Dynamics of Flexible Appendages Mounted on Lagrangian Point Satellites

Paper number

IAC-06-C1.3.03

Author

Mr. Brian Wong, McGill University, Canada

Coauthor

Prof. Arun Misra, McGill University, Canada

Year

2006

Abstract

The search for extra solar system planets is one of the major goals of astronomy. A new generation of planet finding observatories, such as the Terrestrial Planet Finder (TPF) and the Darwin mission, is designed to directly detect Earth-sized planets around the distant stars and analyse their atmosphere for chemical signs that hint at the presence of life.A major challenge to detecting extrasolar planets is that the planets are much dimmer than the star they orbit. A technique called nulling interferometry can combine the signals received from two or more telescopes in a way that dims the starlight by a factor of a million, enabling the faint signals from the planet to be detected. The telescopes in the interferometer have to be cooled to around five degrees Kelvin and be placed in a precise formation, and satisfying these two requirements calls for a different approach to the design of the planet finder and the selection of its orbit. 

 The interferometer formation can be maintained by mounting the separate telescopes on a structure, or by using tethered or free flying formations. Structure- mounted telescopes offer more precise formation control than free flying formations and are more mechanically reliable than tethered formations.  One of the locations considered for the planet finder is around the second Earth-Sun Lagrangian point (L2), region about 1.5 million kilometers from the Earth. At this location, the radiations from the Sun, the Earth and the Moon are all in the same direction as viewed by a spacecraft and can be blocked with a single shield. As L2 revolves around the Sun once a year, the entire celestial sphere can be observed.   

Past research in formation keeping at the Lagrangian point mainly dealt with tethered and free flying satellite formations. For the current research, the interferometer is modelled as five point masses connected together with four flexible booms, arranged in a cross formation. The centeral body is assumed to be relatively more massive than the booms and the end bodies, such that the center of mass of the system is located at the middle mass. The equations of motion of the system are derived using the Lagrangian method. This paper examines the dynamics of the flexible spacecraft, located near the second Sun-Earth Lagrangian point, taking into account the vibrations of the flexible booms. The vibration modes and frequencies of the booms are examined for several cases:  (i) while the system is fixed at L2 with no rotations about its center of mass, (ii) while the system is spinning about its center of mass and (iii) while the system is travelling in a Lyapunov or Halo orbit around L2. Numerical results for the motions of the center of mass and the transverse vibrations of the booms for the above cases would be presented.

Abstract document

IAC-06-C1.3.03.pdf

Manuscript document

IAC-06-C1.3.03.pdf (🔒 authorized access only).

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