Stabilization of the triangular formation of the LISA satellites

Paper number

IAC-06-C1.3.05

Author

Ms. Janneke Bik, European Space Agency (ESA)/ESTEC, The Netherlands

Year

2006

Abstract

The joint ESA-NASA mission Laser Interferometer Space Antenna (LISA) consists of a triangular formation of three satellites. LISA will directly measure gravitational waves generated by compact binaries within our Galaxy and black hole binaries and mergers throughout the Universe. The gravitational waves are detected by measuring the stretching of space-time between the satellites with laser interferometry. The mission will test Einstein’s theory of general relativity and its main goal is to learn more about black holes, the evolution of stars and the Universe, through the new window of information gravitational waves offer.
The satellite formation is a general circular solution of the Hill-Clohessy-Wiltshire equations. This means that in linearised approximation the satellites will describe a circle around a reference point, maintaining a fixed position with respect to each other. The reference point, the centre of the triangle, orbits the Sun in a circular orbit, trailing the Earth at twenty degrees. When evaluating the complete equations of motion of the satellites, the distance between the satellites will vary about two percent and the angle between the arms from one satellite to the others will vary about one degree over the course of one year. Because LISA should be able to measure variations of the arm lengths as accurate as 40 pm it is crucial that the alignment of the telescopes with the connecting laser beam stays within 7 nrad and that the variation of the arm lengths stays as small as possible.
The LISA satellites are equipped with six micro-Newton engines to perform the so called ‘drag free’ control. This control should manoeuvre the satellite around its two cubical proof masses that float in almost perfect free fall within the spacecraft, that protects them from non-gravitational forces like the solar pressure. It is examined if the LISA satellites can be controlled using these micro-Newton engines such that the formation of the satellites stays constant. If this can be achieved no actuation of the telescopes is needed to align them with the incoming Laser beam. The control of the spacecraft is done with open-loop control. PID-control is used to account for the noise of the micro-Newton thrusters. A fuel cost estimation is made and the maximum distance between the satellites for which the formation can be kept constant is examined.

Abstract document

IAC-06-C1.3.05.pdf

Manuscript document

IAC-06-C1.3.05.pdf (🔒 authorized access only).

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