Low-Thrust Maintenance of Libration Orbits
- Paper number
IAC-07-C1.3.09
- Author
Dr. Markus Landgraf, European Space Agency (ESA), Germany
- Coauthor
Dr. Uwe Feucht, European Space Agency/ESOC, Germany
- Year
2007
- Abstract
As libration orbits around the Lagrange points of the Sun-Earth system become more and more important for space science and fundamental physics missions, the need to improve the understanding of the statistical behaviour of the spacecraft state on those trajectories increases. Also, future spacecraft that are part of an interferometer constellation are likely to carry low-thrust propulsion systems, because of the requirement of highly precise proportional thrust control. Two examples of future missions that will employ low-thrust on libration missions are the ESA missions DARWIN, an infrared nulling interferometer for the detection of extra-solar planets, and LISA Pathfinder, a precursor mission that prepares the search for gravitational waves. While the thrust-to-mass ratio of the DARWIN spacecraft is in the order of 10 −5 N kg −1, the value for the LISA Pathfinder mission can be as low as 10 −7 N kg −1. The fundamental questions connected to the mission design of those missions are: given a realistic assumption on the noise environment and the accuracy of orbit determination, what are the statistical properties of the orbit maintenance manoeuvres, i.e., what is the maximum time between manoeuvres, and what is the dwell time of the spacecraft in the vicinity of the libration point after the last manoeuvre? Another question to be answered is what the minimum thrust level that is required for orbit maintenance on a libration trajectory.
Here, the situation is analysed in the linear theory of the motion around the libration points as well as with Monte-Carlo simulations of the problem. The minimum requirement on the thrust level is that the thrust acceleration must be greater than the amplification rate of any velocity dispersion. From linear theory it is known that this dispersion increases exponentially with time. Other, non-exponential contributions to the velocity dispersion can be neglected. Here it is shown that the minimum thrust level is given by the rule that the thrust duration of any orbit maintenance manoeuvre must be shorter than 15 days. Equivalently, for a given thrust level, the dispersion of the spacecraft state must not exceed a critical value, so that the correction manoeuvre can be performed within 15 days. This requirement determines the maximum time between orbit maintenance manoeuvres, given the orbit determination accuracy and the noise environment on the trajectory.
- Abstract document
- Manuscript document
IAC-07-C1.3.09.pdf (🔒 authorized access only).
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