Earth-Moon Distance Research Articles

The cool brown dwarf Gliese 229 B is a close binary.

Owing to their similarities with giant exoplanets, brown dwarf companions of stars provide insights into the fundamental processes of planet formation and evolution. From their orbits, several brown dwarf companions are found to be more massive than theoretical predictions given their luminosities and the ages of their host stars1-3. Either the theory is incomplete or these objects are not single entities. For example, they could be two brown dwarfs each with a lower mass and intrinsic luminosity1,4. The most problematic example is Gliese 229 B (refs. 5,6), which is at least 2-6 times less luminous than model predictions given its dynamical mass of 71.4 ± 0.6 Jupiter masses (MJup) (ref. 1). We observed Gliese 229 B with the GRAVITY interferometer and, separately, the CRIRES+ spectrograph at the Very Large Telescope. Both sets of observations independently resolve Gliese 229 B into two components, Gliese 229 Ba and Bb, settling the conflict between theory and observations. The two objects have a flux ratio of 0.47 ± 0.03 at a wavelength of 2 μm and masses of 38.1 ± 1.0 and 34.4 ± 1.5 MJup, respectively. They orbit each other every 12.1 days with a semimajor axis of 0.042 astronomical units (AU). The discovery of Gliese 229 BaBb, each only a few times more massive than the most massive planets, and separated by 16 times the Earth-moon distance, raises new questions about the formation and prevalence of tight binary brown dwarfs around stars.

On the viscoelastic-electromagnetic-gravitational analogy

The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.

Cyclostratigraphy of late Cambrian marine sedimentary records and reconstruction of Earth-Moon system parameters

The Cambrian period is an important era in geological history, marked by numerous major geological and biological events. To better understand these events, it is important to establish a high-precision chronostratigraphic framework. An astronomical time scale can be created by the identified Milankovitch cycles in well-preserved stratigraphic successions. Duibian B section in Jiangshan (Zhejiang Province, China) is the global stratotype section and point (GSSP) for the Jiangshanian Stage, and this section provides well-preserved records covering the upper Paibian to lower Jiangshanian stages. In this study, we use high-resolution magnetic susceptibility record to conduct cyclostratigraphic analysis of the Duibian B section. Our results indicate that the 2.44 m, 0.84–0.73 m, 0.20–0.19 m, and 0.12–0.09 m sedimentary cycles may represent long-eccentricity, short-eccentricity, obliquity, and precession cycles, respectively. Using the stable 405-kyr eccentricity cycles, we constructed an ∼5.96 Myr floating astronomical time scale to calibrate agnostoid trilobite zones. In addition, we reconstructed the precession rate k from geological records, and our result provides an insight into the Earth-Moon distance and length of day in the late Cambrian (Paibian–Jiangshanian, ∼494.2 Ma). It enriches our understanding of the Earth-Moon evolutionary history in deep time.

More axion stars from strings

We show that if dark matter consists of QCD axions in the post-inflationary scenario more than ten percent of it efficiently collapses into Bose stars at matter-radiation equality. Such a result is mostly independent of the present uncertainties on the axion mass. This large population of solitons, with asteroid masses and Earth-Moon distance sizes, might plausibly survive until today, with potentially interesting implications for phenomenology and experimental searches.

Geological evidence reveals a staircase pattern in Earth’s rotational deceleration evolution

The Earth’s rotation has been decelerating throughout its history due to tidal dissipation, but the variation of the rate of this deceleration through time has not been established. We present a detailed analysis of eight geological datasets to constrain the Earth’s rotational history from 650 to 240 Mya. The results allow us to test physical tidal models and point to a staircase pattern in the Earth’s deceleration from 650 to 280 Mya. During this time interval, the Earth–Moon distance increased by approximately 20,000 km and the length of day increased by approximately 2.2 h. Specifically, there are two intervals with high Earth rotation deceleration, 650 to 500 Mya and 350 to 280 Mya, separated by an interval of stalled deceleration from 500 to 350 Mya. The interval with stalled deceleration is attributed mainly to reduced tidal dissipation due to the continent-ocean configuration at the time, not to changes in Earth’s dynamical ellipticity from continental assembly or glaciation. Modeling indicates that, except for the very recent time, tidal dissipation is the main driver for decelerating Earth rotation. One potential implication of our findings is that the Earth’s tidal dissipation, along with Earth’s rotation deceleration, may play a role in the evolving Earth.

The End of the Eclipse

Scientists are studying how the Earth–Moon distance has changed over time, and what effect that change might have had on our planet. Future changes will extinguish total solar eclipses entirely.

Relationship Between Earth-Moon Distance and Tides

For residents and fishermen in coastal cities, tidal phenomena are a dangerous existence, and for tidal power stations, tidal phenomena will bring clean energy to them. For the formation of tidal phenomena, the most closely related is the distance between the Earth and the Moon. Therefore, this paper collects the tides and Earth-Moon records in New York in 2022, and performs data visualization operations on the data, and uses STL (Seasonal Decomposition of Time Series), MSTL (Multiple Seasonal-Trend Decomposition using Loess) models to predict, so as to explore the concern between the Earth-Moon distance and tides. Monthly seasonality is found from our analysis as well as the general trend which follows the research results regarding to earth moon distance variation. The results show that when the Earth is close enough in the Moon, the tides are more pronounced.

Radon as a possible link between peak spring tides and lemming cycles

There is still no consensus regarding the ultimate cause of the famous 3–4-year population cycles of lemmings. According to the plant stress hypothesis, herbivore population peaks are caused by stress factors that force plants to reallocate stored defensive proteins to transportable and easily digestible N-compounds. One possible plant stress factor is ionization caused by exhalation of the radioactive noble gas radon, which is enhanced after spring tides, i.e., tides at new or full Moon. I hypothesized that increased ionization caused by radon accumulation in the subnivean space after peak spring tides, which occur close to perihelion (31 December–05 January, when the Earth–Sun distance is shortest), and at 3.8-year intervals, results in increased protein digestibility of mosses, which are important food for lemmings. Population outbreaks of Norway lemming Lemmus lemmus occurred two years after peak spring tides during 1871–1910, when also perigee (the time when the Earth–Moon distance is shortest) coincided with spring tides and perihelion. Thereafter this relationship weakened, and lemming peaks became less pronounced and more related to plant seed indices. As we have now entered a new 30-year period with coincidence of spring tide, perihelion and perigee, I predict more regular and pronounced lemming outbreaks in the next decades, unless radon accumulation is prevented by frequent lack of a stable snow cover due to global warming.

Dynamical study of Geminid formation assuming a rotational instability scenario

Context. Various ideas have been proposed to explain the formation of the Geminid meteoroid stream from the asteroid (3200) Phaethon. However, little has been studied regarding whether the Geminid formation could be the result of mass ejection via rotational instability of this asteroid. Aims. In this work, we present the first dynamical study of the Geminid formation taking into account low-velocity mass ejection caused by Phaethon’s rotational instability. Methods. We conducted numerical simulations for 1-mm and 1-cm particles ejected in a wide range of ejection epochs (103–105 yr ago). We computed the minimum orbital intersecting distance (MOID) of the dust particles as the realistic condition, that is, the Earth’s radius and the Earth–Moon distance to be observed as the Geminid meteoroid stream. Results. We found that the low-velocity ejection model produced the Geminid-like meteoroid stream when the dust particles were ejected more than ~2000 yr ago. In this case, close encounters with terrestrial planets would transport some dust particles from the Phaethon orbit (the current MOID is as large as ~460 Earth radii) to the Earth-intersecting orbits. The optimal ejection epoch and the estimated mass were 18 000 yr ago and ~1010–1014 g (<0.1% of the Phaethon mass). Conclusions. Our results suggest that the JAXA DESTINY+ mission has the potential to find evidence of recent rotational instability recorded on the surface of Phaethon.

On the feasibility of primordial black hole abundance constraints using lensing parallax of GRBs

ABSTRACT Primordial black holes, which could have formed during the early Universe through overdensities in primordial density fluctuations during inflation, are potential candidates for dark matter. We explore the use of lensing parallax of gamma-ray bursts (GRBs), which results in different fluxes being observed from two different vantage points, in order to probe the abundance of primordial black holes in the unexplored window within the mass range 10−15 to 10−11 $\mathrm{ {M}_\odot}$. We derive the optical depth for the lensing of GRBs with a distribution of source properties and realistic detector sensitivities. We comment on the ability of the proposed Indian twin satellite mission Daksha in its low Earth orbit to conduct this experiment. If the two Daksha satellites observe 10 000 GRBs simultaneously and the entirety of dark matter is made up of 10−15 to 10−12 $\mathrm{ {M}_\odot}$ black holes, Daksha will detect non-zero lensing events with a probability ranging from 80 to 50 per cent at the bin edges, respectively. Non-detections will not conclusively rule out primordial black holes as dark matter in this mass range. However, we show that meaningful constraints can be obtained in such a case if the two satellites are separated by at least the Earth–Moon distance.

Past extent of lunar permanently shadowed areas.

As the Moon migrated away from Earth, it experienced a major spin axis reorientation. Permanently shadowed regions (PSRs), which are thought to have trapped ices and are a main focus of lunar exploration, appeared and grew after this (Cassini state) transition and are often younger than their host craters. Here, we calculate the lunar spin axis orientation and the extent of PSRs based on recent advances for the time evolution of the Earth-Moon distance. The solar declination reached twice its current value 2.1 billion years (Ga) ago, when the PSR area was about half as large. The PSR area becomes negligible beyond 3.4 Ga ago. The site of an artificial impact in Cabeus Crater, where various volatiles have been detected, became continuously shadowed only about 0.9 Ga ago, and hence, cold-trapping has continued into this relatively recent time period. Overall estimates for the amount of cold-trapped ices have to be revised downward.

Earth's rotation and Earth-Moon distance in the Devonian derived from multiple geological records

Astronomical insolation forcing plays an important role in pacing Earth's climate history, including paleoclimate dynamics, and its imprint can be seen in various geoarchives. Its signature is often evident through typical rhythmic patterns in sediments. The detailed study of those patterns led to a better understanding of orbital climate forcing, while also providing more precise constraints on the geological time scale. Due to the tidal evolution in the Earth-Moon system, the precession and obliquity periods get shorter when going back in time while the main eccentricity 405 kyr period remains stable. While several astrophysical models describe the evolution of the length of precession- and obliquity cycles, few reliable and quantitative geological information from tidalites and astrochronology are available.To better constrain these key astronomical parameters in the distant past, we calculate precession and obliquity properties for the Devonian (∼420-360 million years before present) as reconstructed from a suite of geological datasets. Our results show the period of precession to be 19.4-16.1 kyr, and the dominant p+s3 obliquity period to be 29.50±0.46 long. These findings are compared with and support the presence of oceanic tidal resonances at 300 and 540 Ma, as shown in the recent AstroGeo22 model of the Earth-Moon evolution of (Farhat et al., 2022).

The Uncertainty Analysis of the Entrance Pupil Irradiance for a Moon-Based Earth Radiation Observation Instrument

Moon-Based Earth Radiation Observation (MERO) is expected to improve and enrich the current Earth radiation budget (ERB). For the design of MERO’s instrument and the interpretation of Moon-based data, evaluating the uncertainty of the instrument’s Entrance Pupil Irradiance (EPI) is an important part. In this work, by analyzing the effect of the Angular Distribution Models (ADMs), Earth’s Top of Atmosphere (TOA) flux, and the Earth–Moon distance on the EPI, the uncertainty of EPI is finally studied with the help of the theory of errors. Results show that the ADMs have a stronger influence on the Short-Wave (SW) EPI than those from the Long-Wave (LW). For the change of TOA flux, the SW EPI could keep the attribute of varying hourly time scales, but the LW EPI will lose its hourly-scale variability. The variation in EPI caused by the hourly change of the Moon–Earth distance does not exceed 0.13 mW∙m−2 (1σ). The maximum hourly combined uncertainty reveals that the SW and LW combined uncertainties are about 5.18 and 1.08 mW∙m−2 (1σ), respectively. The linear trend extraction of the EPI demonstrates that the Moon-based data can effectively capture the overall linear change trend of Earth’s SW and LW outgoing radiation, and the uncertainty does not change the linear trend of data. The variation of SW and LW EPIs in the long term are 0.16 mW∙m−2 (SW) and 0.23 mW∙m−2 (LW) per decade, respectively. Based on the constraint of the uncertainty, a simplified dynamic response model is built for the cavity radiometer, a kind of MERO instrument, and the results illuminate that the Cassegrain optical system and electrical substitution principle can realize the detection of Earth’s outing radiation with the sensitivity design goal 1 mW∙m−2.

Detecting sublunar-mass primordial black holes with the Earth-Moon binary system

In this paper we propose a new way to detect sublunar-mass primordial black holes (PBHs) by direct observations of the Earth-Moon binary system.Our method is based on treating PBH as a perturbation term, by assuming that the PBH is far away from the Earth-Moon binary (far greater than 1 AU) and the mass of the PBH is small (less than the lunar mass). This perturbation treatment allows us to develop a framework to calculate the orbits of a generic binary system such as the Earth-Moon binary system. Our numerical results show that the Earth-Moon distance is sensitive to the initial values of the system. In most cases, the long-duration interactions between the PBH and the Earth-Moon system can induce lasting imprints on the Earth-Moon's orbit, and these imprints can accumulate over time, eventually giving rise to observable deviations which can be used to infer the properties of the PBH.

Earth observations from the Moon's surface: dependence on lunar libration

Abstract. Observing the Earth from the Moon's surface has important scientific advantages. The angular diameter of the Earth as seen from the Moon's surface is 1.8–2.0∘ (the angular size varies due to the change in the Earth–Moon distance). The libration of the Moon in latitude reaches an amplitude of 6.68∘ and has a main period of 27.21 d (or 653.1 h). The libration of the Moon in longitude, reaching an amplitude of 7.9∘, has a period of 27.55 d (or 661.3 h). This causes the center of the Earth to move in the Moon's sky in a rectangle measuring 13.4∘ × 15.8∘. The trajectory of the Earth's motion in this rectangle changes its shape within a period of 6 years. This apparent librational movement of the Earth in the Moon's sky complicates observations of the Earth. This paper proposes that this disadvantage be turned into an advantage and that a multi-slit spectrometer be placed on the Moon's surface on a fixed platform. The libration motion and the daily rotation of the Earth will act as a natural replacement for the scanning mechanism.

Reachable set analysis of practical trans-lunar orbit via a retrograde semi-analytic model

Different from the Apollo flight mode, a safer trans-lunar flight mode for the crews is preferred. The previous-arrived lunar module rendezvouses with the crew exploration vehicle at a low lunar destination orbit, and then the crews ride the lunar module to descend the lunar surface sampling destination. The lunar module, which includes the descent and ascent stages, flies from a low Earth orbit to the low lunar destination orbit with two tangential impulses. The low lunar destination orbital reachable set of the practical trans-lunar orbit limits the feasible lunar surface sampling region. Therefore, this paper addresses the low lunar destination orbital reachable set of the practical trans-lunar orbit. A retrograde semi-analytic model is proposed for rapidly computing the practical two-impulse trans-lunar orbit firstly, which refers the ephemeris table twice for more precision perilune orbital elements. The reachable set is generated using the multiple-level traversal searching approach with this retrograde semi-analytic mode. Its envelope is re-checked by the continuation theory with the high-precision orbital model. Besides, some factors that affect the reachable set are also measured. The results show that neither the Earth–Moon distance nor the trans-lunar duration affects the reachable set. However, if the trans-lunar injection inclination is smaller than the inclination of the moon’s path, the reachable set becomes smaller or even reduces into an empty set. In brief, the proposed retrograde semi-analytic model for computing the reachable set provides a helpful and fast tool for selecting an applicable lunar surface sampling site for the manned lunar mission overall design.Graphical

Milankovitch cycles in banded iron formations constrain the Earth–Moon system 2.46 billion years ago

The long-term history of the Earth-Moon system as reconstructed from the geological record remains unclear when based on fossil growth bands and tidal laminations. A possibly more robust method is provided by the sedimentary record of Milankovitch cycles (climatic precession, obliquity, and orbital eccentricity), whose relative ratios in periodicity change over time as a function of a decreasing Earth spin rate and increasing lunar distance. However, for the critical older portion of Earth's history where information on Earth-Moon dynamics is sparse, suitable sedimentary successions in which these cycles are recorded remain largely unknown, leaving this method unexplored. Here we present results of cyclostratigraphic analysis and high-precision U-Pb zircon dating of the lower Paleoproterozoic Joffre Member of the Brockman Iron Formation, NW Australia, providing evidence for Milankovitch forcing of regular lithological alternations related to Earth's climatic precession and orbital eccentricity cycles. Combining visual and statistical tools to determine their hierarchical relation, we estimate an astronomical precession frequency of 108.6 ± 8.5 arcsec/y, corresponding to an Earth-Moon distance of 321,800 ± 6,500 km and a daylength of 16.9 ± 0.2 h at 2.46 Ga. With this robust cyclostratigraphic approach, we extend the oldest reliable datum for the lunar recession history by more than 1 billion years and provide a critical reference point for future modeling and geological investigation of Precambrian Earth-Moon system evolution.

Length of day at c . 1.1 Ga based on cyclostratigraphic analyses of the Nanfen Formation in the North China craton, and its geodynamic implications

Length of day (LOD) varies throughout Earth history, dictated in the long term by the retreat of the Moon and growth of Earth's core. Reconstruction of LOD in deep time has greatly benefited from analyses of the orbital cycle from geological records. The Precambrian database, however, is very limited. Here we present a cyclostratigraphic study on c. 1.1 Ga laminated argillaceous limestones of the Nanfen Formation from the North China craton. Milankovitch cycles are successfully recognized from the consistent cyclical variations of the high-resolution magnetic susceptibility data measured on drillcores from the Nanfen Formation. Sedimentary cycles with wavelengths of 12.45, 10.72 and 9.96 m in three drillcores are interpreted as 405 kyr eccentricity cycles. An obliquity period of 20.9–21.4 kyr and a precession period of 12.7–16.0 kyr are also identified. The Earth–Moon distance and LOD are thus estimated at 3.43 ± 0.04 × 10 8 m and 18.94 ± 0.39 h, respectively. Our new results together with the data previously published reveal an important discontinuity between 1.9 and 1.4 Ga in the evolutionary trend of the LOD. We suggest that Earth's core grew rapidly during the interval, which significantly changed the moment of inertia of the Earth–Moon system, and tidal dissipation again ruled the LOD variations after that stage. Supplementary material: A description of the calculation method, magnetic susceptibility data, anisotropy of magnetic susceptibility data and supplementary figures are available at https://doi.org/10.6084/m9.figshare.c.6086544

Constraints on Earth-Moon dynamical parameters from Eocene cyclostratigraphy

The theoretical prediction of Earth-Moon dynamics in deep geologic time is hampered by limited knowledge of Earth's past tidal dissipation and dynamical ellipticity. Cyclostratigraphy can, however, provide valuable information on the geologic evolution of the Earth-Moon dynamical parameters. Here we investigate Eocene cyclostratigraphy to estimate Earth's precession rate (p), Earth-Moon distance (EMD) and length-of-day (LOD). Two highly-resolved deep sea records are selected from the Atlantic Ocean, with ages centered on 42.5 Ma (40.9–44.3 Ma; IODP Site U1410) and 54.95 Ma (54.1–55.8 Ma; ODP Site 1262). The sedimentary sequences at these sites recorded Milankovitch forcing signals with prominent precession index (Site 1262) and obliquity (Site U1410) frequencies and their amplitude modulations. At Site U1410, amplitude modulation of the main obliquity cycle was tuned to the Earth's 173-kyr orbital inclination (s3-s6) metronome, and at Site 1262, the dominant precession index amplitude modulation to the 405-kyr orbital eccentricity (g2-g5) metronome. This enabled estimation of Earth's precession rate p of 51.486 ± 0.064 arcsec/yr and 51.546 ± 0.168 arcsec/yr for 42.5 Ma and 54.95 Ma, respectively. These p estimates indicate EMD values of 383.710 ± 0.090 × 103 km and 382.625 ± 0.265 × 103 km, and LOD values of 23.679 ± 0.0115 h and 23.667 ± 0.039 h for 42.5 Ma and 54.95 Ma, respectively. These estimates deviate from theoretical predictions based on back calculation assuming present-day tidal dissipation. In particular, a significant discrepancy between the model and observations (cyclostratigraphy) occurs at 54.95 Ma (Site 1262) suggesting contributions from other effects on Earth's rotation, including changes in tidal dissipation and/or Earth's dynamical ellipticity related to mantle convection and the early Eocene global warming.

Orbitally-paced climate change in the early Cambrian and its implications for the history of the Solar System

The early Cambrian was a critical period of Earth history, marked by explosive diversification of metazoans and several profound changes in Earth's surface environments and global climate. A valid temporal framework for the early Cambrian Period and across the major bio-events is poorly constrained, and the key underlying forcings of million-year (Myr) scale sea-level variations in a greenhouse lacking polar ice sheets are still disputed. Here, the high-resolution gamma-ray logs (GR) and Fe/Al records are utilized to conduct cyclostratigraphic analysis of the early Cambrian Stage 2-Stage 3 Qiongzhusi Formation of the Well A borehole in South China. A ∼10.8 Myr-long high-resolution astronomical time scale across Stage 2-Stage 3 is developed by astronomical tuning of gamma-ray logs and Fe/Al series to the stable 405-kyr long-eccentricity cycles. The Myr-scale sea-level fluctuations in the early Cambrian greenhouse are reconstructed through the sedimentary noise modeling of the 405-tuned GR series and agree with sequence stratigraphic interpretations, lithofacies stacking patterns, and depositional environment changes. The antiphase correlation of filtered ∼1.5 Myr cycles of sedimentary noise curves with the ∼1.5 Myr obliquity modulation cycles demonstrates that the variations in land-ocean water exchange linked to changes in poleward moisture and heat transport dominated by ∼1.5 Myr obliquity modulation cycles may be a primary driver for eustasy during non-glacial early Cambrian period. A new resonance state in the early Cambrian Stage 2-Stage 3, manifested by ∼1.5 Myr eccentricity: ∼1.5 Myr obliquity, could be mainly associated with the Earth-Mars secular resonance and constrain the chaotic evolution of the Solar System in deep time. Two independent approaches are employed to reconstruct the history of Earth-Moon system characteristics, including the precession constant, the Earth-Moon distance and the day length. Our results enhance knowledge of the connection of Myr-scale sea-level variations to astronomically induced climate change under greenhouse climate and provide new empirical constraints on the chaotic motion of the Solar System and the evolution of the Earth-Moon System in deep time.