scholarly journals Four-billion year stability of the Earth–Mars belt

2020 ◽  
Vol 500 (1) ◽  
pp. 1151-1157
Author(s):  
Yukun Huang (黄宇坤) ◽  
Brett Gladman
Keyword(s):  
Semimajor Axis ◽  
Orbital Stability ◽  
Terrestrial Planet ◽  
Small Bodies ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
The Earth ◽  
Steady State Model ◽  
Near Earth Objects

ABSTRACT Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the ‘Earth–Mars belt’ from 1.08 < a < 1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04–1.30 au for the age of the Solar system. We show that on this time-scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower ‘Earth–Mars belt’ covering a ∼ (1.09, 1.17) au, e < 0.04, and I < 1° has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the ν3, ν4, and ν6 secular resonances contribute to long-term instability in the outer (1.17–1.30 au) region on Gyr time-scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth–Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the <200 m scale of these NEOs, we estimated the Yarkovsky drift rates in semimajor axis and use these to estimate that a diameter of ∼100 km or larger would allow primordial asteroids in the Earth–Mars belt to likely survive. We conclude that only a few 100-km sized asteroids could have been present in the belt’s region at the end of the terrestrial planet formation.

Primordial Stability of the Earth–Mars Belt

2020 ◽  
Author(s):  
Yukun Huang ◽  
Brett Gladman
Keyword(s):  
Semimajor Axis ◽  
Orbital Stability ◽  
Terrestrial Planet ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Yarkovsky Effect ◽  
The Earth ◽  
Steady State Model ◽  
Near Earth Objects

<p>Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the 'Earth–Mars belt' from 1.08 au<a<1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04–1.30 au for the age of the Solar system. We show that on this time scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower 'Earth–Mars belt' covering a∼(1.09,1.17) au, e<0.04, and I<1◦ has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the ν3, ν4, and ν6 secular resonances contribute to long-term instability in the outer (1.17–1.30 au) region on Gyr time scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth–Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the <200m scale of these NEOs, we estimated the Yarkovsky effect drift rates in semimajor axis, and use these to estimate that a diameter of ∼100km or larger would allow primordial asteroids in the Earth–Mars belt to likely survive. We conclude that only a few 100 km scale asteroids could have been present in the belt’s region at the end of the terrestrial planet formation.</p>

scholarly journals Forming terrestrial planets and delivering water

2015 ◽  
Vol 11 (A29B) ◽  
pp. 427-430
Author(s):  
Kevin J. Walsh
Keyword(s):  
Planet Formation ◽  
Semimajor Axis ◽  
Giant Planet ◽  
Terrestrial Planet ◽  
Giant Planets ◽  
Asteroid Belt ◽  
Terrestrial Planets ◽  
The Earth ◽  
Building Models ◽  
Rich Material

AbstractBuilding models capable of successfully matching the Terrestrial Planet's basic orbital and physical properties has proven difficult. Meanwhile, improved estimates of the nature of water-rich material accreted by the Earth, along with the timing of its delivery, have added even more constraints for models to match. While the outer Asteroid Belt seemingly provides a source for water-rich planetesimals, models that delivered enough of them to the still-forming Terrestrial Planets typically failed on other basic constraints - such as the mass of Mars.Recent models of Terrestrial Planet Formation have explored how the gas-driven migration of the Giant Planets can solve long-standing issues with the Earth/Mars size ratio. This model is forced to reproduce the orbital and taxonomic distribution of bodies in the Asteroid Belt from a much wider range of semimajor axis than previously considered. In doing so, it also provides a mechanism to feed planetesimals from between and beyond the Giant Planet formation region to the still-forming Terrestrial Planets.

scholarly journals The orbital stability of planets trapped in the first-order mean-motion resonances

Icarus ◽  
2012 ◽  
Vol 221 (2) ◽  
pp. 624-631 ◽  
Author(s):  
Yuji Matsumoto ◽  
Makiko Nagasawa ◽  
Shigeru Ida
Keyword(s):  
Orbital Stability ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion

scholarly journals Formation of terrestrial planets from planetesimals around M dwarfs

2007 ◽  
Vol 3 (S249) ◽  
pp. 305-308
Author(s):  
Masahiro Ogihara ◽  
Shigeru Ida
Keyword(s):  
Terrestrial Planet ◽  
Terrestrial Planets ◽  
Type I ◽  
M Dwarfs ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Habitable Zones ◽  
Pile Up ◽  
Solar Type ◽  
Water Contents

AbstractWe have investigated accretion of terrestrial planets from planetesimals around M dwarfs through N-body simulations including the effect of tidal interaction with disk gas. Because of low luminosity of M dwarfs, habitable zones around them are located near the disk inner edge. Planetary embryos undergo type-I migration and pile up near the disk inner edge. We found that after repeated close scatterings and occasional collisions, three or four planets eventually remain in stable orbits in their mean motion resonances. Furthermore, large amount of water-rich planetesimals rapidly migrate to the terrestrial planet regions from outside of the snow line, so that formed planets in these regions have much more water contents than those around solar-type stars.

scholarly journals Design and ballistic analysis of the mission for long-term study of the asteroid Apophis by a nanosatellite with an electric rocket propulsion system

2020 ◽  
Vol 4 (3) ◽  
pp. 161-170
Author(s):  
O. L. Starinova ◽  
E. A. Sergaeva ◽  
A. Yu. Shornikov
Keyword(s):  
Propulsion System ◽  
Gravitational Attraction ◽  
Term Study ◽  
Small Bodies ◽  
Rocket Propulsion ◽  
Gravitational Fields ◽  
Optimal Speed ◽  
Long Term Study ◽  
The Earth

The paper considers non-spherical objects with low gravitational attraction, such as asteroids, satellites of the planet and comets. We considered possibility of a mission to small bodies of the solar system of irregular shape on the example of the asteroid Apophis. The authors of the article suggest using a nanoclass spacecraft with an electric rocket propulsion system for a long mission to study Apophis. The purpose of this work is to determine the necessary costs of the working body for all stages of the mission, which includes reaching the asteroid, forming and maintaining a given orbit relative to it. The gravity of the Earth, Sun, and asteroid is taken into account when modeling the controlled movement of the spacecraft. When a spacecraft is moving relative to an asteroid, its gravitational field is described as a superposition of the gravitational fields of two rotating massive points. In this paper, it is proposed to divide the mission into two sections for preliminary ballistic design. The first optimal speed heliocentric flight Earth-asteroid Apophis with the alignment of the speed of the spacecraft and the asteroid. The second is the movement in the vicinity of the asteroid, which includes the optimal speed maneuver for forming the working orbit and maintaining the working orbit for a given time.

scholarly journals Strategy for NEO follow-up observations

2012 ◽  
Vol 10 (H16) ◽  
pp. 185-185
Author(s):  
Milos Tichy ◽  
Michaela Honkova ◽  
Jana Ticha ◽  
Michal Kocer
Keyword(s):  
Small Bodies ◽  
Time Uncertainty ◽  
The Earth ◽  
Observation Strategy ◽  
On Line ◽  
Single Night ◽  
Uncertainty Map ◽  
The Impact ◽  
Near Earth Objects

AbstractThe Near-Earth Objects (NEOs) belong to the most important small bodies in the solar system, having the capability of close approaches to the Earth and even possibility to collide with the Earth. In fact, it is impossible to calculate reliable orbit of an object from a single night observations. Therefore it is necessary to extend astrometry dataset by early follow-up astrometry. Follow-up observations of the newly discovered NEO candidate should be done over an arc of several hours after the discovery and should be repeated over several following nights. The basic service used for planning of the follow-up observations is the NEO Confirmation Page (NEOCP) maintained by the Minor Planet Center of the IAU. This service provides on-line tool for calculating geocentric and topocentic ephemerides and sky-plane uncertainty maps of these objects at the specific date and time. Uncertainty map is one of the most important information used for planning of follow-up observation strategy for given time, indicating also the estimated distance of the newly discovered object and including possibility of the impact. Moreover, observatories dealing with NEO follow-up regularly have prepared their special tools and systems for follow-up work. The system and strategy for the NEO follow-up observation used at the Klet Observatory are described here. Methods and techniques used at the Klet NEO follow-up CCD astrometric programme, using 1.06-m and 0.57-m telescopes, are also discussed.

scholarly journals A first analysis of the mean motion of CHAMP

2003 ◽  
Vol 1 ◽  
pp. 95-101
Author(s):  
F. Deleflie ◽  
P. Exertier ◽  
P. Berio ◽  
G. Metris ◽  
O. Laurain ◽  
...  
Keyword(s):  
Orbital Motion ◽  
Surface Forces ◽  
The Moon ◽  
Orbital Elements ◽  
Champ Satellite ◽  
Mean Motion ◽  
The Earth ◽  
The Mean ◽  
Low Altitude

Abstract. The present study consists in studying the mean orbital motion of the CHAMP satellite, through a single long arc on a period of time of 200 days in 2001. We actually investigate the sensibility of its mean motion to its accelerometric data, as measures of the surface forces, over that period. In order to accurately determine the mean motion of CHAMP, we use “observed" mean orbital elements computed, by filtering, from 1-day GPS orbits. On the other hand, we use a semi-analytical model to compute the arc. It consists in numerically integrating the effects of the mean potentials (due to the Earth and the Moon and Sun), and the effects of mean surfaces forces acting on the satellite. These later are, in case of CHAMP, provided by an averaging of the Gauss system of equations. Results of the fit of the long arc give a relative sensibility of about 10-3, although our gravitational mean model is not well suited to describe very low altitude orbits. This technique, which is purely dynamical, enables us to control the decreasing of the trajectory altitude, as a possibility to validate accelerometric data on a long term basis.Key words. Mean orbital motion, accelerometric data

The functional relation between three-body mean motion resonances and Yarkovsky drift speeds

2021 ◽  
Vol 507 (4) ◽  
pp. 5796-5803
Author(s):  
I Milić Žitnik
Keyword(s):  
Time Delays ◽  
Semimajor Axis ◽  
Functional Relation ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Drift Speed ◽  
Functional Relations ◽  
Numerical Integrations ◽  
Three Body ◽  
Good Agreement

ABSTRACT We examined the motion of asteroids across the three-body mean motion resonances (MMRs) with Jupiter and Saturn and with the Yarkovsky drift speed in the semimajor axis of the asteroids. The research was conducted using numerical integrations performed using the Orbit9 integrator with 84 000 test asteroids. We calculated time delays, dtr, caused by the seven three-body MMRs on the mobility of test asteroids with 10 positive and 10 negative Yarkovsky drift speeds, which are reliable for Main Belt asteroids. Our final results considered only test asteroids that successfully crossed over the MMRs without close approaches to the planets. We have devised two equations that approximately describe the functional relation between the average time 〈dtr〉 spent in the resonance, the strength of the resonance SR, and the semimajor axis drift speed da/dt (positive and negative) with the orbital eccentricities of asteroids in the range (0, 0.1). Comparing the values of 〈dtr〉 obtained from the numerical integrations and from the derived functional relations, we analysed average values of 〈dtr〉 in all three-body MMRs for every da/dt. The main conclusion is that the analytical and numerical estimates of the average time 〈dtr〉 are in very good agreement, for both positive and negative da/dt. Finally, this study shows that the functional relation we obtain for three-body MMRs is analogous to that previously obtained for two-body MMRs.

scholarly journals Probing the interior of asteroid Apophis: a unique opportunity in 2029

2012 ◽  
Vol 10 (H16) ◽  
pp. 481-482
Author(s):  
Patrick Michel ◽  
J. Y. Prado ◽  
M. A. Barucci ◽  
O. Groussin ◽  
A. Hérique ◽  
...  
Keyword(s):  
Close Approach ◽  
Small Bodies ◽  
The Earth ◽  
Space Agency ◽  
Fundamental Information ◽  
Different Populations ◽  
Access Information ◽  
Scientific Value ◽  
Near Earth Objects

AbstractThe near Earth asteroid (99942) Apophis, discovered in 2004, (with a diameter of about 270 meters) will come back very close to the Earth on April 13, 2029.The close approach of Apophis to the Earth in 2029 will present an unique opportunity for characterizing this object, serving both science and mitigation purposes. The object will be easily visible from the Earth and it can be expected that its shape and thermal properties will be well determined from ground based observations. However, the characterization of its interior will not be achievable from purely terrestrial observations. Such a characterization, beyond its high scientific value, is essential for planning any mitigation operation, should it be necessary in the future.Near Earth objects are a precious source of information as they represent a mixture of different populations of small bodies containing fundamental information on the origin and early evolution of the solar system.Monitoring the response of Apophis to the gravitational constraints induced by its close approach to the Earth may provide a way to access information on its internal structure.A study to identify some affordable mission scenarii for such a mission is presently underway at CNES (the French Space Agency).We will present the scientific and mitigation objectives of such a mission as well as the preliminary results of the mission analysis and the main system characteristics.

scholarly journals N-body simulations of terrestrial planet growth with resonant dynamical friction

2019 ◽  
Vol 489 (2) ◽  
pp. 2159-2176 ◽  
Author(s):  
Spencer C Wallace ◽  
Thomas R Quinn
Keyword(s):  
Mass Distribution ◽  
Surface Density ◽  
Terrestrial Planet ◽  
Asteroid Belt ◽  
Dynamical Friction ◽  
Intermediate Mass ◽  
Small Bodies ◽  
Mean Motion Resonances ◽  
Growth Modes ◽  
Planetary Embryo

ABSTRACT We investigate planetesimal accretion via a direct N-body simulation of an annulus at 1 au orbiting a 1 M$\odot$ star. The planetesimal ring, which initially contains N = 106 bodies is evolved into the oligarchic growth phase. Unlike previous lower resolution studies, we find that the mass distribution of planetesimals develops a bump at intermediate mass after the oligarchs form. This feature marks a boundary between growth modes. The smallest planetesimals are packed tightly enough together to populate mean motion resonances with the oligarchs, which heats the small bodies, enhancing their growth. If we depopulate most of the resonances by decreasing the width of the annulus, this effect becomes weaker. To clearly demonstrate the dynamics driving these growth modes, we also examine the evolution of a planetary embryo embedded in an annulus of collisionless planetesimals. In this case, we find that the resonances push planetesimals away from the embryo, decreasing the surface density of the bodies adjacent to the embryo. This effect only occurs when the annulus is wide enough and the mass resolution of the planetesimals is fine enough to populate the resonances. The bump we observe in the mass distribution resembles the 100 km power-law break seen in the size distribution of asteroid belt objects. Although the bump produced in our simulations occurs at a size larger than 100 km, we show that the bump location is sensitive to the initial planetesimal mass, which implies that this feature is potentially useful for constraining planetesimal formation models.

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