primary surface particle motion and yorp-driven expansion of asteroid binaries

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?


• 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


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:


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


• Insert Matrix Clip


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


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:



• Similar changes across a particle’s impact …

• … and for a particle’s gravitational interaction during flight:

trajectory endpoints from prob. matrix



• 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.


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

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0.5x 10

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ng

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r m

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of A

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a (

kg*m

2/s

)

xyz

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*m2/s

)

xyz



• 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

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-1

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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

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x 10-10

time (sec)

in A

lph

a s

pin

ra

te,

(

rad

/s)

Z component



• (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

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time (sec)

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f in

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(kg

m2)

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XXIA

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ZZ

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time (sec)

in to

tal m

ass

of A

lph

a (

kg)


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

)

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k 2 (

kg

s /

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, 1

02

0 )

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103

104

0.3

0.31

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number of particles

ave

rag

e m

ass

lofti

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ra

te (

kg/s

)

102

103

104

105

0

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1

number of particles

ave

rag

e m

ass

lofti

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ra

te, p

art

icle

ma

ss avg. mdot (kg/s)particle mass ( 106 kg)


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

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xyz

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(kg

*m2/s

)xyz



• 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

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x 10-6

time (sec)

in

Alp

ha

sp

in r

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rad

/s)

xyz

0 2 4 6 8 10

x 105

-3

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x 10-9

Z component


• 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


0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

x 106

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a (

kg)

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x 106

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f in

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yad

(kg

m2)

IA

XXIA

YYIA

ZZ


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?


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


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


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.


• Insert Matrix Clip

primary surface particle motion and yorp-driven expansion of asteroid binaries

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university of

aerospace engineering