# Resonances and close approaches. I. The Titan-Hyperion case

@article{Bevilacqua1980ResonancesAC,
title={Resonances and close approaches. I. The Titan-Hyperion case},
author={Roberto Bevilacqua and Ornella Menchi and Andrea Milani and Anna Maria Nobili and Paolo Farinella},
journal={The moon and the planets},
year={1980},
volume={22},
pages={141-152}
}
• Published 1 April 1980
• Physics, Geology
• The moon and the planets
AbstractThe orbits of Titan and Hyperion represent an interesting case of orbital resonance of order one (ratio of periods 3/4), which can be studied within a reasonable accuracy by means of the planar restricted three-body problem. The behaviour of this resonance has been investigated by numerical integrations, of which we show the results in terms of the Poincaré mapping in the plane of the coordinates η = ✓[(2L − 2G)] cos ( $$\tilde \omega$$ H − t)and ξ = −,✓[(2L − 2G)] sin ( \tilde…
15 Citations

### Influence of a second satellite on the rotational dynamics of an oblate moon

The gravitational influence of a second satellite on the rotation of an oblate moon is numerically examined. A simplified model, assuming the axis of rotation perpendicular to the (Keplerian) orbit

### An example of stable chaos in the Solar System

• Physics, Geology
Nature
• 1992
MANY planets have been shown to have chaotic instabilities in their orbital motions, but the long-term significance of this is not fully understood1. The eccentricity of Mercury, for example, changes

### HYPERION AS A DUST SOURCE IN THE SATURNIAN SYSTEM

• Physics, Geology
• 1997
We argue that Hyperion may act as a reasonably effective source of dust in the Saturnian system. Hypervelocity impacts of interplanetary grains and of dust particles from the outermost moon Phoebe

### Traditional formation scenarios fail to explain 4:3 mean motion resonances

• Physics, Geology
• 2012
At least two multi-planetary systems in a 4:3 mean motion resonance have been found by radial velocity surveysy. These planets are gas giants and the systems are only stable when protected by a

### Transfer Design Exploiting Resonant Orbits and Manifolds in the Saturn-Titan System

• Physics
• 2013
The application of dynamical systems techniques to trajectory design has demonstrated that employing invariant manifolds and resonant flybys expands the trajectory options and potentially reduces the

### The Exoplanet Handbook

1. Introduction 2. Radial velocities 3. Astrometry 4. Timing 5. Microlensing 6. Transits 7. Imaging 8. Host stars 9. Brown dwarfs and free-floating planets 10. Formation and evolution 11. Interiors

## References

SHOWING 1-10 OF 15 REFERENCES

### Instabilities in dynamical systems : applications to celestial mechanics : proceedings of the NATO Advanced Study Institute held at Cortina d'Ampezzo, Italy, July 30-August 12, 1978

I: Fundamental Considerations of Stability.- Simple Non-Integrable Systems with Two Degrees of Freedom.- Instabilities in Systems of Three Degrees of Freedom.- Perturbed Twist Maps, Homoclinic Points

### Orbital Resonances in the Solar System

Orbital resonances are defined as any system of two or more satellites (including planets) orbiting the same primary and whose orbital mean motions are in a ratio of small whole numbers. Known

### Evolution of satellite resonances by tidal dissipation.

Analysis of a realistic model shows how satellites' gravitational interaction can halt their differential tidal evolution when resonant commensurabilities of their orbital periods are reached. The

### Differentiable dynamical systems

This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a