scholarly journals Accretion of the Moon from non-canonical discs

2014 ◽  
Vol 372 (2024) ◽  
pp. 20130256 ◽  
Author(s):  
J. Salmon ◽  
R. M Canup
Keyword(s):  
Angular Momentum ◽  
Rotation Period ◽  
Major Axis ◽  
The Moon ◽  
Large Excess ◽  
Semi Major Axis ◽  
Earth’S Mantle ◽  
The Earth ◽  
Post Impact ◽  
Impact Simulations

Impacts that leave the Earth–Moon system with a large excess in angular momentum have recently been advocated as a means of generating a protolunar disc with a composition that is nearly identical to that of the Earth's mantle. We here investigate the accretion of the Moon from discs generated by such ‘non-canonical’ impacts, which are typically more compact than discs produced by canonical impacts and have a higher fraction of their mass initially located inside the Roche limit. Our model predicts a similar overall accretional history for both canonical and non-canonical discs, with the Moon forming in three consecutive steps over hundreds of years. However, we find that, to yield a lunar-mass Moon, the more compact non-canonical discs must initially be more massive than implied by prior estimates, and only a few of the discs produced by impact simulations to date appear to meet this condition. Non-canonical impacts require that capture of the Moon into the evection resonance with the Sun reduced the Earth–Moon angular momentum by a factor of 2 or more. We find that the Moon's semi-major axis at the end of its accretion is approximately 7 R ⊕ , which is comparable to the location of the evection resonance for a post-impact Earth with a 2.5 h rotation period in the absence of a disc. Thus, the dynamics of the Moon's assembly may directly affect its ability to be captured into the resonance.

Influence of some resonances on the inclination of a satellite

2020 ◽  
Author(s):  
Timothée Vaillant ◽  
Alexandre C. M. Correia
Keyword(s):  
Major Axis ◽  
The Moon ◽  
Semi Major Axis ◽  
Tidal Dissipation ◽  
The Earth ◽  
Hamiltonian Model ◽  
The Future ◽  
The Mean ◽  
Over Time ◽  
Probability Of Capture

<p align="justify">Knowing if the inclination of a satellite with respect to the equator of its planet is primordial can give hints on its origin and its formation. However, several mechanisms are able to modify its inclination during its evolution. The orbit of a satellite evolves over time and because of the tidal dissipation its semi-major axis can notably decrease or increase. Therefore the satellite can encounter several resonances in which it can potentially be captured. Some resonances are able to modify the equatorial inclination of a satellite. Touma and Wisdom (1998) noted that a resonance called ‘eviction’ between the mean motion of the Earth and the ascending node frequency of the Moon could increase by several degrees the equatorial inclination of the early Moon and could explain the present orientation of its orbit. Yokoyama (2002) studied these resonances for Phobos and Triton and observed that several resonances of this type can increase the equatorial inclination of Phobos in the future.</p> <p align="justify"> </p> <p align="justify">In this work, we study the different existing ‘eviction’ resonances to determine their possible influence on the equatorial inclination of a satellite. When a satellite goes through such a resonance, the capture is not certain and as noted by Yokoyama (2002), the probability of capture depends on several parameters as the obliquity of the planet and the interaction between other resonances. We consider the case of Phobos where we search to estimate the probability of a capture in an ‘eviction’ resonance by using an analytical Hamiltonian model and numerical simulations. This work will then notably estimate the probability that Phobos will be captured in the future in an ‘eviction’ resonance able to modify significantly its inclination and will measure the influence of the different parameters over the probability of capture.</p> <p align="justify"> </p> <p align="justify"><span lang="en-US">Acknowledgments: </span>The authors acknowledge support from project POCI-01-0145-FEDER-029932 (PTDC/FIS-AST/29932/2017), funded by FEDER through COMPETE 2020 (POCI) and FCT.</p> <p align="justify"> </p> <p align="justify">References:</p> <p align="justify"> </p> <p align="justify">Touma J. and Wisdom J., Resonances in the Early Evolution of the Earth-Moon System. <em>The Astronomical Journal</em>, 115:1653–1663, 1998.</p> <p align="justify">Yokoyama T., Possible effects of secular resonances in Phobos and Triton. <em>Planetary and Space Science</em>, 50:63–77, 2002.</p>

scholarly journals Que pourra-t-on deduire des mesures de distance terre-lune par laser?

1974 ◽  
Vol 61 ◽  
pp. 269-274
Author(s):  
J. Kovalevsky
Keyword(s):  
Major Axis ◽  
Radio Interferometry ◽  
The Moon ◽  
Semi Major Axis ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Observational Errors ◽  
External Check

Although several lunar laser ranging stations exist, only one is now fully operational: the McDonald station with internal observational errors of less than 15 cm. The interpretation of the data involves a great number of parameters relative to the Earth and the Moon which are listed.The lunar laser is particularly fit for those parameters that pertain to the Moon, and with future lasers accurate to 2 or 3 cm, it may be expected that this accuracy will be projected into these parameters. The probable determination of the semi-major axis to 1 cm accuracy for a few months mean would imply a new means of determining the non conservative part of the motion of the Moon. A similar precision is to be expected for the rotation of the Moon. The situation for the Earth parameters (Earth rotation and polar motion) is not so good, because of a rather weak geometry of the problem and the monthly one week gap in the observations. Nevertheless, it will give a very useful external check on other competing methods (radio-interferometry, laser or radio-satellites).

scholarly journals Some Special Types of Orbits around Jupiter

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 183
Author(s):  
Yongjie Liu ◽  
Yu Jiang ◽  
Hengnian Li ◽  
Hui Zhang
Keyword(s):  
Gravity Model ◽  
Small Perturbation ◽  
Equilibrium Points ◽  
Major Axis ◽  
Semi Major Axis ◽  
Ground Track ◽  
The Earth ◽  
Degenerate Equilibrium ◽  
The Mean ◽  
Element Theory

This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of J2 and J4 terms is used here. Compared with special orbits around the Earth, the orbit dynamics differ greatly: (1) There do not exist longitude drifts on stationary orbits due to non-spherical gravity since only J2 and J4 terms are taken into account in the gravity model. All points on stationary orbits are degenerate equilibrium points. Moreover, the satellite will oscillate in the radial and North-South directions after a sufficiently small perturbation of stationary orbits. (2) The inclinations of sun-synchronous orbits are always bigger than 90 degrees, but smaller than those for satellites around the Earth. (3) The critical inclinations are no-longer independent of the semi-major axis and eccentricity of the orbits. The results show that if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase. (4) The inclinations of repeating ground track orbits are monotonically increasing rapidly with respect to the altitudes of orbits.

scholarly journals Angular Momentum and Energy Transfer in a Whitehead's Theory of Gravity

2018 ◽  
Author(s):  
Luis Acedo
Keyword(s):  
Angular Momentum ◽  
Major Axis ◽  
Astronomical Unit ◽  
Net Energy ◽  
Semi Major Axis ◽  
Extended Gravity ◽  
First Case ◽  
Planetary Orbits ◽  
Theory Of Gravity ◽  
New Phenomena

In this paper, we revisit a modified version of the classical Whitehead's theory of gravity in which all possible bilinear forms are considered to define the corresponding metric. Although, this is a linear theory that fails to give accurate results for the most sophisticated predictions of general relativity, such as gravity waves, it can still provide a convenient framework to analyze some new phenomena in the Solar System. In particular, recent development in the accurate tracking of spacecraft and the ephemerides of planetary positions have revealed certain anomalies in relation with our standard paradigm for celestial mechanics. Among them the so-called flyby anomaly and the anomalous increase of the astronomical unit play a prominent role. In the first case the total energy of the spacecraft changes during the flyby and a secular variation of the semi-major axis of the planetary orbits is found in the second anomaly. For this to happen it seems that a net energy and angular momentum transfer is taken place among the orbiting and the central body. We evaluate the total transfer per revolution for a planet orbiting the Sun in order to predict the astronomical unit anomaly in the context of Whitehead's theory. This could lead to a more deeply founded hypothesis for an extended gravity model.

scholarly journals The Shape of the Moon

1972 ◽  
Vol 47 ◽  
pp. 22-31 ◽  
Author(s):  
S. K. Runcorn ◽  
S. Hofmann
Keyword(s):  
Lunar Surface ◽  
Major Axis ◽  
Great Depth ◽  
The Moon ◽  
Method Of Least Squares ◽  
Global Shape ◽  
The Earth ◽  
Intrinsic Scatter ◽  
Simple Statistical Analysis

The determination of the heights of points on the lunar surface by Earth based astronomy using the geometrical librations, although individually of low accuracy, still provides our best method of obtaining the global shape of the Moon. The intrinsic scatter of the results arises from the effects of ‘seeing’ and simple statistical analysis is required to derive valid conclusions about the shape. Baldwin's method of fitting ellipsoidal surfaces to the points on the maria and uplands, separately by the method of least squares proves to be a valuable tool.Analyses of the ACIC points and of the Pic du Midi studies of G. A. Mills show that good first descriptions of the global shape of the Moon for both the maria and uplands are triaxial ellipsoids with their long axes within 10° of the Earth direction, the major axis of the maria being about 1.3 km smaller than that of the uplands. Of particular significance is that the ellipticity of these surfaces is about 2½ times greater than the dynamical ellipticity; thus the non-hydrostatic figure of the Moon is not simply the result of distortion from a uniform Moon during its early history. The angular variation in density within the Moon cannot be simply a phenomena within the crust but must extend to a great depth. Convection could provide an explanation.The departures of the lunar surface from the idealised ellipsoids are also of interest. The circular maria are systematically depressed relative to the maria ellipsoid: can the mascons have adjusted isostatically since their formation? Systematic differences in height between the western and eastern southern uplands are also noted.

scholarly journals Boundary conditions for the formation of the Moon

2015 ◽  
Vol 95 (2) ◽  
pp. 131-139 ◽  
Author(s):  
M. Reuver ◽  
R.J. de Meijer ◽  
I.L. ten Kate ◽  
W. van Westrenen
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Total Angular Momentum ◽  
Nuclear Explosion ◽  
Moment Of Inertia ◽  
The Moon ◽  
Moon System ◽  
Giant Impact ◽  
The Earth ◽  
The Impact

AbstractRecent measurements of the chemical and isotopic composition of lunar samples indicate that the Moon's bulk composition shows great similarities with the composition of the silicate Earth. Moon formation models that attempt to explain these similarities make a wide variety of assumptions about the properties of the Earth prior to the formation of the Moon (the proto-Earth), and about the necessity and properties of an impactor colliding with the proto-Earth. This paper investigates the effects of the proto-Earth's mass, oblateness and internal core-mantle differentiation on its moment of inertia. The ratio of angular momentum and moment of inertia determines the stability of the proto-Earth and the binding energy, i.e. the energy needed to make the transition from an initial state in which the system is a rotating single body with a certain angular momentum to a final state with two bodies (Earth and Moon) with the same total angular momentum, redistributed between Earth and Moon. For the initial state two scenarios are being investigated: a homogeneous (undifferentiated) proto-Earth and a proto-Earth differentiated in a central metallic and an outer silicate shell; for both scenarios a range of oblateness values is investigated. Calculations indicate that a differentiated proto-Earth would become unstable at an angular momentum L that exceeds the total angular momentum of the present-day Earth–Moon system (L0) by factors of 2.5–2.9, with the precise maximum dependent on the proto-Earth's oblateness. Further limitations are imposed by the Roche limit and the logical condition that the separated Earth–Moon system should be formed outside the proto-Earth. This further limits the L values of the Earth–Moon system to a maximum of about L/L0 = 1.5, at a minimum oblateness (a/c ratio) of 1.2. These calculations provide boundary conditions for the main classes of Moon-forming models. Our results show that at the high values of L used in recent giant impact models (1.8 < L/L0 < 3.1), the proposed proto-Earths are unstable before (Cuk & Stewart, 2012) or immediately after (Canup, 2012) the impact, even at a high oblateness (the most favourable condition for stability). We conclude that the recent attempts to improve the classic giant impact hypothesis by studying systems with very high values of L are not supported by the boundary condition calculations in this work. In contrast, this work indicates that the nuclear explosion model for Moon formation (De Meijer et al., 2013) fulfills the boundary conditions and requires approximately one order of magnitude less energy than originally estimated. Hence in our view the nuclear explosion model is presently the model that best explains the formation of the Moon from predominantly terrestrial silicate material.

Evidence from the surface configuration of the Moon on its dynamical evolution

1967 ◽  
Vol 296 (1446) ◽  
pp. 298-303
Keyword(s):  
Lunar Surface ◽  
High Velocity ◽  
Dynamical Evolution ◽  
Great Majority ◽  
Major Axis ◽  
The Moon ◽  
Moon System ◽  
The Past ◽  
The Earth ◽  
High Velocity Impacts

Examination of the Moon through large telescopes reveals a multitude of fine detail down to a scale of 1 km or less. The most prominent feature of the lunar surface is the abundance of circular craters. Many investigators agree that a great majority of these craters have been caused by explosions associated with high velocity impacts. It is further generally assumed that the majority of these high velocity impacts took place during the earliest stages of development of the present Earth-Moon system. The morphology of the Moon surface appears in dynamical considerations in the following way. We know from the work of G. H. Darwin that the Moon has been steadily retreating from the Earth. Dynamical considerations suggest that the period of rotation of the Moon on the average equals its period of revolution about the Earth. Thus when the Moon approaches the Earth, its rotation would be accelerated. Since the Moon, like the Earth, approximates to a fluid body, we should expect that a figure of the Moon would have changed in response to its changing rate of rotation. If the craters formed at a time at which the Moon’s figure was markedly different from the present, then initially circular craters would be deformed and any initially circular depression would tend to change into an elliptically shaped depression, with the major axis of the ellipse along the local meridian. Study of the observed distortions of the craters can give evidence as to the past shape of the Moon, provided the craters formed at a time when the Moon possessed a different surface ellipticity. I should like to examine the limitations the present surface structure places on the past dynamical history of the Moon. I will first review briefly calculations bearing on the dynamical evolution of the Earth-Moon system and the implications these calculations have on the past shape of the lunar surface.

scholarly journals On the Initial Distance of the Moon Forming in the Circumterrestrial Swarm

1972 ◽  
Vol 47 ◽  
pp. 402-404
Author(s):  
E. L. Ruskol
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Outer Boundary ◽  
The Sun ◽  
The Moon ◽  
Present Value ◽  
Primitive Earth ◽  
Moon System ◽  
Initial Distance ◽  
The Earth

According to the Radzievskij-Artemjev hypothesis of the ‘locked’ revolution of the circumplanetary swarms around the Sun, the initial Moon-to-Earth distance and the angular momentum acquired by the Earth through the accretion of the inner part of the swarm can be evaluated. Depending on the concentration of the density to the centre of the swarm we obtain the initial distance for a single protomoon in the range 15–26 Earth radii R and for a system of 3-4 protomoons in the range 3–78 R, if the outer boundary of the swarm equals to the radius of the Hill's sphere (235 R). The total angular momentum acquired by the primitive Earth-Moon system through the accretion of the swarm particles is ½–⅔ of its present value. The rest of it should be acquired from the direct accretion of interplanetary particles by the Earth. The contribution of satellite swarms into the rotation of other planets is relatively less.

Using spacecraft range data and radar observations for the improvement of the orbital elements of planets and parameters of Mars rotation

1996 ◽  
Vol 172 ◽  
pp. 45-48
Author(s):  
E.V. Pitjeva
Keyword(s):  
Major Axis ◽  
Astronomical Unit ◽  
Range Data ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
The Earth ◽  
Electromagnetic Signals ◽  
Least Squares Estimates ◽  
Radar Ranging ◽  
Made In

The extremely precise Viking (1972–1982) and Mariner data (1971–1972) were processed simultaneously with the radar-ranging observations of Mars made in Goldstone, Haystack and Arecibo in 1971–1973 for the improvement of the orbital elements of Mars and Earth and parameters of Mars rotation. Reduction of measurements included relativistic corrections, effects of propagation of electromagnetic signals in the Earth troposphere and in the solar corona, corrections for topography of the Mars surface. The precision of the least squares estimates is rather high, for example formal standard deviations of semi-major axis of Mars and Earth and the Astronomical Unit were 1–2 m.

Subtleties in spherical harmonic synthesis of the gravity field

2020 ◽  
Author(s):  
Ropesh Goyal ◽  
Sten Claessens ◽  
Will Featherstone ◽  
Onkar Dikshit
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Gravitational Constant ◽  
Angular Rate ◽  
Physical Geodesy ◽  
Major Axis ◽  
Gravity Potential ◽  
Semi Major Axis ◽  
The Earth ◽  
Spherical Harmonic Synthesis

&lt;p&gt;Spherical harmonic synthesis (SHS) can be used to compute various gravity functions (e.g., geoid undulations, height anomalies, deflections of vertical, gravity disturbances, gravity anomalies, etc.) using the 4pi fully normalised Stokes coefficients from the many freely available Global Geopotential Models (GGMs). &amp;#160;This requires a normal ellipsoid and its gravity field, which are defined by four parameters comprising (i) the second-degree even zonal Stokes coefficient (J2) (aka dynamic form factor), (ii) the product of the mass of the Earth and universal gravitational constant (GM) (aka geocentric gravitational constant), (iii) the Earth&amp;#8217;s angular rate of rotation (&amp;#969;), and (iv) the length of the semi-major axis (a). GGMs are also accompanied by numerical values for GM and a, which are not necessarily identical to those of the normal ellipsoid.&amp;#160; In addition, the value of W&lt;sub&gt;0,&lt;/sub&gt; the potential of the geoid from a GGM, needs to be defined for the SHS of many gravity functions. W&lt;sub&gt;0&lt;/sub&gt; may not be identical to U&lt;sub&gt;0&lt;/sub&gt;, the potential on the surface of the normal ellipsoid, which follows from the four defining parameters of the normal ellipsoid.&amp;#160; If W&lt;sub&gt;0&lt;/sub&gt; and U&lt;sub&gt;0&lt;/sub&gt; are equal and if the normal ellipsoid and GGM use the same value for GM, then some terms cancel when computing the disturbing gravity potential.&amp;#160; However, this is not always the case, which results in a zero-degree term (bias) when the masses and potentials are different. &amp;#160;There is also a latitude-dependent term when the geometries of the GGM and normal ellipsoids differ.&amp;#160; We demonstrate these effects for some GGMs, some values of W&lt;sub&gt;0&lt;/sub&gt;, and the GRS80, WGS84 and TOPEX/Poseidon ellipsoids and comment on its omission from some public domain codes and services (isGraflab.m, harmonic_synth.f and ICGEM).&amp;#160; In terms of geoid heights, the effect of neglecting these parameters can reach nearly one metre, which is significant when one goal of modern physical geodesy is to compute the geoid with centimetric accuracy.&amp;#160; It is also important to clarify these effects for all (non-specialist) users of GGMs.&lt;/p&gt;

Sign in / Sign up

Export Citation Format

Share Document