N3 Vokrouhlicky - "Yarkovsky and yorp effects paolos legacy"

D. Vokrouhlický (Charles University, Prague)

Talk plan: a) Early days: Lageos 1 inspiration

Talk plan: b) Mid 1990s: Move to planetary

Talk plan: c) Late 1990s: First interesting planetary applications(meteorite transport, NEAs replenishment, family structure,detection idea)

d) > 2000: Yark/YORP mature period

YARKOVSKY and YORP effectsYARKOVSKY and YORP effectsPaoloPaolo’’s legacys legacy

EARLY YEARS: Lageos 1 inspirationEARLY YEARS: Lageos 1 inspiration

Lageos 1 facts

• launch on May 4, 1976• nearly circular orbit at 5900 km and 110deg inclination

• laser-ranged with mcm accuracy• mass 410 kg• initial rotation period 0.6 s but has

been found to exponentially increase with 3y ! e-fold time

• in October 1992 got a twin Lageos 2 on a similar orbit but 52deg inclination


Orbit determination requires empirical accelerations …

Dave Rubincaminterpreted the mean along-track acceleration as the effect of thermal thrust due to absorbed Earth IR radiation…(late 1980s)


From Gauss equations we know …

Hence a simple scaling provides …

Lageos meteoroid

… and thus it should be easy to bring meteoroids to the nearest resonances in the MB(Paolo in ~ 1995).

Other landmark contributions by:

• Dave Rubincam (JGR 1995, 1998) … an independent idea for the Yarkovsky role inmeteorite transport

• Germano Afonso et al. (PSS 1995) … the first numerical integrations of Yarkovskymigrating meteoroids with planetary perturbations

YARKOVSKY EFFECT: meteorite transport…YARKOVSKY EFFECT: meteorite transport…

km size NEAsor family members

Meteorite precursorsHow much would a body move withinits estimated lifetime in the main asteroidbelt?

1 … 0.002 W/m/K2 … 0.02 W/m/K3 … 0.2 W/m/K4 … 2 W/m/Km … 40 W/m/K

Farinella & Vokrouhlický (1998, 1999)


… and so Paolo had the clear vision of a two-stage transport process (late 1990s)


Little later technical tools allowed to directly model meteoroid drift with planetary perturbations included … (Mira Brož)


… or couple the transport with collisional break-ups (Vokrouhlický & Farinella 2000).

YARKOVSKY EFFECT: NEAs replenishment…YARKOVSKY EFFECT: NEAs replenishment…

Rem. Yarkovsky migration has been since shown to be likely the sustainingmechanism of other unstable populations (e.g., close or inside MMRs)

NEO facts: 1. About 220 bodies with H<18 (D>1km) must beresupplied to the NEO zone every My throughthe three main routes (3/1, 6 and weak resonances)to keep the population in steady state

2. Assuming the size distribution asN(<H) ~ 10H

in the range 15.5 < H < 18, observations give 0.26 in the main asteroid belt 0.35 for the NEAs

A “reasonable model” can be contructed to meet these observationalfacts with Yarkovsky effect pushing the H<18 bodies out of MB

YARKOVSKY EFFECT: NEAs replenishment…YARKOVSKY EFFECT: NEAs replenishment…

YARKOVSKY EFFECT: structure of families…YARKOVSKY EFFECT: structure of families…

Farinella & Vokrouhlický (1999)

Known members of the Astrid family:

semimajor axis vs size plot



Polarization of small fragments toward extreme values of semimajoraxis: a trace of their faster drift by thermal forces


Polarization of small fragments toward extreme values of semimajoraxis: a trace of their faster drift by thermal forces




• Family in (a,e) is nearly cut in two near 2.92 AU.

• Both sides of family are bracketed by powerful mean motion resonances(5:2 and 7:3 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 5:2 or right side of 7:3.

Why does this family have such a weird shape?


KoronisKoronis familyfamily

•• Observed Observed

•• ModelModel


1. Large asteroid disrupts and ejects multi-km fragments at velocities consistent with hydrocode results.

2. D < 20 km bodies start drifting inward and outward in semimajor axis a by theYarkovsky effect.

3. These bodies jump over or become trapped by mean motion or secularresonances, which may change their (e, i) values.

4. Family members drifting far enough reach powerful resonances capable of pushing them onto planet-crossing orbits.


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Colors from Sloan Digital Sky SurveyColors from Sloan Digital Sky Survey


Novel quantitative information about the space weathering processes… (Nesvorný et al. 2005).

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Color becomes Color becomes ‘‘redderredder’’ over time over time

Effect of space weathering:Effect of space weathering:spectral changes by solar wind spectral changes by solar wind and micrometeorite impactsand micrometeorite impacts

First measurement of the rate of First measurement of the rate of spectral changes for asteroids spectral changes for asteroids


YARKOVSKY EFFECT: detection issues etc…YARKOVSKY EFFECT: detection issues etc…

Detection possibility of theYarkovsky forces noticed in late 1990s. Requires as accurate astrometry as possible – naturally let to involve planetary radar…

… since then detections have been also achieved for objects without radar data. Yarkovsky forces were also shown important for:

• arc linkage (e.g., 1992 BF), or• impact hazard studies (e.g.,

Apophis, 1999 RQ36)

YARKOVSKY EFFECT: post scriptum…YARKOVSKY EFFECT: post scriptum…


… what’s followed/next:

• Dave Rubincam (2000) introduced YORP as a twin phenomenon to theYarkovsky effect

• discovery of Karin family (2002) initiated hunt for young clusters and asteroid structures; Yarkovsky forces are inevitable part of the age-determination process

• Yarkovsky forces first detected (2003) through the orbit-determination of a small NEA

• YORP first detected (2006) as an acceleration component in rotation of smallNEAs

• …


… what’s followed/next:

George Beekman (2006) discovered the original Yarkovsky pamphlet claimed lost by Öpik (1951)…

Education

N3 Vokrouhlicky - "Yarkovsky and yorp effects paolos legacy"