分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Most recently, machine learning has been used to study the dynamics of integrable Hamiltonian systems and the chaotic 3-body problem. In this work, we consider an intermediate case of regular motion in a non-integrable system: the behaviour of objects in the 2:3 mean motion resonance with Neptune. We show that, given initial data from a short 6250 yr numerical integration, the best-trained artificial neural network (ANN) can predict the trajectories of the 2:3 resonators over the subsequent 18750 yr evolution, covering a full libration cycle over the combined time period. By comparing our ANN's prediction of the resonant angle to the outcome of numerical integrations, the former can predict the resonant angle with an accuracy as small as of a few degrees only, while it has the advantage of considerably saving computational time. More specifically, the trained ANN can effectively measure the resonant amplitudes of the 2:3 resonators, and thus provides a fast approach that can identify the resonant candidates. This may be helpful in classifying a huge population of KBOs to be discovered in future surveys.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： For the Hamiltonian system, this work considers the learning and prediction of the position (q) and momentum (p) variables generated by a symplectic evolution map. Similar to Chen & Tao (2021), the symplectic map is represented by the generating function. In addition, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions, and then train a leap-frog neural network (LFNN) to approximate the generating function between the first (i.e. initial condition) and one of the rest partitions. For predicting the system evolution in a short timescale, the LFNN could effectively avoid the issue of accumulative error. Then the LFNN is applied to learn the behavior of the 2:3 resonant Kuiper belt objects, in a much longer time period, and there are two significant improvements on the neural network constructed in our previous work (Li et al. 2022): (1) conservation of the Jacobi integral ; (2) highly accurate prediction of the orbital evolution. We propose that the LFNN may be useful to make the prediction of the long time evolution of the Hamiltonian system.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Context. More than 10000 Jupiter Trojans have been detected so far. They are moving around the L4 and L5 triangular Lagrangian points of the Sun-Jupiter system and their distributions can provide important clues to the early evolution of the Solar System. Aims. The number asymmetry of the L4 and L5 Jupiter Trojans is a longstanding problem. We aim to test a new mechanism in order to explain this anomalous feature by invoking the jumping-Jupiter scenario. Methods. First, we introduce the orbital evolution of Jupiter caused by the giant planet instability in the early Solar System. In this scenario, Jupiter could undergo an outward migration at a very high speed. We then investigate how such a jump changes the numbers of the L4 (N4) and L5 (N5) Trojans. Results. The outward migration of Jupiter can distort the co-orbital orbits near the Lagrangian points, resulting in L4 Trojans being more stable than the L5 ones. We find that, this mechanism could potentially explain the unbiased number asymmetry of N4/N5~1.6 for the known Jupiter Trojans. The uncertainties of the system parameters, e.g. Jupiter's eccentricity and inclination, the inclination distribution of Jupiter Trojans, are also taken into account and our results about the L4/L5 asymmetry have been further validated. However, the resonant amplitudes of the simulated Trojans are excited to higher values compared to the current population. A possible solution is that collisions among the Trojans may reduce their resonant amplitudes.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Context. More than 10000 Jupiter Trojans have been detected so far. They are moving around the L4 and L5 triangular Lagrangian points of the Sun-Jupiter system and their distributions can provide important clues to the early evolution of the Solar System. Aims. The number asymmetry of the L4 and L5 Jupiter Trojans is a longstanding problem. We aim to test a new mechanism in order to explain this anomalous feature by invoking the jumping-Jupiter scenario. Methods. First, we introduce the orbital evolution of Jupiter caused by the giant planet instability in the early Solar System. In this scenario, Jupiter could undergo an outward migration at a very high speed. We then investigate how such a jump changes the numbers of the L4 (N4) and L5 (N5) Trojans. Results. The outward migration of Jupiter can distort the co-orbital orbits near the Lagrangian points, resulting in L4 Trojans being more stable than the L5 ones. We find that, this mechanism could potentially explain the unbiased number asymmetry of N4/N5~1.6 for the known Jupiter Trojans. The uncertainties of the system parameters, e.g. Jupiter's eccentricity and inclination, the inclination distribution of Jupiter Trojans, are also taken into account and our results about the L4/L5 asymmetry have been further validated. However, the resonant amplitudes of the simulated Trojans are excited to higher values compared to the current population. A possible solution is that collisions among the Trojans may reduce their resonant amplitudes.
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