The Lunar Fossil Figure in a Cassini State

The present ellipsoidal figure of the Moon requires a deformation that is significantly larger than the hydrostatic deformation in response to the present rotational and tidal potentials. This has long been explained as due to a fossil rotational and tidal deformation from a time when the Moon was closer to Earth. Previous studies constraining the orbital parameters at the time the fossil deformation was established find that high orbit eccentricities (e ≳ 0.2) are required at this ancient time, which is difficult to reconcile with the freezing of a fossil figure owing to the expected large tidal heating. We extend previous fossil deformation studies in several ways. First, we consider the effect of removing South Pole−Aitken (SPA) contributions from the present observed deformation using a nonaxially symmetric SPA model. Second, we use the assumption of an equilibrium Cassini state as an additional constraint, which allows us to consider the fossil deformation due to nonzero obliquity self-consistently. A fossil deformation established during Cassini state 1, 2, or 4 is consistent with the SPA-corrected present deformation. However, a fossil deformation established during Cassini state 2 or 4 requires large obliquity and orbit eccentricity (ϵ ∼ 68° and e ∼ 0.65), which are difficult to reconcile with the corresponding strong tidal heating. The most likely explanation is a fossil deformation established during Cassini state 1, with a small obliquity (ϵ ∼ −0.2°) and an orbit eccentricity range that includes zero eccentricity (0 ≤ e ≲ 0.3).

Constraints on Newtonian Interplanetary Point-Mass Interactions in Multicomponent Systems from the Symmetry of Their Cycles

Interplanetary interactions are the largest forces in our Solar System that disturb the planets from their elliptical orbits around the Sun, yet are weak (<10−3 Solar). Currently, these perturbations are computed in pairs using Hill’s model for steady-state, central forces between one circular and one elliptical ring of mass. However, forces between rings are not central. To represent interplanetary interactions, which are transient, time-dependent, and cyclical, we build upon Newton’s model of interacting point-mass pairs, focusing on circular orbits of the eight largest bodies. To probe general and evolutionary behavior, we present analytical and numerical models of the interplanetary forces and torques generated during the planetary interaction cycles. From symmetry, over a planetary interaction cycle, radial forces dominate while tangential forces average to zero. Our calculations show that orbital perturbations require millennia to quantify, but observations are only over ~165 years. Furthermore, these observations are compromised because they are predominantly made from Earth, whose geocenter occupies a complex, non-Keplerian orbit. Eccentricity and inclination data are reliable and suggest that interplanetary interactions have drawn orbital planes together while elongating the orbits of the two smallest planets. This finding is consistent with conservation principles governing the eight planets, which formed as a system and evolve as a system.

A Modified Milankovitch theory that reconciles contradictions with the paleoclimate record

Based upon research results over the past five decades, there has been a general acceptance that the ice ages were initiated by astronomical phenomenon. Specifically, marine, ice and terrestrial paleoclimate data have supported elements of the Milankovitch astronomical theory of the ice ages. However, there remain unresolved problems between the empirical findings and theory. The 100 thousand year problem has been the subject of extensive research since a 100 thousand year cycle that matches the Earth orbit eccentricity period dominates the frequencies found in paleoclimate records. Yet, eccentricity produces an insignificant variation in annual solar energy. Other problems include the Stage 11 problem, the missing interglacials problem, how glaciation is sustained over multiple tens of thousands of years and synchronous hemispheric glaciation. I shall show these problems are resolved by modification of the prevailing Milankovitch theory. In particular, two elements of the theory need modification. One is the limitation of eccentricity's role and the other assuming that glaciation results only from cool summer conditions. By applying the Solar Energy Invariance law to define e-seasons, how eccentricity provides conditions for glaciation is demonstrated. The results show eccentricity variations provide significant solar energy variations at the top of the earth's atmosphere to produce glaciation that is global. Global glaciation results in colder winter glaciation occurring in one hemisphere simultaneous with cool summer glaciation in the other hemisphere. Analysis with these modifications resolves each of the problems.

Dust tail observation and modeling of the interstellar comet 2I/Borisov

&lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;On 30 August 2019 the amateur Borisov discovered a new comet; after few days it was clear from the characteristics of its orbit (eccentricity &gt; 3 and high hyperbolic excess velocity) that the second interstellar object had been detected and the object received the name of 2I/Borisov. &lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;It appears to be very different from 1I/&amp;#8217;Oumuamua and can be considered as the first interstellar comet.&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;According to the first observations the comet had a nucleus with a radius of few km and a dust coma and tail due to the activity started in June 2019 (Jewitt et al., 2019).&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;At the beginning of October we submitted the Discretionary Director Time (DDT) proposal to the TNG in order to monitor the comet. Some images have been acquired, in November and December 2019, with the DOLORES instrument in the R filter.&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;We have applied the dust model described in Fulle et al. (2010), that has been tested on the comet 67P/Churyumov-Gerasimenko and validated with the Rosetta measurements.&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;According to the results of our dust model and the activity model (Fulle et al., 2020) we derived a water flux from the nucleus of 8x10&lt;sup&gt;-6 &lt;/sup&gt;kg m&lt;sup&gt;-2 &lt;/sup&gt;s&lt;sup&gt;-1 &lt;/sup&gt;and a dust loss rate of 35 and 30 kg s&lt;sup&gt;-1 &lt;/sup&gt;in November and December 2019 respectively (Cremonese et al., 2020). This slight decrease has been observed around the perihelion on 8 December, few months later the comet fragmented.&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;In this work we will describe the dust tail observations and the dust model results, even comparing them with the Jupiter family comet 67P.&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Sectionheading&quot;&gt;&lt;span lang=&quot;EN-GB&quot;&gt;References&lt;/span&gt;&lt;span lang=&quot;EN-GB&quot;&gt;:&lt;/span&gt;&lt;/p&gt; &lt;p class=&quot;Abstractsectionheading&quot;&gt;G.Cremonese, et al., 2020, ApJL, 893, L12&lt;/p&gt; &lt;p class=&quot;Abstractsectionheading&quot;&gt;M.Fulle et al., 2010, A&amp;A, 522, A63.&lt;/p&gt; &lt;p class=&quot;Abstractsectionheading&quot;&gt;M.Fulle et al., 2020, MNRAS, 493, 4039.&lt;/p&gt; &lt;p class=&quot;Abstractsectionheading&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;Jewitt et al., 2019, ApJ, 886, L29.&lt;/span&gt;&lt;/p&gt;

High obliquity, high angular momentum Earth as Moon’s origin revisited by Advanced Kinematic Model of Earth-Moon System

Matija Cuk et.al (2016) have proposed a new model for the birth and tidal evolution of our natural satellite Moon, born from lunar accretion of impact generated terrestrial debris in the equatorial plane of high obliquity, high angular momentum Earth. This paper examines their findings critically in the light of Advanced Kinematic Model (AKM) which includes Earth’s obliquity(ɸ), Moon’s orbital plane inclination (α), Moon’s obliquity (β) and lunar’s orbit eccentricity (e). It is shown that AKM’s valid range of application is from 45RE to 60.33RE. The evolution of α, β, e is in correspondence with the simulation results of Matija Cuk et.al (2016) but evolution of Earth’s obliquity has a break at 45RE. According to AKM, earlier than 45RE Earth should achieve 0° obliquity in order to achieve the modern value of eco-friendly 23.44° obliquity. Cuk et al (2016) silent on this point. AKM stands vindicated because using protocol exchange algorithm http://doi.org/10.1038/protex.2019.017, AKM has successfully given precise theoretical formalism of Observed LOD curve for the last 1.2 Gy time span opening the way for early warning and forecasting methods for Earth-quake and sudden Volcanic eruptions. This paper gives us an algorithm to determine the short term and long term changes in Earth’s obliquity which is related to Weather and Climate Extremes. Hence this paper gives us the mathematical tool for predicting the Earth’s climate extreme.

On the secondary’s rotation in a synchronous binary asteroid

ABSTRACT This article studies the secondary’s rotation in a synchronous binary asteroid system in which the secondary enters the 1:1 spin-orbit resonance. The model used is the planar full two-body problem, composed of a spherical primary plus a triaxial ellipsoid secondary. Compared with classical spin-orbit work, there are two differences: (1) influence of the secondary’s rotation on the mutual orbit is considered and (2) instead of the Hamiltonian approach, the approach of periodic orbits is adopted. Our studies find the following. (1) The genealogy of the two families of periodic orbits is the same as that of the families around triangular libration points in the restricted three-body problem. That is, the long-period family terminates on to a short-period orbit travelling N times. (2) In the limiting case where the secondary’s mass is negligible, our results can be reduced to classical spin-orbit theory, by equating the long-period orbit with free libration and the short-period orbit with the forced libration caused by orbit eccentricity. However, the two models show obvious differences when the secondary’s mass is non-negligible. (3) By studying the stability of periodic orbits for a specific binary asteroid system, we are able to obtain the maximum libration amplitude of the secondary (which is usually less than 90°) and the maximum mutual orbit eccentricity that does not break the secondary’s synchronous state. We also find an anti-correlation between the secondary’s libration amplitude and the orbit eccentricity. The (65803) Didymos system is taken as an example to show the results.

100,000-year rhythmicity in glacial cycles and global sea level variations

100,000-year rhythmicity of paleoclimate variations, that aroused in the Late Pleistocene, can be linked with corresponded long-term oscillations of insolation and seafloor volcanism, forced by gravitational forces in Solar system. This conclusion is based on wavelet analysis of variations of the earth’s orbit eccentricity, different paleoclimatic characteristics, and their known spectral estimates and seafloor volcanism data.

Astrometric Solar-System Anomalies and Evolutionary Physical Constants

We have shown that three astrometric solar-system anomalies can be explained satisfactorily by using evolutionary gravitational constant G and speed of light c in the Einstein&rsquo;s field equation. These are: a) the Pioneer acceleration anomaly; b) the anomalous secular increase of Moon-orbit eccentricity; and c) the anomalous secular change in the astronomical unit AU. The gravitational constant G and the speed of light c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant. We also show that the Planck&rsquo;s constant ħ increases as dħ/dt = 1.8ħH0.&nbsp; Additionally, the new approach fits the supernovae Ia redshift vs distance modulus data as well as the standard &Lambda;CDM model with just one adjustable parameter H0.