Design of a Locomotive Engine for Dalian Locomotive

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Pairs of asteroids probably of common origin
David Vokrouhlický David Nesvorný Plan of
the talk a) classical asteroid families (3D
clustering) b)
very young asteroid families (5D clustering)
c) asteroid pairs -
even younger families? or objects
that underwent other types of
catastrophic dissociations? d) further
observations needed to resolve that
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Proper Orbital Elements of Asteroids
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Characteristic Orbital Evolution in the MB
Example (32) Pomona osculating orbital
elements a2.59 AU, e0.083, I5.53 deg
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Characteristic Orbital Evolution in the MB
Example (32) Pomona osculating orbital
elements a2.59 AU, e0.083, I5.53 deg

• ep

• ?p

• Osculating elements

• Proper elements

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Asteroid Families classical
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Asteroid Families classical (historical
excursion)

• K. Hirayama, AJ 31, 185 (1918)

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Asteroid Families Identification technique
(ka5/4, keki2, of the order of unity)
An example Koronis family as a cluster of
objects within a distance d lt 70 m/s from
each other
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Asteroid Families Koronis Karin

• Family in (a,e) is nearly cut in two near 2.92
  AU.
• Both sides of family are bracketed by powerful
  mean motion resonances (52 and 73 MMR with
  Jupiter).
• Family members do not appear to have crossed
  these resonances.
• No substantial contributions of family members in
  both (a,e) and (a,i) can be seen on the left side
  of 52 or right side of 73.

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Asteroid Families Koronis Karin (cntd.)
Koronis family (2.5Gy old) harbors Karin family
(5.8 My old) as a result of a secondary
fragmentation
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Asteroid Families very young ones
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Asteroid Families very young ones (cntd.)
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Asteroid Families very young ones (cntd.)
We searched for asteroid mini-clusters in AstOrb
catalogue of osculating orbital elements using
metrics We found 4 new very young and compact
clusters about (1270) Datura, (14627)
Emilkowalski, (16598) 1992 YC2 and (21509)
Lucascavin.
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Asteroid Families very young ones (cntd.)

• We integrated backwards 840 clones of
• each asteroid
• 20 from the orbital uncertainty interval
• 41 Yarkovsky clones
• Picking 107 of their combinations we
• found past epochs for which
• is smaller than 5 m/s (k11, k21/2).
• This lead us to determine that
• Datura cluster is 450?50 ky old.

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Asteroid Families on a track to even younger
ones
We repeated the AstOrb search for close clusters
relaxing now the condition of 3 members at
least As a result we noted a peculiar
behavior of the cumulative distribution
function N(ltd) for pairs of asteroids.
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Asteroid Families on a track to even younger
ones

• We repeated the AstOrb search for close
• clusters relaxing now the condition of 3
• members at least
• As a result we noted a peculiar behavior
• of the cumulative distribution function
• N(ltd) for pairs of asteroids.
• N(ltd) da
• small d values a 1,
• intermediate d values a 2,
• large d values a 5.

5
2
1
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Asteroid Families on a track to even younger
ones

• We repeated the AstOrb search for close
• clusters relaxing now the condition of 3
• members at least
• As a result we noted a peculiar behavior
• of the cumulative distribution function
• N(ltd) for pairs of asteroids.
• N(ltd) da
• small d values a 1,
• intermediate d values a 2,
• large d values a 5.

2
1
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Asteroid Families on a track to even younger
ones

• We repeated the AstOrb search for close
• clusters relaxing now the condition of 3
• members at least
• As a result we noted a peculiar behavior
• of the cumulative distribution function
• N(ltd) for pairs of asteroids.
• N(ltd) da
• small d values a 1,
• intermediate d values a 2,
• large d values a 5.

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Asteroid Families on a track to even younger
ones
The tightest pairs have similar values of the
mean anomaly M and are only few m/s apart in the
d-metrics.
(we find such tight pairs of orbits among MB,
Hungaria and Hilda orbits only)
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Asteroid Families on a track to even younger
ones
5 x 10-4
2 x 10-4
1 x 10-4
7 x 10-4
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Asteroid Families on a track to even younger
ones
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Asteroid Pairs statistical robustness check

• We created a number of fake MB
• asteroid populations with the same
• (a,e,i) long-range distribution and
• random distribution of (O,?). We
• then repeated our search for the
• closest pairs and constructed N(ltd)
• - curve 2.

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Asteroid Pairs statistical robustness check
2) We used a semi-numerical method to
estimate probability to find n-asteroids in an
elementary volume V d5 pn(d).
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Asteroid Pairs statistical robustness check
2) We used a semi-numerical method to
estimate probability to find n-asteroids in an
elementary volume V d5 pn(d). Summing over
the whole space filled with M cells we obtain
the overall probability to find a cell with n
objects.
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Asteroid Pairs the case of pairs in very young
families
Asteroid pairs in very young families, including
Karin, are very likely just original fragments
thrown onto very similar orbits Note
application of the previous statistical methods
is not straightforward because of
correlation of the secular angles with
(a,e,i)
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Asteroid Pairs the case of pairs in very young
families
indeed, in the Datura case this relation is
still very well preserved.
1) Datura-2003SQ168 tightest to each other
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Asteroid Pairs the case of pairs in very young
families
indeed, in the Datura case this relation is
still very well preserved.
1) Datura-2003SQ168 tightest to each other
2) 2001VN36 in M9/16 exterior resonance
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Asteroid Pairs the case of pairs in very young
families
even in the Karin case, there are still
intrigue and clumpy correlations between (i,O)
and (e,?).
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Asteroid Pairs reconstruction of the formation
state
Holy grail use backward integration of the two
orbits to reconstruct the exact configuration of
the two objects when they became unbound.

• Two principal obstacles
• Lyapunov timescale typically 100-1000 ky
  (different orbital realizations from the
• current uncertainty interval)
• Yarkovsky-clone dispersion typically 20-100 ky
  (different orbital realizations due
• to different values of the Yarkovsky
  forces)

We used 20 orbital clones, 51 Yarko clones ? 1020
possible past histories of each orbit at each
time t in the past we determined their minimum
distance ? (t) in space for 106 synthetic
pairs. (ORBFIT9 for orbit uncertainty, SWIFT_MVS
for orbit propagation)
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Asteroid Pairs reconstruction of the formation
state
(6070) Rheinland (54827) 2001 NQ8
D 4.6,1.8 km asteroids in the inner MB d 5.8
m/s 50,15 year orbital arcs

• 50 ky Yarko-wall

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Asteroid Pairs reconstruction of the formation
state
(6070) Rheinland (54827) 2001 NQ8
D 4.6,1.8 km asteroids in the inner MB d 5.8
m/s 50,15 year orbital arcs

• 50 ky Yarko-wall
• at 17 ky ? min(?(t)) 250 km

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Asteroid Pairs reconstruction of the formation
state
(6070) Rheinland (54827) 2001 NQ8
D 4.6,1.8 km asteroids in the inner MB d 5.8
m/s 50,15 year orbital arcs

• 50 ky Yarko-wall
• at 17 ky ? min(?(t)) 250 km
• compare with 900 km Hill
• sphere of influence of Rheinland

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Asteroid Pairs reconstruction of the formation
state
(6070) Rheinland (54827) 2001 NQ8
D 4.6,1.8 km asteroids in the inner MB d 5.8
m/s 50,15 year orbital arcs

• at the closest encounter relative
• speed is only 0.25 m/s (as opposed
• to 3 m/s escape speed from Rheinland)
• and the out-of-plane component is
• 0.03 m/s

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Asteroid Pairs reconstruction of the formation
state (1270) Datura 2003
SQ168
D 9.5,1.4 km asteroids in the inner MB d 0.9
m/s 80,6 year orbital arcs

• 85 ky Yarko-wall
• at 1 ky ? min(?(t)) 3x105 km
• (to be compared with 2000 km Hill
• sphere of influence of Datura)
• ? just ordinary conjunction of the
• two orbits

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Asteroid Pairs reconstruction of the formation
state (1270) Datura 2003
SQ168
D 9.5,1.4 km asteroids in the inner MB d 0.9
m/s 80,6 year orbital arcs

• consistent with the idea that
• these two asteroids are just
• primordial fragments from 450 ky
• old Datura-family formation (more
• observations of 2003 SQ168 needed to
• determine if an earlier close encounter
• is real)

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Asteroid Pairs speculations about their origin
Is there any common process that produces 75
of the pairs not included in the very young
families?

• Catastrophic collisions yet smaller asteroid
  families
• (large mass ratio does not really fit, nor
  large abundance among Hungarias)
• direct YORP fission
• (plausible, because of low separation
  velocity in the out-of-plane direction and many
• of the dlt10 m/s pairs dominated by the
  (?a,?e) 2D subspace in addition, we estimate
• Dgt5km MB asteroids might be YORP fissioned
  every 2-5 ky)
• retarded YORP fission binary splitting
• (might be closely related to the previous
  mechanism if many of binaries originally
• produced by YORP fission)

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Asteroid Pairs speculations about their origin
What we need next to decide about the origin
of the pairs?

• Various observations might give us necessary
  clues
• light-curve observations might help to better
  constrain the sense and
• range of the Yarkovsky forces they might
  also indirectly hint the YORP
• fission mechanism, since one of the asteroids
  should rotate slowly
• (Dan Scheeres, private comm.)
• astrometry observations that in many cases
  should tighten the orbital
• uncertainty interval
• new surveys (such as PanSTARRS) will complete
  our information (e.g. new
• members in mini-clusters?) and extend the
  data to smaller sizes