Stardust-R: the H2020
Space Debris and Asteroid research network
Distribution of near-Earth asteroids smaller than 100 meters in diameter
Current models of the orbital distribution of near-Earth asteroids (NEAs) do not take into account non-gravitational forces, such as the Yarkovksy and Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effects, and they are tipically valid for objects down to few hundreds of meters in diameter. One of the objectives of our research is to develop a new populaion model of NEAs smaller than 100 meters, that takes into account non-gravitational effects, that could be relevant at this small size.
We performed preliminary numerical simulations of objects arriving to the near-Earth region through the ν6, including the Yarkovsky effect in the dynamical model. The simulations showed that the orbital distribution of these objects is significantly changed, provided that the semi-major axis drift induced by the Yarkovsky effect is large enough (see Figure 1), and also the residence time in the near-Earth region is statistically different.
Currently, we are collaborating with Detlef Koschny from the European Space Agency and with Michael Frühauf from the Technical University of Munich on the development of a new distribution model.
Figure 1. Scheme of the Yarkovsky (top figure) and the YORP (bottom figure) effects on asteroids.
Implementation of Yarkovsky and YORP effects in orbit9 and mercury N-body codes
Figure 2. Scheme of the Yarkovsky (top figure) and the YORP (bottom figure) effects on asteroids.
The Yarkovsky and Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effects are non-gravitational forces
due to thermal radiation affecting asteroids smaller than about 40 km in diameter. The Yarkovsky effect causes a drift in the semi-major axis of the asteroid orbit, and the direction of the drift depends on the rotation on the asteroid itself. If the rotation is coherent with the orbital motion, the thermal radiation is opposite to the orbital velocity, and it causes the semi-major axis to increase. On the contrary, if the rotation is opposite to the orbital motion, the thermal radiation has the same direction of the orbital velocity, and it casues the semi-major axis to decrease. The top panel of Figure 2 shows a scheme of the Yarkovsky effect.
The YORP effect is still due to thermal radiation, and it affects the rotation state of asymmetric objects. Because of the asymmetries, the direction of the thermal re-radiation is not isotropic (see Figure 2, bottom panel), and it produces a non-zero net torque. This torque caused the spin-axis and the rotation period of the asteroid to evolve with time. Since the Yarkovsky effect depends on the spin state these two effects are coupled, and the orbital dynamics should be integrated together with the rotational dynamics.
Since these two effects can not be neglected when analysing the long-term dynamics of small asteroids, we included them in two popular N-body codes used in the astronomical community, namely orbit9 (included in the orbfit package) and mercury. These two packages are suitable for statistical studies of asteroid populations, such as asteroid families. The modified versions of orbfit and mercury are publicly available on GitHub, and they are available to the astronomical community. Details of the implementation can be found on this paper.
Figure 3. The orbit of (469219) Kamo'oalewa (in green) as seen from a
frame co-rotating with the Earth (blue dot). The red curves are the orbits of Mercury,
Venus, and Mars.
Near-Earth asteroid (469219) Kamo'oalewa (previously known as 2016 HO3) is an Earth co-orbital object,
meaning that it is in 1:1 mean motion resonance with our planet. The short-term dynamics is characterized by a
periodic switching between a quasi-satellite configuraition (libration of the critical
angle around 0 deg) and a horseshoe configurations (libration of the critical angle about
180 deg, with an amplitude of almost 180 deg). The orbit, as seen from a frame co-rotating with
the Earth, is shown in Figure 3, and at about t = 2300 yr we can appreciate the switching
from quasi-satellite to horseshoe.
Since this object remains close to the Earth for at
least 300 years in the future, it is a good candidate for future exploration missions. Up
to now, two missions have been proposed: the first one, the Near-Earth Asteroid Characterization and Observation
(NEACO), is a concept study aimed to map the surface, develop a shape model,
estimate the mass, and understand the composition of the surface of Kamo'oalewa; the second one,
the ZhangHe, has been designed by the Chinese Academy of Space Technology and it
consists in a sample-return mission to Kamo'oalewa and the subsequent exploration of the main-belt
comet 133P/Elst-Pizarro.
Due to the small diameter of only about 36 meters, the Yarkovsky effect
may play a significant role in the long-term dynamics.
We investigated the role of the introduction of the Yarkovsky effect by propagating orbital clones
for 10 million years in the future.
The Yarkovsky effect has been estimated assuming different compositions for the surface.
Since surface properties are not known, we took into account the three most likely
possibilities: regolith covering (low thermal conductivity), porous rocky surface
(low to moderate thermal conductivity), and bare rock surface (high thermal conductivity).
Our simulations shown that the Yarkovsky effect may cause asteroid Kamo'oalewa to exit from
the Earth co-orbital region slightly faster than using a purely gravitational model,
especially in the case that regolith is kept on the surface (see Figure 4). Despite this early removal,
Kamo'oalewa might remain an Earth companion for at least 0.5 My in the future, making it
one of the most stable Earth's co-orbital objects known so far, even in the long-term evolution.
Figure 4. The time spent in the Earth co-orbital regions by the orbital
clones of Kamo'oalewa, for different value of thermal conductivity K (green bars). Red
bars are the times obtained using a pureli gravitational model.
Proper elements of resonant planet-crossing asteroids
Figure 5. Comparison between the non-resonant (red curve) and the resonant (blue curve) secular dynamics of the NEO (5381) Sekhmet.
Proper elements are quasi-integrals of the N-body problem, meaning that they are almost constant in time. These quantities permit to describe the long-term evolution of an object with only a few parameters, and they have interesting application in astronomy, such as the identification of asteroid families or the mapping of secular resonances. Contrary to main-belt asteroids, near-Earth asteroids (NEAs) generally have large eccentricity, and therefore they may cross the orbit of one or more planet. A theory of proper elements for NEAs have been developed in the early 2000s, and the values for known objects are now reported on NEODyS.
However, the theory developed so far is valid only when the NEA is not in a mean-motion resonance with a planet. In the paper Proper elements for resonant planet-crossing asteroids, we extended the theory of proper elements of NEAs taking into account the effects of the mean-motion resonance, that could be significant in the long-term dynamics (see Figure 5).
