primary surface particle motion and yorp-driven expansion of asteroid binaries
DESCRIPTION
Primary Surface Particle Motion and YORP-Driven Expansion of Asteroid Binaries Eugene G. Fahnestock Dept. Aerospace Engineering, The University of Michigan [email protected]. Our Systems of Interest…. ≈ 15 ±4 % of NEOs are binary systems (and ≈2-3 % MBAs) - PowerPoint PPT PresentationTRANSCRIPT
Primary Surface Particle Motion and YORP-Driven Expansion of Asteroid
Binaries
Eugene G. Fahnestock
Dept. Aerospace Engineering,
The University of [email protected]
April 21, 2023 2 Fahnestock, Scheeres
Our Systems of Interest…
• ≈15±4% of NEOs are binary systems (and ≈2-3% MBAs)
• Large class of close “asynchronous” binary systems:– Most abundant binary population
– Found among NEOs, MCs, smaller MBAs
– Primary diameter D1 typically <10 km, D2/D1 typically 0.2-0.5
– Large spheroidal / oblate roughly axisymmetric primary (Alpha), rotating faster than orbit rate, spin rate near surface disruption rate
– Smaller elongated / ellipsoidal secondary (Beta), on-average synchronous rotation
– Typified by (66391) 1999 KW4 system
• Fission or mass-shedding due to spin-up by YORP implicated for their formation
• What about evolution of this type of system after that?
April 21, 2023 3 Fahnestock, Scheeres
• Solid-body tidal evolution
• Asymmetric sunlight absorption and thermal re-radiation on Beta
• YORP spin-up of Alpha surface particle motion (“lofting”)
• To work out details of this mechanism and confirm hypothesis…
• Precise dynamic simulation and approx. probabilistic simulation
Evolution Mechanisms, Hypothesis
April 21, 2023 4 Fahnestock, Scheeres
Precise Dynamic Simulation
• First propagate the motion of the binary itself : F2BP – Polyhedral body representation: flexible in shape & resolution– Single polyhedral body and point mass potential
Werner & Scheeres, CMDA, 1997– Mutual potential between two polyhedral bodies
Werner & Scheeres, CMDA, 2005– Gradients of polyhedral mutual potential, use in general integration
of continuous F2BP EOM Fahnestock & Scheeres, CMDA, 2006– Parallel implementation and Lie Group Variational Integrator (LGVI)
discrete EOM Lee, et. al., CMAME, 2006 , Fahnestock & Scheeres, Icarus, 2008
• Propagate non-interacting particles in binary system: RF3BP
– Face, edge dependent dyads and dimensionless scalars are calculated from Alpha and Beta shape models
– Impact detection with Laplacian:
April 21, 2023 5 Fahnestock, Scheeres
KW4 as Demonstration System, Setup
• For RF3BP, batches of particles tiled on facets:
• F2BP runs and RF3BP batches propagated for pole offsets, , same and opposite sides for facet, different
spin rates, {6.51444x10-4, 6.41444x10-4, 6.40444x10-4} rad/s
Beta0.57x0.46x0.35 km~2.8 g/cm3 density17.42 hr rotation period
Alpha1.53x1.49x1.35 km2.0 g/cm3 density2.76 hr rotation periodAlpha spin rate = 6.31343x10-4 rad/s
Mutual Orbit2.55 km semi-major axis17.42 hr orbit periodMass fraction = 0.054
April 21, 2023 6 Fahnestock, Scheeres
• Insert Matrix Clip
April 21, 2023 7 Fahnestock, Scheeres
Choice of Primary Spin Rate for Lofting
• Effort made to identify exact location, binary system parameters for which lofting likely first occurs:
• Facet 4113 chosen location, others nearby possible• ≈1×10−6 rad/s difference in minima for everywhere-lofting spin rate
between opposite side & same side (lower)• Minimum in everywhere-lofting rate at
April 21, 2023 8 Fahnestock, Scheeres
Approximate Probabilistic Simulation
• Hence choice of {6.51444x10-4, 6.41444x10-4, 6.40444x10-4} rad/s
• Obtain probability matrix for RF3BP output data at threshold rates, mapping to locations in re-impact longitude and time of flight, or to other outcomes (allows for transfer to Beta, escape)
• Precise Dynamic Simulation was for “test” particles no influence on motion of binary components
• Instead use probability matrices & associated statistical representation of impact velocity to map particles forward in time
track changes to binary component states w/ particle motion
• Changes with lofting:
April 21, 2023 9 Fahnestock, Scheeres
Approximate Probabilistic Simulation
• Similar changes across a particle’s impact …
• … and for a particle’s gravitational interaction during flight:
trajectory endpoints from prob. matrix
April 21, 2023 10 Fahnestock, Scheeres
Approximate Probabilistic Simulation
• N particles uniformly distributed on surface around Alpha’s equator
• Test current spin rate against thresholds, Alpha radius bound if passing, particles in longitude bin at same/opposite side loft where they go is generated from probability matrix
• Lofted particles re-impacting later are buffered until impact time step
• Apply changes to binary states with each piece of particle motion
• Update states for time step passage
• Externally applied (YORP) ang. acceleration included in this update
• Time step length & buffer adjusted with changes in Alpha spin rate
• We find transient lofting episodes separated by long spin-up times Adjustment to skip over most of long spin up times, for speedup
• Grounded in precise dynamic simulation, but can reach long durations, out to O(104)+ years.
April 21, 2023 11 Fahnestock, Scheeres
Results for Nominal Case
• Case with = 3.0×10−11 rad/s/yr = 9.5129×10−19 rad/s2
• 10 Mt of surface material (≈0.43% of Alpha mass) modeled
• For all cases with small , linear fit to algorithm output at right is almost exactly equivalent to
0 1 2 3 4 5 6 7 8 9
x 1010
-2.5
-2
-1.5
-1
-0.5
0
0.5x 10
11
time (sec)
A
ng
ula
r m
om
en
tum
of A
lph
a (
kg*m
2/s
)
xyz
0 1 2 3 4 5 6 7 8 9
x 1010
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
time (sec)
A
ng
ula
r m
om
en
tum
of B
eta
(kg
*m2/s
)
xyz
0 1 2 3 4 5 6 7 8 9
x 1010
-2
-1
0
1
2
3
4
5
6
7
8x 10
10
time (sec)
A
ng
ula
r m
om
en
tum
of B
eta
+ m
utu
al o
rbit
(kg
*m2/s
)
xyz
April 21, 2023 12 Fahnestock, Scheeres
Results for Nominal Case
• Primary spin rate regulated, doesn’t exceed the imposed threshold at which lofting starts
• Alpha inertia dyad Z-element doesn’t change through lofting episodes
0 1 2 3 4 5 6 7 8 9
x 1010
-4
-3
-2
-1
0
1
2
3
4x 10
-8
time (sec)
in
Alp
ha
sp
in r
ate
, (
rad
/s)
xyz
0 0.5 1 1.5 2 2.5 3
x 1010
-12
-10
-8
-6
-4
-2
0
2
4
x 10-10
time (sec)
in A
lph
a s
pin
ra
te,
(
rad
/s)
Z component
April 21, 2023 13 Fahnestock, Scheeres
Results for Nominal Case
• (time-integral of plot at right )/duration gives average mass aloft
• (Accumulated mass lofted)/ duration gives average mass lofting rate
• For nominal case, have
• Episodic nature of lofting these #’s are activity level metrics only
0 1 2 3 4 5 6 7 8 9
x 1010
-8
-6
-4
-2
0
2
4
6x 10
14
time (sec)
in
dia
go
na
l co
mp
on
en
ts o
f
mo
me
nt o
f in
ert
ia d
yad
(kg
m2)
IA
XXIA
YYIA
ZZ
0 1 2 3 4 5 6 7 8 9
x 1010
-6
-5
-4
-3
-2
-1
0x 10
8
time (sec)
in to
tal m
ass
of A
lph
a (
kg)
April 21, 2023 14 Fahnestock, Scheeres
vs. Angular Acceleration, Mass Parameters
• Eventual phase shift to different behavior occurs with vastly increased applied angular acceleration of primary,
• Great dependence of on above, little dependence on variation of total mass available to loft, varied thru particle size or N
10-20
10-18
10-16
10-14
10-12
10-4
10-2
100
102
104
106
applied ang. acceleration (rad/s2)
ave
rag
e m
ass
lofti
ng
ra
te (
kg/s
)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
k 2 (
kg
s /
rad
, 1
02
0 )
102
103
104
0.3
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4
number of particles
ave
rag
e m
ass
lofti
ng
ra
te (
kg/s
)
102
103
104
105
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
number of particles
ave
rag
e m
ass
lofti
ng
ra
te, p
art
icle
ma
ss avg. mdot (kg/s)particle mass ( 106 kg)
April 21, 2023 15 Fahnestock, Scheeres
Results for Extreme Acceleration Case
• Case with = 1.5×10−13 rad/s2 , still 10 Mt surface material
• Interesting hypothetical scenario, as with propelled spin-up
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 106
-3
-2
-1
0
1
2
3
4
5x 10
-3
time (sec)
A
ng
ula
r m
om
en
tum
of B
eta
(kg
*m2/s
)
xyz
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 106
-4
-3
-2
-1
0
1
2
3
4
5
x 1011
time (sec)
A
ng
ula
r m
om
en
tum
of A
lph
a (
kg*m
2/s
)
xyz
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 106
-6
-4
-2
0
2
4
x 1011
time (sec)
A
ng
ula
r m
om
en
tum
of B
eta
+ m
utu
al o
rbit
(kg
*m2/s
)xyz
April 21, 2023 16 Fahnestock, Scheeres
Results for Extreme Acceleration Case
• Above ≈ 1×10−14 rad/s2, damping effect of same-side particle lofting on Alpha spin rate is overwhelmed
• Alpha spin rate increases 10−6 rad/s, until opposite-side lofting begins runaway spin rate growth, use of same probability matrices not OK
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 106
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10-6
time (sec)
in
Alp
ha
sp
in r
ate
, (
rad
/s)
xyz
0 2 4 6 8 10
x 105
-3
-2
-1
0
1
2
3
4
x 10-9
Z component
April 21, 2023 17 Fahnestock, Scheeres
• Shift to near-continuous lofting with sustained mass loss from Alpha, and sustained changes to inertia dyad…
• Second shift occurs once opposite-side lofting also picks up
Results for Extreme Acceleration Case
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 106
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0x 10
8
time (sec)
in to
tal m
ass
of A
lph
a (
kg)
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
x 106
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2x 10
15
time (sec)
in
dia
go
na
l co
mp
on
en
ts o
f
mo
me
nt o
f in
ert
ia d
yad
(kg
m2)
IA
XXIA
YYIA
ZZ
April 21, 2023 18 Fahnestock, Scheeres
Implications for System Evolution
• Simple formula for semi-major axis growth in response to YORP or other angular acceleration:
• For KW4 and nominal case, gives expansion rate of ≈0.881 m/kyr
• Timescale for orbit growth by factor of over :
• Yields
• This evolution mechanism is several times faster than tidal evolution
• Orbit expansion accelerates as long as mechanism is sustained
• Bodies evolve toward separation rapidly but at some point mechanism must break down
• Then Alpha overspin, large mass loss, possible formation of new component interior to old one?
April 21, 2023 19 Fahnestock, Scheeres
Suggestive Observations…
• Many (≈60) related pairs of bodies, formerly binaries? Vokrouhlicky,Nesvorny
• Triple system (153591) 2001 SN263
Feb 12, 2008
Feb 13, 2008
Feb 14, 2008
April 21, 2023 20 Fahnestock, Scheeres
Conclusions and Questions
• Combination of precise dynamic simulation and statistical simulation confirms hypothesized evolution mechanism
• Maintains primary near surface disruption spin rate, while producing acceleration orbit expansion to separation
• Mechanism operates faster than tidal evolution
• Applies to large class of close asynchronous binary systems
• Need to better characterize exact conditions for lofting onset?– particle physical size distribution (not just mass)
– accounting for contact, friction forces
• Inter-particle interaction?– Particle-particle collision
– Electrostatic and gravitational interaction
April 21, 2023 21 Fahnestock, Scheeres
Acknowledgements
Thanks to: Al Harris, Petr Pravec, Mike Nolan & Steve Ostro
Facilities and Support: JPL Supercomputing and Visualization Facility, JPL/Caltech, NASA ;
E.G.F.’s work supported by a National Science Foundation Graduate Research Fellowship ; D.J.S. acknowledges support by a grant from the NASA Planetary
Geology and Geophysics Program.
April 21, 2023 22 Fahnestock, Scheeres
• Insert Matrix Clip