Numerical Modeling of the Special Features in the Dynamics of Near-Moon Objects

Abstract

This report presents results of investigations into the special features of the orbital evolution of artificial Moon satellites (AMS) by numerical modeling. The motion of 5180 near-moon objects uniformly distributed in the near-moon space was modeled using the program Numerical Modeling of AMS Motion developed by the authors. The special features in the dynamics of near-moon objects are analyzed and the AMS lifetimes in the orbits are estimated depending on the semimajor axis and the orbit inclination. It is shown that this lifetime is very short for a number of near-moon zones, and the reasons for this phenomenon are elucidated.

1. Introduction

Recent interest has been increased in the study of the near-moon space. Attention is focused at the low near-moon orbits. Many authors, in particular, pointed out the existence of a dependence of the satellite lifetime on the orbit height and inclination. This work was aimed at elucidation of reasons for this phenomenon. We consider orbits with semimajor axes in the range from 1.1 to 15 of the Moon radius with inclinations from 0 to 180 degrees, and objects with flight heights of 100 km to compare our results with the results obtained by other authors. Modeling was performed for a 10-year time period taking into account perturbations of the selenopotential up to 50 order harmonics and degrees as well as gravitational effects of the Sun and Earth considered as material points. In addition to the estimation of the AMS lifetimes, we here present results of analysis of the special features in the dynamics of the objects that explain the reasons for the above-indicated phenomenon.

2. Results

The data shown in Figs. 1 and 2 illustrate the main features in the dynamics of the near-moon objects. Figure 1 shows the dependences of the increase in the AMS eccentricity and lifetime on the values of the semimajor axis and inclination for the entire ranges of their values, and Fig. 2 shows these dependences drawn in more detail for the low-orbiting objects. As can be seen, the increase of the eccentricity accompanied by the decrease of the lifetimes of satellites in the orbits is observed both for low and high orbits. Investigations showed that the reasons for this phenomenon differ at different heights, and for high objects, they significantly correlate with the orbital inclinations.

The increase of the eccentricity for the low orbits is caused by the complex structure of the gravitational field of the Moon. It is significant that if we consider only the Moon compression disregarding the special features of the field, no clearly pronounced increase of the eccentricity will be observed, and the lifetimes of all objects will exceed 10 years. These results are in good agreement with the data of other authors [1-3].

To explain the reason for the increase in the eccentricity for intermediate and great heights, we considered the influence of the Lidov–Kozai mechanism [4-6] on the orbital evolution of the AMS using numerical and analytical method [7]. This mechanism is manifested through the resonance and the Lidov–Kozai effect. The Lidov–Kozai effect was estimated based on the presence of the energy transfer between the eccentricity and the inclination while preserving the integral whereas the presence of the sharp Lidov–Kozai resonance was established based on the proximity to zero of the value of the Lidov–Kozai integral for a negative value of the Lidov integral 

Contours of the areas of influence of the mechanism (dark blue curves) and of the Lidov–Kozai effect (red curve) according to our estimates are shown in Fig. 1а. Our analysis of the results (Fig. 1а) has demonstrated that the main source of the eccentricity increase for еру intermediate and high orbits is the influence of the Lidov–Kozai mechanism on the AMS dynamics. The increase in the eccentricity of the high near-equatorial orbits is explained by the direct influence of the Earth.

3. Summary and Conclusions

Our investigations have shown that a significant number of the near-moon objects have short lifetime in the orbit, which is explained by the increase of the eccentricities of their orbits. Analyzing the results obtained, we can conclude that for the low orbits, this phenomenon is caused by the direct influence of the complex gravitational field of the Moon, and for the intermediate and high orbits, it is explained by the influence of the Lidov–Kozai mechanism.

Acknowledgements

This work was supported by the Russian Science Foundation (Scientific Project № 19-72-10022).

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