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 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.

scholarly journals The relationship between the `limiting' Yarkovsky drift speed and asteroid families' Yarkovsky V-shape

2020 ◽  
pp. 25-41
Author(s):  
I. Milic-Zitnik
Keyword(s):  
Interesting Property ◽  
Parent Body ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Drift Speed ◽  
Yarkovsky Effect ◽  
The Mean ◽  
The Relationship ◽  
Asteroid Families

The Yarkovsky effect is an important force to consider in order to understand the long-term dynamics of asteroids. This non-gravitational force affects the orbital elements of objects revolving around a source of heat, especially their semi-major axes. Following the recently defined `limiting' value of the Yarkovsky drift speed at 7x10-5 au/Myr in Milic Zitnik (2019) (below this value of speed asteroids typically jump quickly across the mean motion resonances), we decided to investigate the relation between the asteroid family Yarkovsky V-shape and the `limiting' Yarkovsky drift speed of asteroid's semi-major axes. We have used the known scaling formula to calculate the Yarkovsky drift speed (Spoto et al. 2015) in order to determine the inner and outer `limiting' diameters (for the inner and outer V-shape borders) from the `limiting' Yarkovsky drift speed. The method was applied to 11 asteroid families of different taxonomic classes, origin type and age, located throughout the Main Belt. Here, we present the results of our calculation on relationship between asteroid families' V-shapes (crossed by strong and/or weak mean motion resonances) and the `limiting' diameters in the (a, 1=D) plane. Our main conclusion is that the `breakpoints' in changing V-shape of the very old asteroid families, crossed by relatively strong mean motion resonances on both sides very close to the parent body, are exactly the inverse of `limiting' diameters in the a versus 1=D plane. This result uncovers a novel interesting property of asteroid families' Yarkovsky V-shapes.

scholarly journals The functional relation between mean motion resonances and Yarkovsky force on small eccentricities

2020 ◽  
Vol 498 (3) ◽  
pp. 4465-4471
Author(s):  
I Milić Žitnik
Keyword(s):  
Time Delays ◽  
Semimajor Axis ◽  
Functional Relation ◽  
Orbital Eccentricity ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Drift Speed ◽  
Yarkovsky Effect ◽  
Numerical Integrations ◽  
Time Lead

ABSTRACT This work examines asteroid’s motion with orbital eccentricity in the range (0.1, 0.2) across the two-body mean motion resonance (MMR) with Jupiter due to the Yarkovsky effect. We calculated time delays dtr caused by the resonance on the mobility of an asteroid with the Yarkovsky drift speed. Our final results considered only asteroids that successfully cross over the resonance without close encounters with planets. We found a functional relation that accurately describes dependence between the average time lead/lag 〈dtr〉, the strength of the resonance SR, and the semimajor axis drift speed da/dt with asteroids’ orbital eccentricities in the range (0.1, 0.2). We analysed average values of 〈dtr〉 using this functional relation comparing with obtained values of 〈dtr〉 from the numerical integrations, which were performed in an ORBIT9 integrator with a very large number of test asteroids. We checked the validity of our previous functional relation, derived for asteroids’ orbital eccentricities in the range (0, 0.1), on the present results for eccentricities in the range (0.1, 0.2). Also, we tried to find a unique functional relation for the whole interested interval of asteroids’ orbital eccentricities (0, 0.2) and discussed it.

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 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 Survey of asteroids in retrograde mean motion resonances with planets

2019 ◽  
Vol 630 ◽  
pp. A60 ◽  
Author(s):  
Miao Li ◽  
Yukun Huang ◽  
Shengping Gong
Keyword(s):  
Solar System ◽  
Integration Time ◽  
Potential Candidate ◽  
Resonant Condition ◽  
Mean Motion Resonances ◽  
Orbital Resonance ◽  
Mean Motion ◽  
Resonant Dynamics ◽  
Orbital Resonances

Aims. Asteroids in mean motion resonances (MMRs) with planets are common in the solar system. In recent years, increasingly more retrograde asteroids are discovered, several of which are identified to be in resonances with planets. We here systematically present the retrograde resonant configurations where all the asteroids are trapped with any of the eight planets and evaluate their resonant condition. We also discuss a possible production mechanism of retrograde centaurs and dynamical lifetimes of all the retrograde asteroids. Methods. We numerically integrated a swarm of clones (ten clones for each object) of all the retrograde asteroids (condition code U < 7) from −10 000 to 100 000 yr, using the MERCURY package in the model of solar system. We considered all of the p/−q resonances with eight planets where the positive integers p and q were both smaller than 16. In total, 143 retrograde resonant configurations were taken into consideration. The integration time was further extended to analyze their dynamical lifetimes and evolutions. Results. We present all the meaningful retrograde resonant configurations where p and q are both smaller than 16 are presented. Thirty-eight asteroids are found to be trapped in 50 retrograde mean motion resonances (RMMRs) with planets. Our results confirm that RMMRs with giant planets are common in retrograde asteroids. Of these, 15 asteroids are currently in retrograde resonances with planets, and 30 asteroids will be captured in 35 retrograde resonant configurations. Some particular resonant configurations such as polar resonances and co-orbital resonances are also identified. For example, Centaur 2005 TJ50 may be the first potential candidate to be currently in polar retrograde co-orbital resonance with Saturn. Moreover, 2016 FH13 is likely the first identified asteroid that will be captured in polar retrograde resonance with Uranus. Our results provide many candidates for the research of retrograde resonant dynamics and resonance capture. Dynamical lifetimes of retrograde asteroids are investigated by long-term integrations, and only ten objects survived longer than 10 Myr. We confirmed that the near-polar trans-Neptunian objects 2011 KT19 and 2008 KV42 have the longest dynamical lifetimes of the discovered retrograde asteroids. In our long-term simulations, the orbits of 12 centaurs can flip from retrograde to prograde state and back again. This flipping mechanism might be a possible explanation of the origins of retrograde centaurs. Generally, our results are also helpful for understanding the dynamical evolutions of small bodies in the solar system.

Sign in / Sign up

Export Citation Format

Share Document