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Astron. Astrophys. 364, 327-338 (2000)

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5. Conclusions

One of the main issues of this work is to show the existence of regions of practical stability near the equilateral points of the real Earth-Moon system. As the classical RTBP model is not close enough to the real system, we have used a suitable intermediate model, the BCP. The study of this model has revealed the existence of quasi-stable regions, but outside the Earth-Moon plane. Finally, these regions have been numerically checked against a realistic model of the Solar system obtained from the JPL ephemeris. In this way, we avoid carrying out massive numerical simulations on the JPL model that could result in a prohibitive need of computer time. The results show that a relevant part of the stable regions of the BCP persists in the JPL, at least for 1 000 years.

A natural question is the persistence of these regions for longer time intervals. From the results presented here, we cannot give a conclusive answer to this question. We are currently working on this problem by using improved versions of the BCP, taking into account the Moon's eccentricity and inclination. The regions obtained for these models will be tested against longer numerical integrations of the Solar system. We believe that better models can give a deeper insight into many features of the dynamics, like the role played by resonances in the size and shape of these regions. Moreover, a more accurate determination of these regions could help to extend the quasi-stability times.

One of the possible reasons for interest in the regions around the family VF3 is that they could be a suitable place to look for some kind of dust or even some small asteroids. In this case, it would not be very difficult to send a probe there to pick up some samples. Moreover, these regions plus the regions around the family VF2 could also be of interest for some space missions, since no control is necessary to keep a spacecraft there.

The typical motion for a particle inside this region has been shown in Fig. 14 and Fig. 15. As has been mentioned in Sect. 3.2, it is clear that the largest part of the region corresponds to trajectories that cut the Earth-Moon plane with vertical speeds (relative to that plane) close to either 0.58 or 0.83, in adimensional units. This corresponds to speeds close to either 0.56 or 0.80 km s-1. We note that the motion in the vertical direction is very close to an harmonic oscillator (with a period of a little less than a month), and that these trajectories reach an approximate angular separation over (or under) the Earth-Moon plane of either 30 or 40 degrees. Hence, as it happens in a typical harmonic oscillator, the trajectories must spend most of the time away from the Earth-Moon plane and near their maximum elongation. Then, to have the best chance of finding Trojan asteroids in the Earth-Moon system, one should focus the search around either 30 or 40 degrees over (and under) the Earth-Moon plane. Performing the search near that plane has a much lower chance of success and, even in this case, it can be difficult to confirm an observation since the asteroid is moving at its highest speed. In fact, there are records of a few observations of small dust clouds near the Earth-Moon Lagrangian points, but none of them has been confirmed subsequently (Freitas & Valdes 1980; Valdes & Freitas 1983).

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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