Asteroids orbiting the Solar System establish movement patterns similar to those of Earth, Venus, and Mars, and are classified as co-orbital asteroids. Although their trajectories are not identical to those of rocky planets, these celestial bodies take the same amount of time to complete an orbit around the Sun.
This condition is the result of a gravitational phenomenon known as orbital resonance. Specifically, in the case of planets and their co-orbital asteroids, the resonance involved is of the 1:1 type, implying that they share a very similar orbit around the Sun and have nearly equal orbital periods.
Investigation of Gravitational Interaction
An investigation conducted by Valerio Carruba from the Faculty of Engineering and Sciences (FEG) at Unesp's Guaratinguetá campus analyzed how this resonance can interact with another gravitational mechanism, the von Zeipel–Lidov–Kozai (ZLK) mechanism. The researchers discovered that this interaction can help protect some of these objects against close collisions with the planets.
The work, titled “Co-orbital asteroids of terrestrial planets affected by the von Zeipel–Lidov–Kozai mechanism,” was published in the journal Celestial Mechanics and Dynamical Astronomy and received the CELMEC IX Prize. This award recognizes the best original articles published in the special collections of the said journal. In addition to Carruba's study, the scientific committee selected two other awarded research papers. The three winners will present their findings at the ninth International Meeting of Celestial Mechanics (CELMEC IX), which will take place from September 14 to 18 in San Martino al Cimino, Italy, organized by the Italian Society of Celestial Mechanics and Astrodynamics.
Carruba, coordinator of the MASB (Machine Learning Applied to Small Bodies) research group, stated that the recognition is an achievement both individual and for the group, expressing positive surprise about the award after the article's publication.
Understanding the Concept of a Co-orbital Asteroid
For better understanding, a co-orbital asteroid can be imagined as an object that moves in synchrony with a specific planet, rather than revolving independently around the Sun. Even if their orbits have different shapes and positions, both take approximately the same amount of time to circle the star. This synchronization is a result of 1:1 mean motion resonance.
A notable example of this phenomenon is Jupiter's Trojan asteroids, of which about 11,000 are known. They share the orbit of the gas giant and form dense clusters.
However, the study of co-orbital asteroids of rocky planets presents additional challenges due to the combination of gravitational stability and difficulties in astronomical observation.
Influence of Planetary Mass and Lagrange Points
The first challenge relates to the mass of the planets, which defines the strength of their gravitational 'traps,' called Lagrange points. Each planet has five Lagrange points (L1, L2, L3, L4, and L5). Points L1, L2, and L3 are considered unstable, while L4 and L5 can be stable.
Massive planets, such as Jupiter and Neptune, have wider areas of dynamic stability linked to 1:1 resonance, allowing thousands of small bodies to remain in stable configurations for billions of years, including those associated with points L4 and L5.
In rocky planets, due to their smaller masses, the stability zones of 1:1 resonance are more restricted, making co-orbital bodies more vulnerable to gravitational perturbations from the rest of the Solar System.
Carruba mentions that space telescopes are sent to points L1 and L2, but because they are unstable, they require constant corrections. In contrast, objects at points L4 and L5 can maintain their orbit for much longer periods.
Limitations in Astronomical Observation
Besides the complexity of celestial mechanics, there is a significant observational limitation in mapping these asteroids. While the co-orbitals of gas giants can be seen at night, the co-orbitals of Venus and other inner belt planets are only visible when they are very close to the direction of the Sun in the sky.
This solar proximity makes detecting these rocks difficult, as they are naturally small and dark, due to the Sun's glare and limited observation windows. Carruba points out that there is much imprecision in the knowledge of many orbits, citing Venus as a complicated case, whose asteroids can be observed, on average, only for two weeks every six years.
This difficulty results in a numerical disparity: while gas giants have thousands of known co-orbitals, the total for rocky planets does not exceed a few dozen. Currently, Venus has 21 known co-orbitals, Earth has 54 (plus 15 temporary ones), and Mars, the most studied among the rocky ones, confirms 48 co-orbitals. No Mercury co-orbital is known due to its extreme proximity to the Sun.
The Role of the von Zeipel–Lidov–Kozai (ZLK) Mechanism
The main focus of Carruba's group's study was to understand what happens when co-orbital asteroids, already in 1:1 resonance, also exhibit the dynamics of the von Zeipel–Lidov–Kozai (ZLK) mechanism. This mechanism describes oscillations in the inclination and eccentricity of orbits caused by gravitational perturbations.
In simulations, considering the perturbations from all planets in the Solar System and the Moon, the researchers investigated how this dynamic affects the stability of the co-orbitals of Venus, Earth, and Mars.
While 1:1 resonance maintains synchronized mean motion, the ZLK mechanism can induce changes in eccentricity and inclination. Eccentricity measures the deviation of an orbit from a perfect circle (the more oval, the higher the eccentricity), and inclination refers to the angle of the orbital plane relative to a reference plane. Simply put, ZLK causes these two characteristics to oscillate in a correlated way, like a balancing effect.
Another crucial aspect of ZLK is the orientation of the orbit. In non-resonant situations, the argument of perihelion can vary continuously. In the ZLK state, however, this angle can oscillate or 'precess' around specific centers (0°, 90°, 180°, and 270°), restricting the geometry of the orbit and, in certain configurations, preventing the asteroid from getting too close to a planet, promoting its stability.
Carruba explains that investigating this complex dynamic is vital because many of these co-orbital objects are extremely unstable, exhibiting unpredictable behavior; small trajectory uncertainties can generate large differences in just 150 years.
The search to understand these uncertainties is relevant for space agencies like ESA and NASA, which map potentially dangerous asteroids. The researcher notes that many asteroids are lost, changing configuration or leaving the region, and the instability makes it difficult to predict the new path.
One cited example is asteroid 2025 TV10, identified as a new Venus co-orbital. Its orbit is near a region of minimum orbital intersection distance with Earth, suggesting potential close approaches over millennia. Carruba emphasizes that although it is a dynamically interesting object worthy of monitoring, it is very small and would likely be destroyed in case of atmospheric impact.
The research demonstrated that the ZLK mechanism can stabilize certain orbits, offering a way to 'protect' asteroids from close encounters. Among Earth's co-orbitals in robust ZLK states (with precession at 0° and 180°), no close encounters were observed during the analysis, unlike a non-resonant sample. The simulators were extended to 100 thousand years to verify this protective effect.
The results indicate that, in ZLK states, resonance adds order to a system that would otherwise be chaotic. In certain circumstances, the oscillatory dynamic itself helps keep the asteroid away from close encounters that could drastically alter its trajectory.
For Venus, the researchers have not yet identified any known co-orbitals in a robust ZLK state, but Carruba warns that this might be an observational limitation, leaving some Venusian co-orbitals, especially those with lower eccentricity, unknown.
In Mars, the scenario is different, with only one object, 2017 XG62, identified in a robust ZLK state. Although high inclinations can increase the instability of other Martian co-orbitals, 2017 XG62 remains in a configuration that protects it from close encounters with other rocky planets.
