Solar System dynamics: recent developments

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1 Solar System dynamics: recent developments G. B. Valsecchi, IASF-Roma, INAF, Roma (Italy)

2 Recent developments: planets Dynamics of the planets Slow chaos in planetary motions. Chaotic spins of the inner planets, except the Earth (due to the Moon). The Nice model. Reconstruction of past Earth insolation.

3 Recent developments: satellites Dynamics of the satellites Many new irregular satellites of the giant planets. Dwarf planet and asteroid satellites. Heating of regular satellites through resonance couplings.

4 Recent developments: asteroids Asteroid dynamics Incredible amount of accurate astrometric and orbital data. Slow chaos everywhere in the Main Belt and in many zones of the trans-neptunian region. Identification of young families. Nongravitational forces (meteorite delivery, spin distributions). Near-Earth Asteroids (NEAs).

5 Recent developments: comets Comet dynamics Centaurs, the dynamical link between Jupiter family comets and the trans-neptunian region. The scattered disk. Oort cloud formation/evolution, and the rôle of external perturbers. Nongravitational forces modeling. Meteor storm forecasting.

6 NEO impact monitoring Can we predict an impact? Before 1998 the problem of computing all possible impact solutions for objects with a given set of observations had not been solved. Since orbital evolution is deterministic and is computable with the required accuracy, why do we have a problem? And why do we need to talk about probability? Actually, there is not such a thing as the orbit of an asteroid determined from the observations. There is always a range of possible orbits, all compatible with the observations. Probability is then just a measure of our ignorance.

7 NEO impact monitoring Virtual asteroids and impactors The orbits compatible with the observations of an asteroid can be described as a swarm of Virtual Asteroids (VAs): only one of them is real, but we don t know which one. Each VA follows its own orbit; if one of them has an impact with the Earth, we call it a Virtual Impactor (VI), with an associated Impact Probability (IP) depending upon the statistics of the observational errors. If a NEA has an IP of 1/1 000, through the computation of VAs we can expect to find one VI. However, if the IP is 1/ , to find a VI by brute force we need to compute VAs: too much, even for current computers.

8 NEO impact monitoring NEO impact monitoring Detecting VIs with low IP can be done by arranging VAs along a string, the Line of Variation (LoV). As the VAs proceed on their separate orbits, the string stretches, mostly along track, until it wraps around a large portion of the orbit. If there is a point where the orbits are close to the Earth s orbit, some VAs have close approaches to the Earth.

9 NEO impact monitoring Detecting VIs Interpolation on the string is possible. If two consecutive VAs straddle the Earth, an intermediate VA can be built to find the minimum possible approach distance. The efficiency gain with this computational strategy is more than a factor

10 NEO impact monitoring Impact Monitoring Robots If a VA has an impact with the Earth, we call it a Virtual Impactor (VI), with an associated Impact Probability (IP). In March 1999 we could detect a VI with IP 1/ with only VAs (asteroid 1999 AN 10 ); in November 1999 the software robot CLOMON begun operations in Pisa. Each new NEA is monitored for possible impacts until When VIs are found, they are posted on the Risk Page of NEODyS ( In 2002 the 2 nd generation impact monitoring robots became operational: CLOMON2 (replicated in Valladolid) and Sentry ( Cross-checking has solved the problem of verification, and indeed has increased reliability.

11 Resonant returns and keyholes Resonant returns Many VIs are associated to resonant returns, in which case an encounter with the Earth takes place between now and the collision (we do not discuss here the case of the less frequent non-resonant returns). To understand resonant returns, we study the situation on the the b-plane of the first encounter. This plane contains the planet and is perpendicular to the planetocentric unperturbed velocity U(a, e, i); the vector from the planet to the point in which U crosses the plane is b. Suitable coordinates on the b-plane are the MOID (Minimum Orbital Intersection Distance) and the timing of the test particle with respect to the Earth.

12 Resonant returns and keyholes Keyholes A keyhole (Chodas 1999) is a small region of the b-plane of a specific close encounter of an asteroid with the Earth such that, if the asteroid passes through it, it will hit the planet or have a very close encounter with it at a subsequent return.

13 Resonant returns and keyholes Keyhole locations 1999 AN10: Keyholes in Impact Plane on 2027 Aug 07 4 Orbital solution based on 130-day arc 2034 ( km) 2 Uncertainty ellipse 0 Keyholes that lead to possible impacts Earth ( km) The positions of keyholes in the b-plane of the encounter of 7 August 2027 of 1999 AN 10, for impacts in 2034, 2044, and 2046 (from Chodas 1999).

14 Resonant returns and keyholes Shape and size of an impact keyhole Problem: how varies the distance between two points of the b-plane of the current encounter when considering their images after propagation to the b-plane of the next encounter? Result: the MOID-coordinate on the b-plane is essentially unchanged, the timing-coordinate is stretched by a large factor, depending on the circumstances of the encounter. Geometric consequence: the pre-image of the Earth on the b-plane of the encounter preceding the collision is a thick arclet closely following the shape of the circle corresponding to the suitable orbital period.

15 Resonant returns and keyholes Keyhole locations ¾¼ ¼ ¾¼ ¾¼ ¼ ¾¼ The location of keyholes, on the b-plane of the 7 August 2027 encounter with the Earth of 1999 AN 10, for encounters within 4 Earth radii at the resonant returns in 2040, 2044, 2046.

16 Resonant returns and keyholes Keyholes are useful The V necessary to avoid the 2036 collision of 2004 MN 4 with the Earth (Carusi 2005); the 2029 encounter lowers V by four orders of magnitude.

17 Long-term impact monitoring Long-term impact monitoring Going from one planetary encounter to another, the along-track divergence of nearby orbits grows linearly with time, and can become very large. Sequences of encounters result in multiplicative accumulation of the divergence from each encounter, and thus lead to exponential divergence and chaos, with maximum Lyapounov exponent proportional to encounter frequency.

18 Long-term impact monitoring Long-term impact monitoring It is clear that, no matter how precisely determined is a NEA orbit, the LoV evolution just described will lead, after sufficient time has elapsed, to a situation resembling that of a newly discovered asteroid, with the important difference that practically all the uncertainty will be along-track. Given the sensitivity of encounter outcomes to small changes in the initial conditions, the possibility to extend the predictability horizon for a NEA beyond a certain date depends from the accurate modelling of so-far neglected non-gravitational perturbations like the Yarkovsky effect (cf. Golevka).

Near Earth Objects Dynamic Site. G. B. Valsecchi IAPS-INAF, Roma, Italy

Near Earth Objects Dynamic Site G. B. Valsecchi IAPS-INAF, Roma, Italy What NEODyS is NEODyS is a website providing information and services for all Near Earth Asteroids. In it, each NEA has its own dynamically