The moon after Apollo

The Apollo missions have gradually increased our knowledge of the Moon's chemistry, age, and mode of formation of its surface features and materials Apollo 11 and 12 landings proved that mare materials are volcanic rocks that were derived from deep-seated basaltic melts about 3.7 and 3.2 billion years ago, respectively. Later missions provided additional information on lunar mare basalts as well as the older, anorthositic, highland rocks. Data on the chemical make-up of returned samples were extended to larger areas of the Moon by orbiting geochemical experiments. These have also mapped inhomogeneities in lunar surface chemistry, including radioactive anomalies on both the near and far sides.Lunar samples and photographs indicate that the moon is a well-preserved museum of ancient impact scars. The crust of the Moon, which was formed about 4.6 billion years ago, was subjected to intensive metamorphism by large impacts. Although bombardment continues to the present day, the rate and size of impacting bodies were much greater in the first 0.7 billion years of the Moon's history. The last of the large, circular, multiringed basins occurred about 3.9 billion years ago. These basins, many of which show positive gravity anomalies (mascons), were flooded by volcanic basalts during a period of at least 600 million years. In addition to filling the circular basins, more so on the near side than on the far side, the basalts also covered lowlands and circum-basin troughs.Profiles of the outer lunar skin were constructed from the mapping camera system, including the laser altimeter, and the radar sounder data. Materials of the crust, according to the lunar seismic data, extend to the depth of about 65 km on the near side, probably more on the far side. The mantle which underlies the crust probably extends to about 1100 km depth. It is also probable that a molten or partially molten zone or core underlies the mantle, where interactions between both may cause the deep-seated moonquakes.The three basic theories of lunar origin—capture, fission, and binary accretion—are still competing for first place. The last seems to be the most popular of the three at this time; it requires the least number of assumptions in placing the Moon in Earth orbit, and simply accounts for the chemical differences between the two bodies. Although the question of origin has not yet been resolved, we are beginning to see the value of interdisciplinary synthesis of Apollo scientific returns. During the next few years we should begin to reap the fruits of attempts at this synthesis. Then, we may be fortunate enough to take another look at the Moon from the proposed Lunar Polar Orbit (LPO) mission in about 1979.     

Properties of the solar nebula and the origin of the moon

The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminium, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the Moon in this position, and since the Moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the Moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the Moon, reaching past the orbit of the Earth, establishing conditions which are necessary for capture of the Moon by the Earth. In this orbit the Moon, no longer fully molten, will sweep up additional material containing iron oxide. This history accounts in principle for the two major ways in which the bulk composition of the Moon differs from that of the Allende inclusions.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

月球卫星轨道力学综述

月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。     

The evolution of the Earth-Moon system

The tidally-induced couple acting on the Moon, due to friction between the oceans and their beds, is calculated as a function of the Earth-Moon separation. The function is found to be proportional to 1+d/R ³ , and not the previously used 1/R ⁶. By use of this new function it is found that the present rate of lunar recession gives an acceptable history for the system if it is assumed the Moon was initially in a close geo-stationary orbit 4 billion years ago, when perturbed by the condensation of the Earth's core.     

An Estimate on the Lunar Figure

In 1799 Laplace discovered that the three principal moments of the Moon are not in equilibrium with the Moon's current orbital and rotational state. Some authors suggested that the Moon may carry a fossil figure. More than 3 billion years ago, the liquid Moon was closer to the Earth and revolved faster. Then the Moon migrated outwards and its rotation slowed down. During the early stage of this migration, the Moon was continually subjected to tidal and rotational stretching and formed into an ellipsoid. Subsequently the Moon cooled down and solidified quickly. Eventually, the solid Moon's lithosphere was stable and as a result we may see the very early lunar figure.     

Pre-capture orbits of the moon

If the mass of the Earth was not considerably larger than at present, the pre-capture orbit of the Moon was in the range 0.9–1.1 A.U. Capture occurred within several 10⁸ years after formation of the Moon.     

Relation of a contracting earth to the apparent accelerations of the sun and moon

The tidal theory of the evolution of the lunar orbit has remained inconsistent with the observational values of the apparent secular accelerations of the Sun and Moon since it was first developed by Jeffreys in 1920. Allowance for a changing moment of inertia of the Earth enables the discrepancy to be completely removed if a decrease is occurring at a rate of just about the amount already required by the phase-change theory of the nature of the terrestrial core. The agreement of the resulting theory with the latest determinations of the lunar acceleration increases confidence in the phase-change hypothesis. On the other hand the theory renders it most unlikely that a changing constant of gravitation will prove necessary to account for the observations. On the present theory of itself the Moon would have been extremely close to the Earth only about 10⁹ yr ago which suggests that some additional process may at times have influenced the lunar orbit.     

Direct and indirect capture of near-Earth asteroids in the Earth–Moon system

Near-Earth asteroids have attracted attention for both scientific and commercial mission applications. Due to the fact that the Earth–Moon \(\hbox {L}_{1}\) and \(\hbox {L}_{2}\) points are candidates for gateway stations for lunar exploration, and an ideal location for space science, capturing asteroids and inserting them into periodic orbits around these points is of significant interest for the future. In this paper, we define a new type of lunar asteroid capture, termed direct capture. In this capture strategy, the candidate asteroid leaves its heliocentric orbit after an initial impulse, with its dynamics modeled using the Sun–Earth–Moon restricted four-body problem until its insertion, with a second impulse, onto the \(\hbox {L}_{2}\) stable manifold in the Earth–Moon circular restricted three-body problem. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid’s initial obit to the stable manifold associated with Earth–Moon \(\hbox {L}_{2}\) point. Results show that the direct asteroid capture strategy needs a shorter flight time compared to an indirect asteroid capture, which couples capture in the Sun–Earth circular restricted three-body problem and subsequent transfer to the Earth–Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth–Moon system.     

The evolution of the moon

The thermal evolution of the Moon as it can be defined by the available data and theoretical calculations is discussed. A wide assortment of geological, geochemical and geophysical data constrain both the present-day temperatures and the thermal history of the lunar interior. On the basis of these data, the Moon is characterized as a differentiated body with a crust, a 1000-km-thick solid mantle (lithosphere) and an interior region (core) which may be partially molten. The presence of a crust indicates extensive melting and differentiation early in the lunar history. The ages of lunar samples define the chronology of igneous activity on the lunar surface. This covers a time span of about 1.5 billion yr, from the origin to about 3.16 billion yr ago. Most theoretical models require extensive melting early in the lunar history, and the outward differentiation of radioactive heat sources.Thermal history calculations, whether based on conductive or convective computation codes define relatively narrow bounds for the present day temperatures in the lunar mantle. In the inner region of the 700 km radius, the temperature limits are wider and are between about 100 and 1600°C at the center of the Moon. This central region could have a partially or totally molten core.The lunar heat flow values (about 30 ergs/cm²s) restrict the present day average uranium abundance to 60 ± 15 ppb (averaged for the whole Moon) with typical ratios of K/U = 2000 and Th/U = 3.5. This is consistent with an achondritic bulk composition for the Moon.The Moon, because of its smaller size, evolved rapidly as compared to the Earth and Mars. The lunar interior is cooling everywhere at the present and the Moon is tectonically inactive while Mars could be and the Earth is definitely active.     

Origin and evolution of the earth-moon system

The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a normal satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors.Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood.The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact 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.     

Thermal evolutions of the terrestrial planets

The thermal evolution of the Moon, Mercury, Mars, Venus and hypothetical minor planets is calculated theoretically, taking into account conduction, solid-state convection, and differentiation. An assortment of geological, geochemical, and geophysical data is used to constrain both the present day temperatures and thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. Initial temperatures and core formation play the most important roles in the early differentiation. The size of the planet is the primary factor in determining its present day thermal state. A planetary body with radius less than 1000 km is unlikely to reach melting given heat source concentrations similar to terrestrial values and in the absence of intensive early heating such as short half-life radioactive heating and inductive heating.Studies of individual planets are constrained by varying amounts of data. Most data exist for the Earth and Moon. The Moon is a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. It is presently cooling rapidly and is relatively inactive tectonically.Mercury most likely has a large core. Thermal calculations indicate it may have a 500 km thick solid lithosphere, and the core may be partially molten if it contains some heat sources. If this is not the case, the planet's interior temperatures are everywhere below the melting curve for iron. The thermal evolution is dominated by core separation and the high conductivity of iron which makes up the bulk of Mercury.Mars, intermediate in size among the terrestrial planets, is assumed to have differentiated an Fe–FeS core. Differentiation and formation of an early crust is evident from Mariner and Viking observations. Theoretical models suggest that melting and differentiation of the mantle silicates has occurred at least up until 1 billion years ago. Present day temperature profiles indicate a relatively thick (250 km) lithosphere with a possible asthenosphere below. The core is molten.Venus is characterized as a planet similar to the Earth in many respects. Core formation probably occurred during the first billion years after the formation. Present day temperatures indicate a partially molten upper mantle overlain by a 100 km thick lithosphere and a molten Fe–Ni core. If temperature models are good indicators, we can expect that today, Venus has tectonic processes similar to the Earth's.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

Gravitational lunar capture based on bicircular model in restricted four body problem

Gravitational capture is a useful phenomenon in the design of the low energy transfer (LET) orbit for a space mission. In this paper, gravitational lunar capture based on the Sun–Earth–Moon bicircular model (BCM) in the restricted four body problem is studied. By the mechanical analysis in the space near the Moon, we first propose a new parameter \(k\) , the corrected ratio of the radial force, to investigate the influence of the radial force on the capture eccentricity in the BCM. Then, a parametric analysis is performed to detect the influences on the corrected ratio \(k\) . Considering the restriction of time-of-flight and corrected ratio, we investigate, respectively, the minimum capture eccentricity and the corrected minimum capture eccentricity. Via numerical analysis, we discover two special regions on the sphere of capture, in which the capture point possesses the global minimum capture eccentricity and corrected capture eccentricity. They denote the optimal capture regions in terms of minimizing the fuel consumption of the maneuver. According to the results obtained, some suggestions on the design of the LET orbit are given.     

Satellite aided capture

A two body, patched conic analysis is presented for a planetary capture mode in which a gravity assist by an existing natural satellite of the planet aids in the capture. An analytical condition sufficient for capture is developed and applied for the following planet/satellite systems: Earth/Moon, Jupiter/Ganymede, Jupiter/Callisto, Saturn/Titan and Neptune/Triton. Co-planar, circular planetary orbits are assumed. Three sources of bodies to be captured are considered: spacecraft launched from Earth, bodies entering the solar system from interstellar space, and bodies already in orbit around the Sun. Results show that the Neptune/Triton system has the most capability for satellite aided capture of those studied. It can easily capture bodies entering the Solar System from interstellar space. Its ability to capture spacecraft launched from Earth is marginal and can only be decided with better definition of physical properties. None of the other systems can capture bodies from these two sources, but all can capture bodies already in orbit around the Sun under appropriate conditions.     

Consequences of a geosynchronous phase for the moon

Fission from the Earth's mantle explains why the density of the Moon is similar to that of the Earth's mantle.If following the fission origin of the Moon, the Earth-Moon distance increases progressively, the Moon can recollect chemicals evaporated by the Earth but not volatile enough to be lost as gases.In this way, the surface of the Moon can be enriched in refractory elements as most of the authors have proposed.At 3 Earth radii the long geosynchronous phase allows the formation of a solid crust which will record the Earth's magnetic field and the equilibrium hydrostatic from at that distance.When geosynchronism is broken the Moon will recede; its shape will no longer fit the hydrostatic form. The crust will either break or will exercise pressure on the lower layers. Meteor craters will allow lava to come to the surface. Such flows will be very large where the shape of the crust does not fit at all the geosynchronous form. Large lava flows will appear this way on the near side where the shape has changed the most. The new lava flows no longer record the magnetic field of the Earth because with the end of the synchronous position the field is alternative for the Moon; only the remanent field can influence the new lava.Three out of five samples dated at 3.6 b.y. suggest nevertheless that the field decreased slowly without becoming alternative. This means that the geosynchronous phase may have lasted longer and put the Moon on a more distant orbit, as Alfvén and Arrhenius suggested.The interpretation of lunar magnetism as influenced by the Earth cannot discard any interpretation or suggestion of its own lunar magnetic process. It is quite possible that both mechanisms have worked as some samples show.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademic Nazionale del Lincei in Rome, Italy.     

On the model of the accumulation of the moon compatible with the data on the composition and the age of lunar rocks

It is suggested that the overall early melting of the lunar surface is not necessary for the explanation of facts and that the structure of highlands is more complicated than a solidified anorthositic ‘plot’. The early heating of the interior of the Moon up to 1000K is really needed for the subsequent thermal history with the maximum melting 3.5 × 10⁹ yr ago, to give the observed ages for mare basalts. This may be considered as an indication that the Moon during the accumulation retained a portion of its gravitational energy converted into heat, which may occur only at rapid processes. A rapid (t < 10³ yr) accretion of the Moon from the circumterrestrial swarm of small particles would give necessary temperature, but it is not compatible with the characteristic time 10⁸ yr of the replenishment of this swarm which is the same as the time-scale of the accumulation of the Earth. It is shown that there were conditions in the circumterrestial swarm for the formation at a first stage of a few large protomoons. Their number and position is evaluated from the simple formal laws of the growth of satellites in the vicinity of a planet. Such ‘systems’ of protomoons are compared with the observed multiple systems, and the conclusion is reached that there could have been not more than 2–3 large protomoons with the Earth. The tidal evolution of protomoon orbits was short not only for the present value of the tidal phase-lag but also for a considerably smaller value. The coalescence of protomoons into a single Moon had to occur before the formation of the observed relief on the Moon. If we accept the age 3.9 × 10⁹ yr for the excavation of the Imbrium basin and ascribe the latter to the impact of an Earth satellite, this collision had to be roughly at 30R, whereR is the radius of the Earth, because the Moon at that time had to be somewhere at this distance. Therefore, the protomoons had to be orbiting inside 20–25R, and their coalescence had to occur more than 4.0x10⁹ yr ago. The energy release at coalescence is equivalent to several hundred degrees and even 1000 K. The process is very rapid (of the order of one hour). Therefore, the model is valid for the initial conditions of the Moon.     

Disturbance compensating control of orbit radially aligned two-craft Coulomb formation

This paper investigates the orbit radial stabilization of a two-craft virtual Coulomb structure about circular orbits and at Earth–Moon libration points. A generic Lyapunov feedback controller is designed for asymptotically stabilizing an orbit radial configuration about circular orbits and collinear libration points. The new feedback controller at the libration points is provided as a generic control law in which circular Earth orbit control form a special case. This control law can withstand differential solar perturbation effects on the two-craft formation. Electrostatic Coulomb forces acting in the longitudinal direction control the relative distance between the two satellites and inertial electric propulsion thrusting acting in the transverse directions control the in-plane and out-of-plane attitude motions. The electrostatic virtual tether between the two craft is capable of both tensile and compressive forces. Using the Lyapunov’s second method the feedback control law guarantees closed loop stability. Numerical simulations using the non-linear control law are presented for circular orbits and at an Earth–Moon collinear libration point.     

Lunar shape does not record a past eccentric orbit

The Moon has long been known to have an overall shape not consistent with expected past tidal forces. It has recently been suggested (Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652-655) that the present lunar moments of inertia indicate a past high-eccentricity orbit and, possibly, a past non-synchronous spin-orbit resonance. Here I show that the match between the lunar shape and the proposed orbital and spin states is much less conclusive than initially proposed. Garrick-Bethell et al. (Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652-655) spin and shape evolution scenarios also completely ignore the physics of the capture into such resonances, which require prior permanent deformation, as well as tidal despinning to the relevant resonance. If the early lunar orbit was eccentric, the Moon would have been rotating at an equilibrium non-synchronous rate determined by it eccentricity. This equilibrium supersynchronous rotation would be much too fast to allow a synchronous spin-orbit lock at e = 0.49, while the capture into the 3:2 resonance is possible only for a very constrained lunar eccentricity history and assuming some early permanent lunar tri-axiality. Here I show that large impacts in the early history of the Moon would have frequently disrupted this putative resonant rotation, making the rotation and eccentricity solutions of Garrick-Bethell et al. (Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652-655) unstable. I conclude that the present lunar shape cannot be used to support the hypothesis of an early eccentric lunar orbit.     

A note on the limits of stability for the restricted problem of three bodies as applied to the Sun-Earth-Moon system

The Sun-Earth-Moon system is modeled by the restricted problem of three bodies, and the curves of zero velocity are used to define the limits of stability of the Moon's orbit about the Earth. By holding the relative distances fixed, and maintaining the circular velocities of the Earth and Moon while their masses are varied by a common factor (=m _E/m _E=m _M/m _M), it is found that the possibility of the Moon leaving Earth orbit and orbiting the Sun exists for the range of values 0.005<<0.4.