Mainbelt Asteroids

AS3141 Benda Kecil dalam Tata SuryaProdi Astronomi 2007/2008

B. Dermawan

Solar System Formation (1)

• Early stages (a-d)• A lot of steps between d and e• Protoplanetary disk is hot near the Sun

and cold far from the Sun, condensation of gas depending on temperature

• Formation and growth of planetesimals (strongly dependent on relative velocity)

• Formation of terrestrial and giant planets

• Early Jupiter prevents planetesimals growth in its neighborhood origin of asteroids

Solar System Formation (2)

• Comets originate in the Kuiper-belt at about 40 AU from the Sun

• Long-period comets are scattered into Oort cloud, disturbed and isotropized by the influence of passing stars and the galactic bulge

• Short-period comets go directly from Kuiper-belt to the inner solar system

• Meteorites come from the surfaces of asteroids and from Mars to the Earth. Their measurements in the laboratory has contributed greatly to our knowledge about solar system formation

Discoveries & Numbering

• Main Belt (Ceres 1801 dwarf planet 2006)• Near-Earth Objects (Eros 1898)• Trojans (Achilles 1906)• Cometary (Hidalgo 1920)• Centaurs (Chiron 1977)

• Trans-Neptunians (Pluto 1930; 1992 QB1 1992)

• Minor planet numbers: (100) in 1868; (1000) in 1923; (10000) in 1999; (100000) in 2005• 25 Oct 07 numbered: 168313, total: 387205

Topics

Orbits and their evolution Asteroid families Asteroid’s Size Distribution & Collision Mainbelt resonances

Orbits & Their Evolution

• The vast majority of the asteroids depicted are in the main asteroid belt

• Trojans are shown leading and trailing the position of Jupiter

• Aten, Apollo, and Amor asteroids are seen in the inner solar system, crossing the orbits of Mars and Earth

Orbits & Their Evolution

Main-belt between 2.1 and 3.3 AU Kirkwood gaps coincide with resonance locations

relative to Jupiter, which may be unstable or stable At inner edge of asteroid belt 6 resonance with

Saturn’s apse rate ~2300 asteroids occupy Jupiter L4 (1242) and L5

(1048) triangular lagrangian points (Trojans), Martian Trojans (1,3), Saturnian Trojans (6,0)

[13 Nov 07] Unstable orbits: Amors (1.017 < q < 1.3), Apollos

(q < 1.017, a > 1), Atens (a < 1), all small objects

Orbital Elements Time of perihelion

passage, T Semimajor axis, a Eccentricity, e Inclination, i Argument of perihelion, Longitude of ascending

node, ω

Ascending node

Ω Osculating elements and

their epoch Periodic and secular

perturbations

Proper Elements

Over time spans of ~105 yr a remains on the average constant e and i show periodic oscillations, coupled to

variations of and , respectively (ep,ip) are proper elements

Histograms 25 Oct 2007

SDSS Colors of MBAsIvezić et al. 2002

a* 0.89(g-r) + 0.45(r-i) – 0.57

Asteroid FamiliesSDSS, Ivezić et al. 2002

Osculating & Proper Orbital Elements

Observed at a particular epoch. Not constant in time caused by gravitational perturbations

Practically constant over tens to hundreds of million of years

a detailed calculation

Asteroid Family

Objects (fragments) obtained from disruption of a common parent body in a catastrophic collision

~35 % of asteroids in the main-belt are family members

Identification:Identification:• Get some knowledge about the collisional evolution Get some knowledge about the collisional evolution

in the Main-beltin the Main-belt• Obtain information about the internal structure of the Obtain information about the internal structure of the

parent bodyparent body

Satisfactory Methods

Hierarchical Clustering Method (HCM) (Zappala et al. 1990, 1995) Wavelet Analysis Method (WAM) (Bendjoya et al. 1993, 1997)

Both methods:• Imply ‘heavy’ computational time;• Require ad-hoc parameters or threshold

definitions

Decomposition

Families

Nesvorný et al. 2005

Background Asteroids

Terminologies

Cluster: the most prominent groupingClumps: few members but clearly distinct from the

backgroundClans: merge very gradually into the background

density (complex group)Tribes: less statistically significant against the

background Interlopers: temporarily resides in a family/cluster

Families among MBAs

Families are indicative of collisional process between asteroids aa [au] [au]

sin

sin

ii

0

0.1

0.2

0.3

2.2 2.4 2.6 2.8 3.0 3.2

NysaNysa

VestaVesta

PolanaPolana

CeresCeres

MariaMaria

DoraDora

MassaliaMassalia

AdeonaAdeona

LydiaLydia

ErigoneErigone

LiberatrixLiberatrix

MisaMisa

MerxiaMerxia

VeritasVeritas

AugustaAugusta

RafitaRafita

ChlorisChloris

HenanHenan

NemesisNemesis

ReginitaReginita

NocturnaNocturna

MeliboeaMeliboea

BrasiliaBrasiliaFainaFainaTunicaTunica

JeromeJerome

HestiaHestia

AstridAstrid

BowerBower

TaiyuanTaiyuan

HankoHanko

JunoJuno

HygieaHygiea

VincentinaVincentina

KilopiKilopi

SulamitisSulamitisSimpsonSimpson

AeoliaAeolia

AstaAsta

VibiliaVibilia

TheobaldaTheobalda

CeplechaCeplechaBernesBernes

NaemaNaemaNeleNele

49454945

TsurugistanTsurugistan

LaodicaLaodicaDejaniraDejanira

HoffmeisterHoffmeisterAmnerisAmneris

FloraFlora

ThemisThemis

EunomiaEunomia

KoronisKoronis

EosEos

1981 EO191981 EO19

19811981EO82EO82

1981 UC11981 UC1

1965 SB1965 SB

1985 RU11985 RU1

KarinKarin

The Age of Asteroid Family Craters counting + production rate (rare visits + unknown constrained factors) Track the orbital evolution of the family members backwards

in time (limited to families < 10 Myr) Compare the evolution model of the size freq. distribution with

observations (poorly unknown some parameters) Deduce from the spin axis distribution of a family (certain special circumstances) Calculate the dispersing time via Yarkovsky thermal forces (unknown initial ejection velocities)

Asteroid Families

Nesvorný et al. 2005

Young Asteroid Families

293 Brasilia 80 95 C/X ~50

606 Brangane 30 30 S ~50

Nesvorný et al. 2003

Nesvorný et al. 2005

Size Distribution & Collisional Evolution

N(R) = N0(R/R0)-, for Rmin < R < Rmax

A population of evolving bodies will at the end arrive at a power law size distribution with = 3.5, provided the collision process is self-similar

= 3.5 implies that most of the mass is in the largest body and most of the surface area in the smallest bodies

Collision:Vesc from Ceres = 0.6 km s-1. Thus, most collisions

are eruptive or destructiveFamilies with similar a, e, and iDust bands

Asteroid Collision (1)

• Distance traveled in time T: V×T• Volume cut out by the target area: R2×VT• Number of collisions: N = R2VT×n• Average time between collisions:

VnRt

2

1

Asteroid Collision (2)

Typical relative velocity: V 5 km/s Estimate the Main Belt volume by a donut at

2.5 AU from the Sun with a cross-sectional radius = 0.55 AU volume ~ 51025 km3

Total number of asteroids larger than a given radius R:

R > 1 km ~ 5105

R > 10 km ~ 2103

R > 100 km ~ 35

Size Distribution

Nine estimates

Davis et al. 2002

Size Dist. of MBA Families

Shallower slopes than the background

Morbidelli et al. 2003

Resonance: General Types

Spin-orbit resonance: a commensurability of the rotation period of a satellite with the period of its orbital revolution

Secular resonance: a commensurability of the frequencies of precession of the orientation of orbits (direction of perihelion and of the orbit normal)

Mean motion resonance: the orbital periods of two bodies are close to a ratio of small integers

Spin-orbit Resonance (1)

o Ex: spin-locked state of the Moon, most natural satellites (Pluto-Charon, Saturn-Titan), binary stellar systems

o 1:1 spin-orbit resonance (synchronous spin state)o For a non-spherically shaped satellite (principal moment

of inertia: A < B < C, is the orientation relative to the direction of periapse of the orbit, f = f(t) is the true anomaly, and r = r(t) is the distance from the planet), equation of motion (e.o.m):

C

ABf

r

GM

2

)(3 ;2cos

3

Spin-orbit Resonance (2)

Rotational symmetry (B = C): no torque from the planet and the satellite’s spin in unperturbed

If B C and the orbit is circular, e.o.m is similar to that of the common pendulum

The width of the 1:1 spin-orbit resonance (n is the orbital mean motion) is

n 22Δ

Spin-orbit Resonance (3)

Case when the orbit is non-circular and small eccentricity

2212 2sin72sin2sin entntentn

Two new terms corresponding to the 1:2 and the 3:2 spin-orbit resonances

The width of the 3:2 spin-orbit resonance is a factor (7e/2) smaller than the 1:1

Ex.: the 3:2 spin orbit resonance of Mercury (88d:59d)

Orbital Resonances (1)

Three degrees of freedom: three angular variables [1] the motion of the planet: the frequency revolution

around the Sun,

[2] orientation of the orbit in space: the slow frequencies of precession of the direction of perihelion and the pole of the orbit plane

For a multi-planet system: secular resonances involves commensurabilities amongst [2]; mean motion resonances are commensurabilities of [1]

Orbital Resonances (2) Most cases: a clear separation of [1] & [2] time

scales A coupling between [1] & [2] chaotic dynamics The boundaries (or separatrices) of mean

resonances are often the site for such interactions between secular and mean motion resonances

Ex. of “hybrid” resonance (a commensurability of a secular precession frequency with an orbital mean motion): the angular velocity of the apsidal precession rate of a ringlet within the C-ring of Saturn is commensurate with the orbital mean motion of Titan the Titan 1:0 apsidal resonance

Mean Motion Resonance (MMR)

First order resonance

Second order resonance

21

32

~/Δ enn

21

2 ~/Δ enn

Malhotra 1998

MMR (2)

o Mean motion commensurabilities amongst the Jovian and Saturnian satellites

o No exact resonance in the Uranian satellites system

o The role of the small but significant splitting of MMR and the interaction of neighboring resonances

o Destabilize a previously established resonance MMR lifetimes

MMR (3): Stability

Stable

Unstable

Nesvorný et al. 2002

MMR (4): chaotic diffusion

2J:1 & 3J:1 MMR

MMR (5): MBAs global structure• Overlapping MMR causes chaotic orbits• “Stable chaos”: have strongly chaotic orbits yet are

stable on long interval time (three-body resonances)

Nesvorný et al. 2002

MMR (6): MBAs global structure

Each resonance corresponds to one V-shaped region except the large first-order MMRs with Jupiter

Nesvorný et al. 2002

Secular Resonances (1)

• A planetary precessing ellipse of fixed semimajor axis, ap, eccentricity, ep, and precession rate pp g

• g0 is proportional to the mass of the perturbing planet and is also a function of the orbital semimajor axis of the particle relative to that of the planet

• Secular resonance occurs when g0 equals gp

• Effect: to amplify the orbital eccentricity of the particle

Secular Resonances (2)

Specific secular resonance: “Kozai resonance”, or “Kozai mechanism”

1:1 commensurability of the secular precession rates of the perihelion and the orbit normal such that the argument of perihelion is stationary (or librates)

Requires significant orbital eccentricity and inclination (causes coupled oscillations)

Well known ex.: Pluto whose argument of perihelion librates about 90 deg.

Secular Resonances (3)

Empty zones along resonant surfaces

Isolation of groups (Hungaria, Phocaea)

Carruba & Michtchenko 2007

New Result (Carruba & Michtchenko 2007)

Identifying families: Frequency approach

New Result (Carruba & Michtchenko 2007)

Eos

Koronis