The population of natural Earth satellites

Abstract: We have for the first time calculated the population characteristics of the Earth's irregular natural satellites (NES) that are temporarily captured from the near-Earth-object (NEO) population. The steady-state NES size-frequency and residence-time distributions were determined under the dynamical influence of all the massive bodies in the solar system (but mainly the Sun, Earth, and Moon) for NEOs of negligible mass. To this end, we compute the NES capture probability from the NEO population as a function of the latter's heliocentric orbital elements and combine those results with the current best estimates for the NEO size-frequency and orbital distribution. At any given time there should be at least one NES of 1-meter diameter orbiting the Earth. The average temporarily-captured orbiter (TCO; an object that makes at least one revolution around the Earth in a co-rotating coordinate system) completes $(2.88\pm0.82)\rev$ around the Earth during a capture event that lasts $(286\pm18)\days$. We find a small preference for capture events starting in either January or July. Our results are consistent with the single known natural TCO, 2006 RH$_{120}$, a few-meter diameter object that was captured for about a year starting in June 2006. We estimate that about 0.1% of all meteors impacting the Earth were TCOs.

The Population of Natural Earth Satellites

The paper by Granvik, Vaubaillon, and Jedicke provides a comprehensive analysis of the temporarily captured natural satellite (NES) population of Earth. Utilizing near-Earth objects (NEOs) as a source population, the research determines the steady-state characteristics of these satellites that are captured from the heliocentric stream and orbit Earth transiently. This rigorous investigation presents a well-defined statistical framework for understanding NES size-frequency distribution, capture probabilities, and associated residence times under the gravitational influences of the Sun, Earth, and Moon.

Key Findings

1. Size-Frequency Distribution and Capture Probability: The paper calculates for the first time the NES size-frequency distribution and capture probabilities correlated with the heliocentric orbital elements of NEOs. The analysis concludes that there should be at least one NES with a diameter of approximately one meter orbiting Earth at any given time.

2. Capture Event Characteristics: Temporarily Captured Orbiters (TCOs) undergo an average of 2.88 revolutions around Earth, with an average capture duration of 286 days. Interestingly, the capture events are slightly more likely to originate in January or July, reflecting a periodic dynamic influenced by the Earth's heliocentric orbit.

3. Empirical Validation: The findings are consistent with the properties of the only known natural TCO, 2006 RH$_{120}$, which had been captured earlier in 2006 for about a year. The similarity in metrics between this single observed event and the derived average statistics lends credibility to the theoretical model.

4. Impact Probability: The residence-time distributions suggest that approximately 0.1% of impacting meteors on Earth were previously NES, implying a distinctive orbital evolutionary mechanism for these meteorites.

Methodological Advances

The research uses a sophisticated analytical approach to establish the capture probabilities using heliocentric orbital elements. By marrying this probabilistic model with current NEO orbital distributions and size-frequency distributions, the authors effectively detail the statistical likelihood of a trajectory leading to a temporary Earth capture. Additionally, by leveraging the minor variation in heliocentric distances (0.87 AU to 1.15 AU) and factoring in low inclinations, the researchers simulate interactions at scales not typically resolved in asteroid surveys.

Theoretical and Practical Implications

The analysis offers both theoretical and practical insights into smaller asteroids' dynamics and behavior, providing an empirical foundation for future studies. The published results motivate prospects for NES missions, which can provide a "remote laboratory" for long-term studies on the physical properties of diminutive celestial bodies. Prospective retrieval missions to these captured objects could offer unprecedented scientific opportunities for characterizing material previously inaccessible without impacting Earth.

Future Research Directions

This study suggests several avenues for further inquiry. Improved detection techniques could enhance NES identification and observation, lending further data to refine the probabilistic models and understand NEO orbital mechanics better. Additionally, a deeper analysis of the influence of non-gravitational forces on small NEO dynamics could yield more granular population statistics, particularly given the growing resolution of observational apparatus.

Overall, this paper builds a fundamental understanding of Earth's temporary satellites, inviting further exploration into minor body dynamics within Earth's celestial neighborhood.