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1.
The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error. By the latter we mean the difference between the computed orbit and the dynamical behaviour of the real physical system, whatever the causes. The analysis of these causes requires an interdisciplinary effort: there are physical model and parameters errors, algorithm and discretisation errors, rounding off errors and reliability problems in the computer hardware and system software, as well as instabilities in the dynamical system. We list all the sources of integration error we are aware of and discuss their relevance in determining the present limit to the time span of a meaningful integration of the orbit of the planets. At present this limit is of the order of 108 years for the outer planets. We discuss in more detail the truncation error of multistep algorithms (when applied to eccentric orbits), the coefficient error, the method of Encke and the associated coordinate change error, the procedures used to test the numerical integration software and their limitations. Many problems remain open, including the one of a realistic statistical model of the rounding off error; at present, the latter can only be described by a semiempirical model based upon the simpleN
2 formula (N=number of steps, =machine accuracy), with an unknown numerical coefficient which is determined only a posteriori. 相似文献
2.
P. Farinella A. Milani A. M. Nobili P. Paolicchi V. Zappala' 《Earth, Moon, and Planets》1983,28(3):251-258
In the set of small satellites of Saturn recently imaged by the Voyager probes, we can observe the transition from irregularly-shaped, strength-dominated objects to larger, gravity-dominated bodies with shapes roughly fitting the theoretical equilibrium figures. The transition occurs for a radius of 100±50 km, corresponding to a typical material strength of the order of 107 dynes cm?2. We discuss briefly the cases of Mimas, Enceladus, Hyperion, Phoebe and the small coorbital and F-ring shepherding moons, showing that an analysis of the shape data can often provide interesting results on the physical properties, origin and collisional history of these objects. 相似文献
3.
P. Farinella A. Milani A. M. Nobili P. Paolicchi V. Zappala 《Earth, Moon, and Planets》1984,30(1):39-42
The Voyager images have shown that Mimas and Enceladus have regular shapes, with topography of the order of 1% of the diameter. Therefore, we can compare the global shapes of these satellites with the corresponding figures of gravitational equilibrium. In the case of Mimas, this comparison rules out a homogeneous interior, but implies the existence of a denser, presumably rocky core within this small icy satellite. 相似文献
4.
An analysis of ordered and chaotic regions of motion in the outer asteroid belt has shown that once the eccentricity of Jupiter is introduced the chaotic regions of the circular model are quite easily depleted. This suggests that also objects in neighbouring regions must be strongly perturbed. Therefore it is not surprising that many outer belt asteroids have been reported in the literature as resonant or anyway dynamically protected. By using the planar elliptic restricted 3-body model we have investigated the motion of outer belt asteroids which had not been suspected to librate. We find 3 cases of libration and 11 cases of e, coupling that can be explained within the theory of secular resonances. It is thus established that in the outer belt only resonant and dynamically protected asteroids can have lifetimes of the same order as the age of the Solar System. 相似文献
5.
Anna M Nobili 《Celestial Mechanics and Dynamical Astronomy》1988,45(1-3):293-304
Modern computer technology allows dynamical astronomers to investigate the long term stability of real systems as thoroughly as ever. However, the process is not straightforward and new problems need to be solved. This work deals with only one such problem: the construction-from the numerical integration- of a secular perturbation theory that is able to describe the dynamical behavior of the system. The discussion refers to the outer planets and is based on the knowledge acquired by the author during her participation in project LONGSTOP. A digital filter is used in order to reduce the output and eliminate short periodic terms. Filtering uncovers long term variations in the semimajor axes. From the filtered output a secular perturbation theory is constructed in the assumption that the solution is regular, as secular perturbation theories can only be constructed for regular solutions. If we succeed, this means that the solution is indeed regular for the computed span of time; if not-and this can be established in a rigorous way-it has to be concluded a posteriori that the solution is not regular. The LONGSTOP 1A and 1B integrations show well that as the timespan of the integration increases it is possible to detect the non-regular behavior of the solution. This happens in the eccentricity of Saturn at the 10–4 level. 相似文献
6.
We present new counts of stars in M15, using plates inB, V andU. We are able to explore relatively close to the central parts of the cluster (0.1 pc) and we derive the best fitting parameters for the star distribution. 相似文献
7.
A simple explanation of some characteristics of the present distribution of number vs. semimajor axis and number vs. eccentricity of the asteroids is obtained in the framework of the restricted three-body problem, choosing suitable initial conditions. We compare the results with the numerical ones by Lecar and Franklin (1973), and we try to explain the depletion of the zone beyond 3.2 A.U. as a possible effect of a primeval collisional process. 相似文献
8.
We assume that the solar tidal action on accreting protoplanets forced them to corotation. If this is true, and assuming a subsequent conservation of spin angular momentum, we can easily get a rough explanation of: (1) the actual rotation periods of the planets, (2) the trend toward small inclination angles for the rotation axes, (3) the existence of a relation between rotational angular momenta and planetary masses similar to the empirical ones due to McDonald (1964). Hartmann and Larson (1967) and Fish (1967). 相似文献
9.
Celestial Mechanics and Dynamical Astronomy - 相似文献
10.
From the first Voyager pictures, the shape of Mimas appears to be spherical within a few percents. If this result is confirmed, either Mimas's density is higher than 2 g cm–3, or this small satellite has a core-mantle differentiated structure. 相似文献