age-dating of lunar and meteorite samples and theoretical work in solar system dynamics, a plausible interpretation of these data is as follows. The NEO population is the source of Population 2 and it has been in near-steady state over the past ～ 3.7-3.8 Gyr; these objects are derived from the main asteroid belt by size-dependent non-gravitational effects that favor the ejection of smaller asteroids. However, Population 1 was composed of main belt as- teroids ejected from their source region in a size-independent manner, possibly by means of gravitational resonance sweeping during orbit migration of giant planets; this caused the so-called Late Heavy Bombardment （LHB）. The LHB began some time before ～3.9 Gyr, peaked and declined rapidly over the next ～ 100 to 300 Myr, and possibly more slowly from about 3.8-3.7 Gyr to ～2 Gyr. A third crater population （Population S） consisted of secondary impact craters that can dominate the cratering record at small diameters.展开更多
The Moon has no significant atmosphere, thus its surface is exposed to solar ultraviolet radiation and the solar wind. Photoemission and collection of the solar wind electrons and ions may result in lunar surface char...The Moon has no significant atmosphere, thus its surface is exposed to solar ultraviolet radiation and the solar wind. Photoemission and collection of the solar wind electrons and ions may result in lunar surface charging. On the dayside, the surface potential is mainly determined by photoelectrons, modulated by the solar wind;while the nightside surface potential is a function of the plasma distribution in the lunar wake. Taking the plasma observations in the lunar environment as inputs, the global potential distribution is calculated according to the plasma sheath theory, assuming Maxwellian distributions for the surface emitted photoelectrons and the solar wind electrons. Results show that the lunar surface potential and sheath scale length change versus the solar zenith angle, which implies that the electric field has a horizontal component in addition to the vertical one. By differentiating the potential vertically and horizontally, we obtain the global electric field. It is found that the vertical electric field component is strongest at the subsolar point,which has a magnitude of 1 V m-1. The horizontal component is much weaker, and mainly appears near the terminator and on the nightside, with a magnitude of several mV m-1. The horizontal electric field component on the nightside is rotationally symmetric around the wake axis and is strongly determined by the plasma parameters in the lunar wake.展开更多
We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperatu...We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean annual insolation as a function of varying astronomical parameters. A harmonic oscillator model is applied to integrate the lunar orbit and Earth’s rotation with the tidal torque dependent on the dominant natural frequency of ocean. An ocean geometry acts as a bridge between temperature and oceanic frequency. On assumptions of a fixed hemispherical continent and an equatorial circular lunar orbit, considering only the 41 kyr periodicity of Earth’s obliquity ε and the M2 tide, simulations are performed near tidal resonance for 106 yr. It is verified that the climate can influence the tidal evolution via ocean. Compared with the tidal evolution with constant ε, that with varying ε is slowed down;the EarthMoon distance oscillates in phase with ε before the resonance maximum but exactly out of phase after that;the displacement of the oscillation is in positive correlation with the difference between oceanic frequency and tidal frequency.展开更多
Now we use the Jacobian integral of circular restricted three-body problem to establish a testing function of the stability of satellites. This method of criterion may be applied to the stability problem of satellites...Now we use the Jacobian integral of circular restricted three-body problem to establish a testing function of the stability of satellites. This method of criterion may be applied to the stability problem of satellites when the six elements of the instantaneous orbit of the satellite with respect to its parent planet are known. By means of an electronic computer, we can find the stable region of a satellite with a quasi-circular orbit. The boundary surface of this region is a nearly oblate ellipsoid. The volume of this enclosed space is much smaller than that of binding by Hill surface and that of 'sphere of action'. As the expressions of relative kinetic energy of a satellite with respect to its parent planet have the same form for the direct as well as the retrograde orbits, they can coexist in the same region at the same time.展开更多
We determine the proportions of two mixed crater populations distinguishable by size distributions on the Moon. A ＂multiple power-law＂ model is built to formulate crater size distribution N（D） ∝ D-αwhose slope ...We determine the proportions of two mixed crater populations distinguishable by size distributions on the Moon. A ＂multiple power-law＂ model is built to formulate crater size distribution N（D） ∝ D-αwhose slope α varies with crater diameter D. This model is then used to fit size distributions of lunar highland craters and Class 1 craters. The former is characterized by α = 1.17 ± 0.04, 1.88 ± 0.07,3.17 ± 0.10 and 1.40 ± 0.15 for D ranges ~ 10- 49, 49- 120, 120- 251 and ~ 251- 2500 km, while the latter has a single slope α = 1.96 ± 0.14 for about 10- 100 km. They are considered as Population 1 and2 crater size distributions, whose sum is then fitted to the global size distribution of lunar craters with D between 10 and 100 km. Estimated crater densities of Population 1 and 2 are 44 × 10-5and 5 × 10-5km-2respectively, leading to the proportion of the latter being 10%. This result underlines the need for more thoroughly investigating Population 1 craters and their related impactors, the primordial main-belt asteroids, which dominated the late heavy bombardment.展开更多
The surface of the Moon is highly cratered due to impacts of meteorites, asteroids, comets and other celestial objects. The origin, size, structure, age and composition vary among craters. We study a total of 339 crat...The surface of the Moon is highly cratered due to impacts of meteorites, asteroids, comets and other celestial objects. The origin, size, structure, age and composition vary among craters. We study a total of 339 craters observed by the Lunar Reconnaissance Orbiter Camera （LROC）. Out of these 339 craters, 214 craters are known （named craters included in the IAU Gazetteer of Planetary Nomenclature） and 125 craters are unknown （craters that are not named and objects that are absent in the IAU Gazetteer）. We employ images taken by LROC at the North and South Poles and near side of the Moon. We report for the first time the study of unknown craters, while we also review the study of known craters conducted earlier by previous researchers. Our study is focused on measurements of diameter, depth, latitude and longitude of each crater for both known and unknown craters. The diameter measurements are based on considering the Moon to be a spherical body. The LROC website also provides a plot which enables us to measure the depth and diameter. We found that out of 214 known craters, 161 craters follow a linear relationship between depth （d） and diameter （D）, but 53 craters do not follow this linear relationship. We study physical dimensions of these 53 craters and found that either the depth does not change significantly with diameter or the depths are extremely high relative to diameter （conical）. Similarly, out of 125 unknown craters, 78 craters follow the linear relationship between depth （d） and diameter （D） but 47 craters do not follow the linear relationship. We propose that the craters following the scaling law of depth and diameter, also popularly known as the linear relationship between d and D, are formed by the impact of meteorites having heavy metals with larger dimension, while those with larger diameter but less depth are formed by meteorites/celestial objects having low density material but larger diameter. The craters with very high depth and with very small diameter are perhaps formed by the impact of meteorites that have very high density but small diameter with a conical shape. Based on analysis of the data selected for the current investigation, we further found that out of 339 craters, 100 （29.5%） craters exist near the equator, 131 （38.6%） are in the northern hemisphere and 108 （31.80%） are in the southern hemisphere. This suggests the Moon is heavily cratered at higher latitudes and near the equatorial zone.展开更多
A new non-simplified model of formation flying is derived in the presence of an oblate main- body and third-body perturbation. In the proposed model, considering the perturbation of the third- body in an inclined orbi...A new non-simplified model of formation flying is derived in the presence of an oblate main- body and third-body perturbation. In the proposed model, considering the perturbation of the third- body in an inclined orbit, the effect of obliquity （axial tilt） of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite. From a new point of view, J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit, are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion. To validate the accuracy of the model presented in this study, an auxiliary model was constructed as the Main-body Center based Relative Motion （MCRM） model. Finally, the importance of the main-body＇s obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping. The main-body＇s obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit （PCO） formations.展开更多
基金supported by the Paris Astronomical Data Centre(PADC)at Observatoire de Paris.
文摘In this comment on the article“Locating the source field lines of Jovian decametric radio emissions”by Wang YM et al.,2020,we discuss the assumptions used by the authors to compute the beaming angle of Jupiter’s decametric emissions induced by the moon Io.Their method,relying on multi-point radio observations,was applied to a single event observed on 14th March 2014 by Wind and both STEREO A/B spacecraft from~5 to~16 MHz.They have erroneously identified the emission as a northern(Io-B type)instead of a southern one(Io-D type).We encourage the authors to update their results with the correct hemisphere of origin and to test their method on a larger sample of Jupiter-Io emissions.
基金supported by SNSF grant IZKOZ-2_154380partly supported by SNF 200021_149252
文摘To better understand Earth's present tectonic style-plate tectonics—and how it may have evolved from single plate(stagnant lid) tectonics, it is instructive to consider how common it is among similar bodies in the Solar System. Plate tectonics is a style of convection for an active planetoid where lid fragment(plate) motions reflect sinking of dense lithosphere in subduction zones, causing upwelling of asthenosphere at divergent plate boundaries and accompanied by focused upwellings, or mantle plumes;any other tectonic style is usefully called "stagnant lid" or "fragmented lid". In 2015 humanity completed a 50+ year effort to survey the 30 largest planets, asteroids, satellites, and inner Kuiper Belt objects,which we informally call "planetoids" and use especially images of these bodies to infer their tectonic activity. The four largest planetoids are enveloped in gas and ice(Jupiter, Saturn, Uranus, and Neptune)and are not considered. The other 26 planetoids range in mass over 5 orders of magnitude and in diameter over 2 orders of magnitude, from massive Earth down to tiny Proteus; these bodies also range widely in density, from 1000 to 5500 kg/m^3. A gap separates 8 silicate planetoids with ρ = 3000 kg/m^3 or greater from 20 icy planetoids(including the gaseous and icy giant planets) with ρ = 2200 kg/m^3 or less. We define the "Tectonic Activity Index"(TAI), scoring each body from 0 to 3 based on evidence for recent volcanism, deformation, and resurfacing(inferred from impact crater density). Nine planetoids with TAI = 2 or greater are interpreted to be tectonically and convectively active whereas 17 with TAI <2 are inferred to be tectonically dead. We further infer that active planetoids have lithospheres or icy shells overlying asthenosphere or water/weak ice. TAI of silicate(rocky) planetoids positively correlates with their inferred Rayleigh number. We conclude that some type of stagnant lid tectonics is the dominant mode of heat loss and that plate tectonics is unusual. To make progress understanding Earth's tectonic history and the tectonic style of active exoplanets, we need to better understand the range and controls of active stagnant lid tectonics.
文摘We review previously published and newly obtained crater size-frequency distributions in the inner solar system. These data indicate that the Moon and the ter- restrial planets have been bombarded by two populations of objects. Population 1, dominating at early times, had nearly the same size distribution as the present-day asteroid belt, and produced heavily cratered surfaces with a complex, multi-sloped crater size-frequency distribution. Population 2, dominating since about 3.8-3.7 Gyr, had the same size distribution as near-Earth objects （NEOs） and a much lower im- pact flux, and produced a crater size distribution characterized by a differential -3 single-slope power law in the crater diameter range 0.02 km to 100 km. Taken to- gether with the results from a large body of work on age-dating of lunar and meteorite samples and theoretical work in solar system dynamics, a plausible interpretation of these data is as follows. The NEO population is the source of Population 2 and it has been in near-steady state over the past ～ 3.7-3.8 Gyr; these objects are derived from the main asteroid belt by size-dependent non-gravitational effects that favor the ejection of smaller asteroids. However, Population 1 was composed of main belt as- teroids ejected from their source region in a size-independent manner, possibly by means of gravitational resonance sweeping during orbit migration of giant planets; this caused the so-called Late Heavy Bombardment （LHB）. The LHB began some time before ～3.9 Gyr, peaked and declined rapidly over the next ～ 100 to 300 Myr, and possibly more slowly from about 3.8-3.7 Gyr to ～2 Gyr. A third crater population （Population S） consisted of secondary impact craters that can dominate the cratering record at small diameters.
基金supported by the Key Research Program of the Chinese Academy of Sciences(Grant No.XDPB11)
文摘The Moon has no significant atmosphere, thus its surface is exposed to solar ultraviolet radiation and the solar wind. Photoemission and collection of the solar wind electrons and ions may result in lunar surface charging. On the dayside, the surface potential is mainly determined by photoelectrons, modulated by the solar wind;while the nightside surface potential is a function of the plasma distribution in the lunar wake. Taking the plasma observations in the lunar environment as inputs, the global potential distribution is calculated according to the plasma sheath theory, assuming Maxwellian distributions for the surface emitted photoelectrons and the solar wind electrons. Results show that the lunar surface potential and sheath scale length change versus the solar zenith angle, which implies that the electric field has a horizontal component in addition to the vertical one. By differentiating the potential vertically and horizontally, we obtain the global electric field. It is found that the vertical electric field component is strongest at the subsolar point,which has a magnitude of 1 V m-1. The horizontal component is much weaker, and mainly appears near the terminator and on the nightside, with a magnitude of several mV m-1. The horizontal electric field component on the nightside is rotationally symmetric around the wake axis and is strongly determined by the plasma parameters in the lunar wake.
基金funded by the National Key Research and Development Program of China (2017YFC0305905)the Natural Science Foundation of Zhejiang Province (LR16E090001)NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization (U1709204)
文摘We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean annual insolation as a function of varying astronomical parameters. A harmonic oscillator model is applied to integrate the lunar orbit and Earth’s rotation with the tidal torque dependent on the dominant natural frequency of ocean. An ocean geometry acts as a bridge between temperature and oceanic frequency. On assumptions of a fixed hemispherical continent and an equatorial circular lunar orbit, considering only the 41 kyr periodicity of Earth’s obliquity ε and the M2 tide, simulations are performed near tidal resonance for 106 yr. It is verified that the climate can influence the tidal evolution via ocean. Compared with the tidal evolution with constant ε, that with varying ε is slowed down;the EarthMoon distance oscillates in phase with ε before the resonance maximum but exactly out of phase after that;the displacement of the oscillation is in positive correlation with the difference between oceanic frequency and tidal frequency.
文摘Now we use the Jacobian integral of circular restricted three-body problem to establish a testing function of the stability of satellites. This method of criterion may be applied to the stability problem of satellites when the six elements of the instantaneous orbit of the satellite with respect to its parent planet are known. By means of an electronic computer, we can find the stable region of a satellite with a quasi-circular orbit. The boundary surface of this region is a nearly oblate ellipsoid. The volume of this enclosed space is much smaller than that of binding by Hill surface and that of 'sphere of action'. As the expressions of relative kinetic energy of a satellite with respect to its parent planet have the same form for the direct as well as the retrograde orbits, they can coexist in the same region at the same time.
基金supported by the National Key Basic Research Program of China (973 program, No. 2013CB834900)the National Natural Science Foundation of China (Nos. 11003010 and 11333002)+3 种基金the Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences (Grant No. XDB09000000)the Natural Science Foundation for the Youth of Jiangsu Province (No. BK20130547)the 985 project of Nanjing UniversitySuperiority Discipline Construction Project of Jiangsu Province
文摘We determine the proportions of two mixed crater populations distinguishable by size distributions on the Moon. A ＂multiple power-law＂ model is built to formulate crater size distribution N（D） ∝ D-αwhose slope α varies with crater diameter D. This model is then used to fit size distributions of lunar highland craters and Class 1 craters. The former is characterized by α = 1.17 ± 0.04, 1.88 ± 0.07,3.17 ± 0.10 and 1.40 ± 0.15 for D ranges ~ 10- 49, 49- 120, 120- 251 and ~ 251- 2500 km, while the latter has a single slope α = 1.96 ± 0.14 for about 10- 100 km. They are considered as Population 1 and2 crater size distributions, whose sum is then fitted to the global size distribution of lunar craters with D between 10 and 100 km. Estimated crater densities of Population 1 and 2 are 44 × 10-5and 5 × 10-5km-2respectively, leading to the proportion of the latter being 10%. This result underlines the need for more thoroughly investigating Population 1 craters and their related impactors, the primordial main-belt asteroids, which dominated the late heavy bombardment.
文摘The surface of the Moon is highly cratered due to impacts of meteorites, asteroids, comets and other celestial objects. The origin, size, structure, age and composition vary among craters. We study a total of 339 craters observed by the Lunar Reconnaissance Orbiter Camera （LROC）. Out of these 339 craters, 214 craters are known （named craters included in the IAU Gazetteer of Planetary Nomenclature） and 125 craters are unknown （craters that are not named and objects that are absent in the IAU Gazetteer）. We employ images taken by LROC at the North and South Poles and near side of the Moon. We report for the first time the study of unknown craters, while we also review the study of known craters conducted earlier by previous researchers. Our study is focused on measurements of diameter, depth, latitude and longitude of each crater for both known and unknown craters. The diameter measurements are based on considering the Moon to be a spherical body. The LROC website also provides a plot which enables us to measure the depth and diameter. We found that out of 214 known craters, 161 craters follow a linear relationship between depth （d） and diameter （D）, but 53 craters do not follow this linear relationship. We study physical dimensions of these 53 craters and found that either the depth does not change significantly with diameter or the depths are extremely high relative to diameter （conical）. Similarly, out of 125 unknown craters, 78 craters follow the linear relationship between depth （d） and diameter （D） but 47 craters do not follow the linear relationship. We propose that the craters following the scaling law of depth and diameter, also popularly known as the linear relationship between d and D, are formed by the impact of meteorites having heavy metals with larger dimension, while those with larger diameter but less depth are formed by meteorites/celestial objects having low density material but larger diameter. The craters with very high depth and with very small diameter are perhaps formed by the impact of meteorites that have very high density but small diameter with a conical shape. Based on analysis of the data selected for the current investigation, we further found that out of 339 craters, 100 （29.5%） craters exist near the equator, 131 （38.6%） are in the northern hemisphere and 108 （31.80%） are in the southern hemisphere. This suggests the Moon is heavily cratered at higher latitudes and near the equatorial zone.
文摘A new non-simplified model of formation flying is derived in the presence of an oblate main- body and third-body perturbation. In the proposed model, considering the perturbation of the third- body in an inclined orbit, the effect of obliquity （axial tilt） of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite. From a new point of view, J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit, are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion. To validate the accuracy of the model presented in this study, an auxiliary model was constructed as the Main-body Center based Relative Motion （MCRM） model. Finally, the importance of the main-body＇s obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping. The main-body＇s obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit （PCO） formations.
