American Institute of Mathematical Sciences

Advanced
June  2007, 7(4): 755-778. doi: 10.3934/dcdsb.2007.7.755

On the uncertainty of the minimal distance between two confocal Keplerian orbits

Giovanni F. Gronchi 1, and  Giacomo Tommei 1,

1. 

Dipartimento di Matematica, Universitá di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy, Italy

Received  February 2006 Revised  January 2007 Published  March 2007

We introduce a regularization for the minimal distance maps, giving the locally minimal values of the distance between two points on two confocal Keplerian orbits. This allows to define a meaningful uncertainty for the minimal distance also when orbit crossings are possible, and it is useful to detect the possibility of collisions or close approaches between two celestial bodies moving approximatively on these orbits, with important consequences in the study of their dynamics. An application to the orbit of a recently discovered near-Earth asteroid is also given.
Keywords: orbit distance, Regularization, covariance propagation..
Mathematics Subject Classification: Primary: 70F15; Secondary: 70F1.
Citation: Giovanni F. Gronchi, Giacomo Tommei. On the uncertainty of the minimal distance between two confocal Keplerian orbits. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 755-778. doi: 10.3934/dcdsb.2007.7.755
[1]

Shao-Xia Qiao, Li-Jun Du. Propagation dynamics of nonlocal dispersal equations with inhomogeneous bistable nonlinearity. Electronic Research Archive, , () : -. doi: 10.3934/era.2020116
[2]

Kha Van Huynh, Barbara Kaltenbacher. Some application examples of minimization based formulations of inverse problems and their regularization. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020074
[3]

Liping Tang, Ying Gao. Some properties of nonconvex oriented distance function and applications to vector optimization problems. Journal of Industrial & Management Optimization, 2021, 17 (1) : 485-500. doi: 10.3934/jimo.2020117
[4]

Jia Cai, Guanglong Xu, Zhensheng Hu. Sketch-based image retrieval via CAT loss with elastic net regularization. Mathematical Foundations of Computing, 2020, 3 (4) : 219-227. doi: 10.3934/mfc.2020013
[5]

Cheng Peng, Zhaohui Tang, Weihua Gui, Qing Chen, Jing He. A bidirectional weighted boundary distance algorithm for time series similarity computation based on optimized sliding window size. Journal of Industrial & Management Optimization, 2021, 17 (1) : 205-220. doi: 10.3934/jimo.2019107

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences