On the non-uniform distribution of the angular elements of near-Earth objects

Abstract

We examine the angular distributions of near-Earth objects (NEOs) which are often regarded as uniform. The apparent distribution of the longitude of ascending node, Ω, is strongly affected by well-known seasonal effects in the discovery rate of NEOs. The deviation from the expected π-periodicity in the apparent distribution of Ω indicates that its intrinsic distribution is slightly enhanced along a mean direction,Ω = 111 • ; approximately 53% of NEOs have Ω values within ±90 • ofΩ. We also find that each subgroup of NEOs (Amors, Apollos and Atens) has different observational selection effects which cause different non-uniformities in the apparent distributions of their arguments of perihelion ω, and longitudes of perihelion ̟. For their intrinsic distributions, our analysis reveals that the Apollo asteroids have non-uniform ω due to secular dynamics associated with inclination-eccentricity-ω coupling, and the Amors' ̟ distribution is peaked towards the secularly forced eccentricity vector. The Apollos' ω distribution is axial, favoring values near 0 and 180 • ; the two quadrants centered at 0 and 180 • account for 55% of the Apollos' ω values. The Amors' ̟ distribution peaks near̟ = 4 • ; sixtyone percent of Amors have ̟ within ±90 • of this peak. We show that these modest but statistically significant deviations from uniform random distributions of angular elements are owed to planetary perturbations, primarily Jupiter's. It is remarkable that this strongly chaotic population of minor planets reveals the presence of Jupiter in its angular distributions.

Geometric characterization of the Arjuna orbital domain

“…4 in JeongAhn & Malhotra 2014). In sharp contrast, most observed Arjunas appear clustered towards values of Ω where a lower fraction Table 1. of objects is found by JeongAhn & Malhotra (2014). That distribution is tentatively explained by JeongAhn & Malhotra as the result of secular perturbations by Jupiter.…”

“…In other words, 10 objects out of 13 reach perihelion far from the nodes. This is at odds with the overall distribution of arguments of perihelion of observed NEOs found by JeongAhn & Malhotra (2014), indicating that Arjunas are a somewhat distinct dynamical group. The values of the longitude of the ascending node of four objects are close to that of the Earth.…”

Orbital Alignment of Main-belt Comets

“…The alignment of osc values for osculating eccentricity-excited objects around J is evident (Figure 3d), in agreement with the observed osc alignment of currently active MBCs (blue circles), while the current osculating angular elements of other active asteroids (black crosses) are more broadly distributed. The osculating eccentricity of an object is maximized when 2ω osc = 180 • , where ω osc circulates due to secular perturbations (Kozai 1962;JeongAhn & Malhotra 2014), which explains the clustering of ω osc values at 90 • and 270 • for osculating eccentricity-excited objects ( Figure 3c, black histogram). This combination of ω osc -clustering at 90 • and 270 • and osc -clustering near 0 • then results in a weak concentration of Ω osc values (which are equivalent to osc − ω osc ) near 90 • and 270 • (Figure 3b, black histogram).…”

Towards a theoretical determination of the geographical probability distribution of meteoroid impacts on Earth

“…The distribution of asteroids and meteoroids in the Solar System is not uniform, either in physical or configuration space (see eg. Bottke et al 2002, JeongAhn & Malhotra 2014. Although the Earth is a small planet as compared to the scale of asteroid orbits and one may expect that impactors should come from every direction in sky, the complex relative dynamics between the population of parent bodies and the Earth, the focusing effect of Earth's gravitational field and even the presence of the Moon, could create non-trivial geographical patterns of impacts.…”