Tethered spacecraft in an asteroid gravitational environment
- Paper number
IAC-17,D4,5,15,x40589
- Author
Prof. Alexander Burov, A.A.Dorodnicyn Computing Centre, FRC Computer Science and Control, Russian Academy of Sciences & Higner School of Economics, Russian Federation
- Coauthor
Prof. Anna Guerman, Centre for Mechanical and Aerospace Science and Technologies (C-MAST), Portugal
- Coauthor
Prof. Ivan Kosenko, Dorodnitsyn Computing Center, Russian Academy of Sciences, Russian Federation
- Coauthor
Mr. Vasily Nikonov, FRC Computer science and control, Russian Academy of Sciences, Russian Federation
- Year
2017
- Abstract
We examine dynamics of spacecraft tethered to the surface of an asteroid in the framework of a quite simple analytical model. The problem of existence and stability of equililibria for an inverted pendulum suspended at a point of a uniformly rotating asteroid with an arbitrary mass distribution is considered. Conditions of existence and stability are expressed as functions of pendulum's length. The results are compared with those obtained for terrestrial and lunar gravitational conditions. The feasibility of the asteroid elevator with a massless inextensible tether is also discussed. It is known that in vicinity of natural bodies an inverted pendulum exhibits instability due to the combination of gravitational and centrufugal forces; this instability relates to the local maximum of the augmented potential. As is also known, a very long inverted penulum is stable due to the local minimum of the augmented potential provided by the centrfugal force. Naturally, it is expected that the interval between the maximum and minimum of the augmented potential should contain bifurcations and intermediate relative equilibria related to a saddlepoint of the augmented potential. This effect has been detected in [1,2] for a lunar pendulum anchored in a plane of the lunar orbit (see also [3,4]). For a pendulum suspended at a point in the Earth equator, similar properties have been detected in [5]. The results are compared with those obtained for terrestrial and lunar gravitational conditions. The feasibility of the asteroid elevator with a massless inextensible tether is also discussed (cf. [6,7]). [1] Ricard N. {\' E}tude en stabilit{\'e} de l'ascenseur lunaire. Rapport d'activit{\' e}. Moscou. Juin 2004.35 p. [2] Burov A.A. and Ricard N. On lunar elevator. Proc.XXIX Academic Conference on Cosmonautics. Moscow,2005. [3] Burov A.A., Guerman A.D., Kosenko I.I. Equilibrium configurations and control of a moon-anchored tethered system. Advances in the Astronautical Sciences. 2013. Vol.146, pp.251-266. [4] Burov A.A., Guerman A.D., Kosenko I.I. Dynamics of moon elevator. 65th International Astronautical Congress, Toronto, Canada. IAC-14-D4.3.9. [5] Burov A.A., Kosenko I.I. Stability and bifurcations of relative equilibria of a pendulum suspended on the equator. Cosmic Research. 2013. Vol.51. Issue 3, pp.209–212. [6] Synge J.L. On the Behaviour, According to Newtonian Theory, of a Plumb Line or Pendulum Attached to an Artificial Satellite. Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences. 1959. Vol.60,pp.1-6 [7] Blitzer Leon, Equilibrium and stability of a pendulum in an orbiting spaceship. American Journal of Physics. 1979. Vol.47,p.241.- Abstract document
- Manuscript document
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