DOCSLIB.ORG

A Population of Main Belt Asteroids Co-Orbiting with Ceres and Vesta ⇑ Apostolos A

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Population of Main Belt Asteroids Co-Orbiting with Ceres and Vesta ⇑ Apostolos A Icarus 217 (2012) 27–42 Contents lists available at SciVerse ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus A population of Main Belt Asteroids co-orbiting with Ceres and Vesta ⇑ Apostolos A. Christou a, , Paul Wiegert b a Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland, UK b The University of Western Ontario, Department of Physics and Astronomy, London, Ontario, Canada N6A 3K7 article info abstract Article history: We have carried out a search for Main Belt Asteroids (MBAs) co-orbiting with the large MBA Vesta and Received 16 July 2011 the dwarf planet Ceres. Through improving the search criteria used in Christou (Christou, A.A. [2000b]. Revised 18 October 2011 Astron. Astrophys. 356, L71–L74) and numerical integrations of candidate coorbitals, we have identified Accepted 19 October 2011 approximately 51 (44) objects currently in co-orbital libration with Ceres (Vesta). We show that these Available online 28 October 2011 form part of a larger population of transient coorbitals; 129 (94) MBAs undergo episodes of co-orbital libration with Ceres (Vesta) within a 2 Myr interval centred on the present. The lifetime in the resonance Keywords: is typically a few times 105 yr but can exceed 2  106 yr. The variational properties of the orbits of sev- Asteroids, Dynamics eral co-orbitals were examined. It was found that their present states with respect to the secondary are Asteroid Ceres 5 Asteroid Vesta well determined but knowledge of it is lost typically after 2  10 yr. Objects initially deeper into the coorbital region maintain their coorbital state for longer. Using the model of Namouni et al. (Namouni, F., Christou, A.A., Murray, C.D. [1999]. Phys. Rev. Lett. 83, 2506–2509) we show that their dynamics are similar to those of temporary coorbital NEAs of the Earth and Venus. As in that case, the lifetime of res- onant libration is dictated by planetary secular perturbations, the inherent chaoticity of the orbits and close encounters with massive objects other than the secondary. In particular we present evidence that, while in the coorbital state, close encounters with the secondary are generally avoided and that Ceres affects the stability of tadpole librators of Vesta. Finally we demonstrate the existence of Quasi-Satellite orbiters of both Ceres and Vesta and conclude that decametre-sized objects detected in the vicinity of Vesta by the DAWN mission may, in fact, belong to this dynamical class rather than be bona-fide (i.e. Keplerian) satellites of Vesta. Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction and inclination modifies considerably the topology of coorbital dynamics near the secondary mass. It results in the appearance The coorbital resonance, where the gravitational interaction of bounded eccentric orbits (Quasi-Satellites; Mikkola and Inna- between two bodies with nearly the same orbital energy leads to nen, 1997) and, in three dimensions, ‘‘compound’’ orbits and stable stable and predictable motion, is ubiquitous in the Solar System. transitions between the different modes of libration. Further, he Objects attended by known co-orbital companions include Jupiter, demonstrated numerically that these results hold when the full Mars as well as the saturnian satellites Tethys, Dione, Janus and R3BP is considered. In this case, the appearance of new types of Epimetheus (see Christou (2000a) for a review). More recently, compound orbits, such as asymmetric modes or compounds of tad- the planet Neptune was added to this list (Sheppard and Trujillo, poles and retrograde satellites, was shown in Namouni et al. (1999) 2006) while an additional coorbital of Dione was discovered by to be due to the secular evolution of the coorbital potential. Such the Cassini mission (Murray et al., 2005). In all these cases, the mo- types of coorbital libration were identified in the motion of the ob- tion has been shown to be stable against all but the most slow-act- ject highlighted by Wiegert et al. (1997) as well as other near-Earth ing perturbations (Lissauer et al., 1985; Levison et al., 1997; Brasser asteroids but the secular forcing of the potential in that case is pro- et al., 2004; Scholl et al., 2005). vided by planetary secular perturbations (Namouni et al., 1999; The discovery of a coorbital attendant of the Earth on a highly Christou, 2000a). The expected characteristics of the population inclined and eccentric orbit (Wiegert et al., 1997, 1998) motivated of co-orbitals of Earth and Venus were investigated by Morais new theoretical work in the field. Namouni (1999), using Hill’s and Morbidelli (2002, 2006) respectively. approximation to the Restricted Three Body Problem (R3BP) Christou (2000b), motivated by Pluto’s ability, as demonstrated showed analytically that the introduction of large eccentricity by Yu and Tremaine (1999) and Nesvorny´ et al. (2000), to trap other Edgeworth–Kuiper Belt objects in co-orbital motion with it- ⇑ Corresponding author. Fax: +44 2837 527174. self, demonstrated in turn that Main Belt Asteroids can co-orbit E-mail addresses: [email protected] (A.A. Christou), [email protected] (P. Wiegert). with the dwarf planet 1 Ceres and the large Main Belt Asteroid 0019-1035/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2011.10.016 28 A.A. Christou, P. Wiegert / Icarus 217 (2012) 27–42 (MBA) 4 Vesta. Four such asteroids were identified, two co-orbiting with Ceres and two with Vesta. 0.002 Here we report the results of a search for additional coorbitals of these two massive asteroids. This was motivated partly by the large growth in the number of sufficiently well-known MBA orbits 0.001 Ceres during the intervening decade, but also a refinement of the search criterion used in the work by Christou. As a result, we find over 200 ) / a 0.000 new transient co-orbital MBAs of Ceres and Vesta. In this work we Ceres examine their ensemble properties, use existing dynamical models - a to understand how they arise and identify similarities with co- 1372 -0.001 orbital populations elsewhere in the Solar System, in particular (a the transient coorbital NEAs of Earth and Venus. -0.002 The paper is organised as follows: In the next Section we expose our Search methodology, in particular those aspects which differ from the search carried out by Christou (2000b). In Section 3 we 0 50 100 150 200 describe the statistics of coorbital lifetime and orbital element dis- tribution found in our integrations. In addition, we examine the 0.0004 robustness of the dynamical structures we observe. In Section 4 we investigate the degree to which the model of Namouni et al. (1999) can reproduce the observed dynamics. Section 5 deals with 0.0002 Ceres the effects of additional massive asteroids in the three-body dynamics while Section 6 focuses on the stability of so-called Qua- ) / a 0.0000 si-Satellite orbits. Finally, Section 7 summarises our conclusions Ceres and identifies further avenues of investigation. - a 1372 -0.0002 (a 2. Search methodology -0.0004 Christou (2000b) searched for candidate Ceres coorbitals by 0 2000 4000 6000 8000 10000 employing the osculating semimajor axis ar of the asteroid relative to that of Ceres (equal to (a À aCeres)/aCeres) to highlight objects that time (years) merited further investigation. This method, although it led to the Fig. 1. Comparison of proper, averaged and osculating semimajor axis for Asteroid successful identification of two coorbitals, 1372 Haremari and 1372 Haremari during a numerical 104 yr numerical integration of its orbit. See text 8877 Rentaro, ignores the existence of high frequency variations for details. in a due to perturbations by the planets, especially Jupiter. This is illustrated in the upper panel of Fig. 1 where the evolution of ar for Asteroid 1372 Haremari, one of the objects identified by Chris- Knezˇevic´ and Milani that was available as of 09/2008 at the AstDys tou, is depicted. A periodic term of amplitude 0.001 apparently online information service (http://hamilton.dm.unipi.it/astdys/ propsynth/numb.syn). A total of 648 and 514 Main-Belt Asteroids causes ar to move in and out of Ceres’ coorbital zone (bounded by the dashed horizontal lines) every 20 yr. On the other hand, an ob- respectively with proper semimajor axes within ±a of those of Ceres and Vesta were identified. Table 1 shows the parameters rel- ject with ar 6 would have a conjunction with Ceres every P6  104 yr. Here =(l/3)1/3 denotes Hill’s parameter in the Circu- evant to this search for the massive asteroids. The second row pro- lar Restricted Three-Body Problem for a secondary body with a vides the mass ratio l of the asteroid relative to the mass of the mass l scaled to that of the central body (in this case, the Sun). This Sun, the third row its Hill parameter , the fourth row the asteroids’ suggests that coorbital motion should be insensitive to these varia- synthetic proper semimaxor axis ap as given in the database and tions and that a low-pass filtered semimajor axis would work better the fifth row the product ap  which is the half-width of the coor- as an indicator of libration in the 1:1 resonance with Ceres. We have bital region in AU. chosen this to be the synthetic proper semimajor axis (hereafter re- The state vectors of these asteroids at Julian Date 2451545.0 ferred to as ‘‘proper semimajor axis’’) as defined by Knezˇevic´ and were retrieved from HORIZONS (Giorgini et al., 1996) and numer- Milani (2000). Synthetic proper elements are numerically-derived ically integrated 1 myr in the past and in the future using a model constants of an asteroid’s motion under planetary perturbations.
Load more

Recommended publications
  • Astro2020 Science White Paper Modeling Debris Disk Evolution
    Astro2020 Science White Paper Modeling Debris Disk Evolution Thematic Areas Planetary Systems Formation and Evolution of Compact Objects Star and Planet Formation Cosmology and Fundamental Physics Galaxy Evolution Resolved Stellar Populations and their Environments Stars and Stellar Evolution Multi-Messenger Astronomy and Astrophysics Principal Author András Gáspár Steward Observatory, The University of Arizona [email protected] 1-(520)-621-1797 Co-Authors Dániel Apai, Jean-Charles Augereau, Nicholas P. Ballering, Charles A. Beichman, Anthony Boc- caletti, Mark Booth, Brendan P. Bowler, Geoffrey Bryden, Christine H. Chen, Thayne Currie, William C. Danchi, John Debes, Denis Defrère, Steve Ertel, Alan P. Jackson, Paul G. Kalas, Grant M. Kennedy, Matthew A. Kenworthy, Jinyoung Serena Kim, Florian Kirchschlager, Quentin Kral, Sebastiaan Krijt, Alexander V. Krivov, Marc J. Kuchner, Jarron M. Leisenring, Torsten Löhne, Wladimir Lyra, Meredith A. MacGregor, Luca Matrà, Dimitri Mawet, Bertrand Mennes- son, Tiffany Meshkat, Amaya Moro-Martín, Erika R. Nesvold, George H. Rieke, Aki Roberge, Glenn Schneider, Andrew Shannon, Christopher C. Stark, Kate Y. L. Su, Philippe Thébault, David J. Wilner, Mark C. Wyatt, Marie Ygouf, Andrew N. Youdin Co-Signers Virginie Faramaz, Kevin Flaherty, Hannah Jang-Condell, Jérémy Lebreton, Sebastián Marino, Jonathan P. Marshall, Rafael Millan-Gabet, Peter Plavchan, Luisa M. Rebull, Jacob White Abstract Understanding the formation, evolution, diversity, and architectures of planetary systems requires detailed knowledge of all of their components. The past decade has shown a remarkable increase in the number of known exoplanets and debris disks, i.e., populations of circumstellar planetes- imals and dust roughly analogous to our solar system’s Kuiper belt, asteroid belt, and zodiacal dust.
    [Show full text]
  • (121514) 1999 UJ7: a Primitive, Slow-Rotating Martian Trojan G
    A&A 618, A178 (2018) https://doi.org/10.1051/0004-6361/201732466 Astronomy & © ESO 2018 Astrophysics ? (121514) 1999 UJ7: A primitive, slow-rotating Martian Trojan G. Borisov1,2, A. A. Christou1, F. Colas3, S. Bagnulo1, A. Cellino4, and A. Dell’Oro5 1 Armagh Observatory and Planetarium, College Hill, Armagh BT61 9DG, Northern Ireland, UK e-mail: [email protected] 2 Institute of Astronomy and NAO, Bulgarian Academy of Sciences, 72, Tsarigradsko Chaussée Blvd., 1784 Sofia, Bulgaria 3 IMCCE, Observatoire de Paris, UPMC, CNRS UMR8028, 77 Av. Denfert-Rochereau, 75014 Paris, France 4 INAF – Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025 Pino Torinese (TO), Italy 5 INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125, Firenze, Italy Received 15 December 2017 / Accepted 7 August 2018 ABSTRACT Aims. The goal of this investigation is to determine the origin and surface composition of the asteroid (121514) 1999 UJ7, the only currently known L4 Martian Trojan asteroid. Methods. We have obtained visible reflectance spectra and photometry of 1999 UJ7 and compared the spectroscopic results with the spectra of a number of taxonomic classes and subclasses. A light curve was obtained and analysed to determine the asteroid spin state. Results. The visible spectrum of 1999 UJ7 exhibits a negative slope in the blue region and the presence of a wide and deep absorption feature centred around ∼0.65 µm. The overall morphology of the spectrum seems to suggest a C-complex taxonomy. The photometric behaviour is fairly complex. The light curve shows a primary period of 1.936 d, but this is derived using only a subset of the photometric data.
    [Show full text]
  • Origin and Evolution of Trojan Asteroids 725
    Marzari et al.: Origin and Evolution of Trojan Asteroids 725 Origin and Evolution of Trojan Asteroids F. Marzari University of Padova, Italy H. Scholl Observatoire de Nice, France C. Murray University of London, England C. Lagerkvist Uppsala Astronomical Observatory, Sweden The regions around the L4 and L5 Lagrangian points of Jupiter are populated by two large swarms of asteroids called the Trojans. They may be as numerous as the main-belt asteroids and their dynamics is peculiar, involving a 1:1 resonance with Jupiter. Their origin probably dates back to the formation of Jupiter: the Trojan precursors were planetesimals orbiting close to the growing planet. Different mechanisms, including the mass growth of Jupiter, collisional diffusion, and gas drag friction, contributed to the capture of planetesimals in stable Trojan orbits before the final dispersal. The subsequent evolution of Trojan asteroids is the outcome of the joint action of different physical processes involving dynamical diffusion and excitation and collisional evolution. As a result, the present population is possibly different in both orbital and size distribution from the primordial one. No other significant population of Trojan aster- oids have been found so far around other planets, apart from six Trojans of Mars, whose origin and evolution are probably very different from the Trojans of Jupiter. 1. INTRODUCTION originate from the collisional disruption and subsequent reaccumulation of larger primordial bodies. As of May 2001, about 1000 asteroids had been classi- A basic understanding of why asteroids can cluster in fied as Jupiter Trojans (http://cfa-www.harvard.edu/cfa/ps/ the orbit of Jupiter was developed more than a century lists/JupiterTrojans.html), some of which had only been ob- before the first Trojan asteroid was discovered.
    [Show full text]
  • Long-Term Orbital and Rotational Motions of Ceres and Vesta T
    A&A 622, A95 (2019) Astronomy https://doi.org/10.1051/0004-6361/201833342 & © ESO 2019 Astrophysics Long-term orbital and rotational motions of Ceres and Vesta T. Vaillant, J. Laskar, N. Rambaux, and M. Gastineau ASD/IMCCE, Observatoire de Paris, PSL Université, Sorbonne Université, 77 avenue Denfert-Rochereau, 75014 Paris, France e-mail: [email protected] Received 2 May 2018 / Accepted 24 July 2018 ABSTRACT Context. The dwarf planet Ceres and the asteroid Vesta have been studied by the Dawn space mission. They are the two heaviest bodies of the main asteroid belt and have different characteristics. Notably, Vesta appears to be dry and inactive with two large basins at its south pole. Ceres is an ice-rich body with signs of cryovolcanic activity. Aims. The aim of this paper is to determine the obliquity variations of Ceres and Vesta and to study their rotational stability. Methods. The orbital and rotational motions have been integrated by symplectic integration. The rotational stability has been studied by integrating secular equations and by computing the diffusion of the precession frequency. Results. The obliquity variations of Ceres over [ 20 : 0] Myr are between 2◦ and 20◦ and the obliquity variations of Vesta are between − 21◦ and 45◦. The two giant impacts suffered by Vesta modified the precession constant and could have put Vesta closer to the resonance with the orbital frequency 2s s . Given the uncertainty on the polar moment of inertia, the present Vesta could be in this resonance 6 − V where the obliquity variations can vary between 17◦ and 48◦.
    [Show full text]
  • 15:1 Resonance Effects on the Orbital Motion of Artificial Satellites
    doi: 10.5028/jatm.2011.03032011 Jorge Kennety S. Formiga* FATEC - College of Technology 15:1 Resonance effects on the São José dos Campos/SP – Brazil [email protected] orbital motion of artificial satellites Rodolpho Vilhena de Moraes Abstract: The motion of an artificial satellite is studied considering Federal University of São Paulo geopotential perturbations and resonances between the frequencies of the São José dos Campos/SP – Brazil mean orbital motion and the Earth rotational motion. The behavior of the [email protected] satellite motion is analyzed in the neighborhood of the resonances 15:1. A suitable sequence of canonical transformations reduces the system of differential equations describing the orbital motion to an integrable kernel. *author for correspondence The phase space of the resulting system is studied taking into account that one resonant angle is fixed. Simulations are presented showing the variations of the semi-major axis of artificial satellites due to the resonance effects. Keywords: Resonance, Artificial satellites, Celestial mechanics. INTRODUCTION some resonance’s region. In our study, it satellites in the neighbourhood of the 15:1 resonance (Fig. 1), or satellites The problem of resonance effects on orbital motion with an orbital period of about 1.6 hours will be considered. of satellites falls under a more categorical problem In our choice, the characteristic of the 356 satellites under in astrodynamics, which is known as the one of zero this condition can be seen in Table 1 (Formiga, 2005). divisors. The influence of resonances on the orbital and translational motion of artificial satellites has been extensively discussed in the literature under several aspects.
    [Show full text]
  • Orbital Resonances and Chaos in the Solar System
    Solar system Formation and Evolution ASP Conference Series, Vol. 149, 1998 D. Lazzaro et al., eds. ORBITAL RESONANCES AND CHAOS IN THE SOLAR SYSTEM Renu Malhotra Lunar and Planetary Institute 3600 Bay Area Blvd, Houston, TX 77058, USA E-mail: [email protected] Abstract. Long term solar system dynamics is a tale of orbital resonance phe- nomena. Orbital resonances can be the source of both instability and long term stability. This lecture provides an overview, with simple models that elucidate our understanding of orbital resonance phenomena. 1. INTRODUCTION The phenomenon of resonance is a familiar one to everybody from childhood. A very young child is delighted in a playground swing when an older companion drives the swing at its natural frequency and rapidly increases the swing amplitude; the older child accomplishes the same on her own without outside assistance by driving the swing at a frequency twice that of its natural frequency. Resonance phenomena in the Solar system are essentially similar – the driving of a dynamical system by a periodic force at a frequency which is a rational multiple of the natural frequency. In fact, there are many mathematical similarities with the playground analogy, including the fact of nonlinearity of the oscillations, which plays a fundamental role in the long term evolution of orbits in the planetary system. But there is also an important difference: in the playground, the child adjusts her driving frequency to remain in tune – hence in resonance – with the natural frequency which changes with the amplitude of the swing. Such self-tuning is sometimes realized in the Solar system; but it is more often and more generally the case that resonances come-and-go.
    [Show full text]
  • The Origin of the High-Inclination Neptune Trojan 2005 TN53 J
    A&A 464, 775–778 (2007) Astronomy DOI: 10.1051/0004-6361:20066297 & c ESO 2007 Astrophysics The origin of the high-inclination Neptune Trojan 2005 TN53 J. Li, L.-Y. Zhou, and Y.-S. Sun Department of Astronomy, Nanjing University, Nanjing 210093, PR China e-mail: [email protected] Received 25 August 2006 / Accepted 20 November 2006 ABSTRACT Aims. We explore the formation and evolution of the highly inclined orbit of Neptune Trojan 2005 TN53. Methods. With numerical simulations, we investigated a possible mechanism for the origin of the high-inclination Neptune Trojans as captured into the Trojan-type orbits by an initially eccentric Neptune during its eccentricity damping and rapid inward migration, then migrating to the present locations locked in Neptune’s 1:1 mean motion resonance. ◦ Results. Two 2005 TN53-type Trojans out of our 2000 test particles were produced with inclinations above 20 , moving on tadpole orbits librating around Neptune’s leading Lagrange point. Key words. methods: numerical – celestial mechanics – minor planets, asteroids – solar system: formation 1. Introduction Table 1. Orbital elements of 2005 TN53 in heliocentric frame referred to the J2000.0 ecliptic plane at epoch 2005 October 7. The uncertainties Trojan asteroids are small objects that share the semimajor axis at the 3 σ level in a, e, i are ± 0.1 AU, ± 0.01, and ± 0.1◦, respectively. of their host planet. They orbit the Sun with the same period as the planet and are said to be settled in the planet’s 1:1 mean mo- a (AU) ei(◦) Ω (◦) ω (◦) M (◦) tion resonance (MMR).
    [Show full text]
  • Long-Term Evolution of the Neptune Trojan 2001 QR322
    Mon. Not. R. Astron. Soc. 347, 833Ð836 (2004) Long-term evolution of the Neptune Trojan 2001 QR322 R. Brasser,1 S. Mikkola,1 T.-Y. Huang,2 P. Wiegert3 and K. Innanen4 1Tuorla Observatory, University of Turku, Piikkio,¬ Finland 2Deptartment of Astronomy, Nanjing University, Nanjing, China 3Astronomy Unit, Queen’s University, Kingston, ON, Canada 4Deptartment of Physics and Astronomy, York University, Toronto, ON, Canada Accepted 2003 October 1. Received 2003 September 9; in original form 2003 April 23 ABSTRACT We simulated more than a hundred possible orbits of the Neptune Trojan 2001 QR322 for the age of the Solar system. The orbits were generated randomly according to the probability density derived from the covariance matrix of the orbital elements. The test trajectories librate ◦ ◦ around Neptune’s L4 point, with amplitudes varying from 40 to 75 and libration periods varying from 8900 to 9300 yr. The ν 18 secular resonance plays an important role. There is a separatrix of the resonance so that the resonant angle switches irregularly between libration and circulation. The orbits are chaotic, with observed Lyapunov times from 1.7 to 20 Myr, approximately. The probability of escape to a non-Trojan orbit in our simulations was low, and only occurred for orbits starting near the low-probability edge of the orbital element distribution (largest values of initial semimajor axis and small eccentricity). This suggests that the Trojan may well be a primordial object. Key words: celestial mechanics Ð minor planets, asteroids Ð Solar system: general. in the element vector q were computed as 1 INTRODUCTION According to the Minor Planet Center, 1571 Trojan asteroids have 6 been discovered.
    [Show full text]
  • Arxiv:1603.07071V1
    Dynamical Evidence for a Late Formation of Saturn’s Moons Matija Cuk´ Carl Sagan Center, SETI Institute, 189 North Bernardo Avenue, Mountain View, CA 94043 [email protected] Luke Dones Southwest Research Institute, Boulder, CO 80302 and David Nesvorn´y Southwest Research Institute, Boulder, CO 80302 Received ; accepted Revised and submitted to The Astrophysical Journal arXiv:1603.07071v1 [astro-ph.EP] 23 Mar 2016 –2– ABSTRACT We explore the past evolution of Saturn’s moons using direct numerical in- tegrations. We find that the past Tethys-Dione 3:2 orbital resonance predicted in standard models likely did not occur, implying that the system is less evolved than previously thought. On the other hand, the orbital inclinations of Tethys, Dione and Rhea suggest that the system did cross the Dione-Rhea 5:3 resonance, which is closely followed by a Tethys-Dione secular resonance. A clear implica- tion is that either the moons are significantly younger than the planet, or that their tidal evolution must be extremely slow (Q > 80, 000). As an extremely slow-evolving system is incompatible with intense tidal heating of Enceladus, we conclude that the moons interior to Titan are not primordial, and we present a plausible scenario for the system’s recent formation. We propose that the mid-sized moons re-accreted from a disk about 100 Myr ago, during which time Titan acquired its significant orbital eccentricity. We speculate that this disk has formed through orbital instability and massive collisions involving the previous generation of Saturn’s mid-sized moons. We identify the solar evection resonance perturbing a pair of mid-sized moons as the most likely trigger of such an insta- bility.
    [Show full text]
  • Modeling the Evection Resonance for Trojan Satellites: Application to the Saturn System C
    A&A 620, A90 (2018) https://doi.org/10.1051/0004-6361/201833735 Astronomy & © ESO 2018 Astrophysics Modeling the evection resonance for Trojan satellites: application to the Saturn system C. A. Giuppone1, F. Roig2, and X. Saad-Olivera2 1 Universidad Nacional de Córdoba, Observatorio Astronómico, IATE, Laprida 854, 5000 Córdoba, Argentina e-mail: [email protected] 2 Observatório Nacional, Rio de Janeiro, 20921-400, RJ, Brazil Received 27 June 2018 / Accepted 6 September 2018 ABSTRACT Context. The stability of satellites in the solar system is affected by the so-called evection resonance. The moons of Saturn, in par- ticular, exhibit a complex dynamical architecture in which co-orbital configurations occur, especially close to the planet where this resonance is present. Aims. We address the dynamics of the evection resonance, with particular focus on the Saturn system, and compare the known behav- ior of the resonance for a single moon with that of a pair of moons in co-orbital Trojan configuration. Methods. We developed an analytic expansion of the averaged Hamiltonian of a Trojan pair of bodies, including the perturbation from a distant massive body. The analysis of the corresponding equilibrium points was restricted to the asymmetric apsidal corotation solution of the co-orbital dynamics. We also performed numerical N-body simulations to construct dynamical maps of the stability of the evection resonance in the Saturn system, and to study the effects of this resonance under the migration of Trojan moons caused by tidal dissipation. Results. The structure of the phase space of the evection resonance for Trojan satellites is similar to that of a single satellite, differing in that the libration centers are displaced from their standard positions by an angle that depends on the periastron difference $2 − $1 and on the mass ratio m2=m1 of the Trojan pair.
    [Show full text]
  • Orbital Resonance and Solar Cycles by P.A.Semi
    Orbital resonance and Solar cycles by P.A.Semi Abstract We show resonance cycles between most planets in Solar System, of differing quality. The most precise resonance - between Earth and Venus, which not only stabilizes orbits of both planets, locks planet Venus rotation in tidal locking, but also affects the Sun: This resonance group (E+V) also influences Sunspot cycles - the position of syzygy between Earth and Venus, when the barycenter of the resonance group most closely approaches the Sun and stops for some time, relative to Jupiter planet, well matches the Sunspot cycle of 11 years, not only for the last 400 years of measured Sunspot cycles, but also in 1000 years of historical record of "severe winters". We show, how cycles in angular momentum of Earth and Venus planets match with the Sunspot cycle and how the main cycle in angular momentum of the whole Solar system (854-year cycle of Jupiter/Saturn) matches with climatologic data, assumed to show connection with Solar output power and insolation. We show the possible connections between E+V events and Solar global p-Mode frequency changes. We futher show angular momentum tables and charts for individual planets, as encoded in DE405 and DE406 ephemerides. We show, that inner planets orbit on heliocentric trajectories whereas outer planets orbit on barycentric trajectories. We further TRY to show, how planet positions influence individual Sunspot groups, in SOHO and GONG data... [This work is pending...] Orbital resonance Earth and Venus The most precise orbital resonance is between Earth and Venus planets. These planets meet 5 times during 8 Earth years and during 13 Venus years.
    [Show full text]
  • Martian Moon's Orbit Hints at an Ancient Ring of Mars
    Martian Moon’s Orbit Hints at an Ancient Ring of Mars PRESS RELEASE DATE June 2, 2020 CONTACT Rebecca McDonald Director of Communications SETI Institute [email protected] +1 650-960-4526 Photo credit: https://solarsystem.nasa.gov/moons/mars-moons/deimos/in-depth/ June 2, 2020, Mountain View, CA – Scientists from the SETI Institute and Purdue University have found that the only way to produce Deimos’s unusually tilted orbit is for Mars to have had a ring billions of years ago. While some of the more massive planets in our solar system have giant rings and numerous big moons, Mars only has two small, misshapen moons, Phobos and Deimos. Although these moons are small, their peculiar orbits hide important secrets about their past. For a long time, scientists believed that Mars’s two moons, discovered in 1877, were captured asteroids. However, since their orbits are almost in the same plane as Mars’s equator, that the moons must have formed at the same time as Mars. But the orbit of the smaller, more distant moon Deimos is tilted by two degrees. “The fact that Deimos’s orbit is not exactly in plane with Mars’s equator was considered unimportant, and nobody cared to try to explain it,” says lead author Matija Ćuk, a research scientist at the SETI Institute. “But once we had a big new idea and we looked at it with new eyes, Deimos’s orbital tilt revealed its big secret.” This significant new idea was put forward in 2017 byĆ uk’s co-author David Minton, professor at Purdue University and his then-graduate student Andrew Hesselbrock.
    [Show full text]