Resonance Effects in Planetary Rings I Spiral Waves

  • Alexei M. Fridman
  • Nikolai N. Gorkavyi
Part of the Astronomy and Astrophysics Library book series (AAL)


We have already met the formation of a spiral wave in Sect. 6.1 where we calculated the trajectories of particles near a separate satellite. When the distance of the particle from the satellite increases the wavelength of the excited wave increases and its amplitude decreases— as can be seen in Fig. 6.2. Nonetheless there are special, resonance regions in the rings where the effect of the satellite is again very strong. The physics of this effect is well known: an oscillator — such as a molecule, a pendulum, or a swing — is excited if an eigenfrequency of its oscillations is the same as the frequency of an external driving force or stands in simple ratio, such as 1:2, 2:3, 3:4, ..., to that frequency. A particle in the ring, moving along a circle, can undoubtedly be considered as an oscillator with eigenfrequency Ω. A satellite with its gravitational field is a driving force with frequency Ω s. If, for instance, Ω = 2Ω s for each two orbits of the particle the satellite has completed a single one and if the particle approaches the satellite at the apocentre of its orbit all subsequent approaches will take place at the same point: the perturbations add up and the particle trajectory changes significantly. However, if this resonance is slightly disturbed the encounters between the particle and the satellite will take place at different points of the particle orbit and the effect of the satellite will be negligibly small.


Optical Depth Density Wave Resonance Effect Spiral Wave Resonance Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Alexei M. Fridman
    • 1
    • 2
  • Nikolai N. Gorkavyi
    • 3
  1. 1.Institute of Astronomy RASMoscow State UniversityMoscowRussia
  2. 2.Sternberg Astronomical InstituteMoscow State UniversityMoscowRussia
  3. 3.Crimean Astrophysical ObservatoryGoddard Space Flight CenterGreenbeltUSA

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