V.V.Sidorenko

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Quasi-satellite orbits in the context of
coorbital dynamics

• V.V.Sidorenko
• (Keldysh Institute of Applied Mathematics,
  Moscow, RUSSIA)
• A.V.Artemyev, A.I.Neishtadt, L.M.Zelenyi
• (Space Research Institute, Moscow, RUSSIA)

Moscow, 2012
2
Quasi-satellite orbits
(based on pictures from http//www.astro.uwo.ca/w
iegert/quasi/quasi.html)
11 mean motion resonance!
Resonance phase jl-l librates around 0 (l and
l are the mean longitudes of the asteroid and of
the planet)
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Quasi-satellite orbits
Historical background

• J. Jackson (1913) the first(?) discussion of
  QS-orbits
• A.Yu.Kogan (1988), M.L.Lidov, M.A.Vashkovyak
  (1994) the consideration of the QS-orbits in
  connection with the russian space project
  Phobos
• Namouni(1999) , Namouni et. al (1999), S.Mikkola,
  K.Innanen (2004), - the investigations of the
  secular evolution in the case of the motion in
  QS-orbit

Real asteroids in QS-orbits
2002VE68 Venus QS 2003YN107, 2004GU9,
2006FV35 Earth QS 2001QQ199, 2004AE9
Jupiters QS
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Secular effects examples
Nonplanar circular restricted three-body problem
Sun-Planet-Asteroid
Parameters
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Phase portrait of the slow motion mathching of
the trajectories on the uncertainty curve
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Scaling
A the motion in QS-orbit is perpetual
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Nonplanar circular restricted three-body problem
Sun-Planet-Asteroid
Time scales at the resonance T1 - orbital motions
periods T2 - timescale of rotations/oscillations
of the resonant argument (some
combination of asteroid and planet mean
longitudes) T3 - secular evolution of
asteroids eccentricity e, inclination
i, argument of prihelion ? and ascending
node longitude O .
T1 ltlt T2 ltlt T3
Strategy double averaging of the motion equations
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Resonant approximation
Scale transformation
Slow variables
Slow-fast system

• approximate
• integral of
• the problem

SF-Hamiltonian
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Regular variables
Relationship with the Keplerian elements
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Averaging over the fast subsystem solutions on
the level ? ?
Problem what solution of the fast subsystem
should be used for averaging ?
QS-orbit or HS-orbit?
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Asteroid 164207 (2004GU9)
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Asteroid 164207 (2004GU9)
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Asteroid 164207 (2004GU9 )
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Asteroid 164207 (2004GU9)
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Asteroid 2006FV35
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Asteroid 2006FV35
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Conclusions

• Row classification of slow evolution scenarios is
  presented
• The criterion to distinguish between the
  perpertual and temporarily motion in QS-orbit is
  established