The distributions of positions of Minimal Orbit Intersection Distances among Near Earth Asteroids

https://doi.org/10.1016/j.asr.2012.04.005Get rights and content

Abstract

This paper presents the distributions of the positions of the Minimal Orbit Intersection Distances (MOID) among three subgroups of the Near Earth Asteroids (NEAs). This includes 683 Atens, 4185 Apollos and 3538 Amors which makes over 15 millions combinations of the pairs of orbits. The results which are obtained in this analysis show very interesting distributions of positions of the MOIDs and circumstances of close approaches of the asteroids and emphasize influence of different orbital elements on these distributions.

Highlights

► We examined the distribution of positions of MOIDs between Near Earth Asteroids. ► Most probable circumstances of close approaches and possible collisions are found. ► Results can be used for development of fast algorithms for MOIDs determination.

Introduction

Analysis of the distribution of orbital elements of the points corresponding to the MOIDs between the NEAs is important for several purposes. This allows the estimation of the probability of collisions between the asteroids and the most probable circumstances of these collisions, and also the close approaches. Since every collision between the NEAs can produce a new Potentially Hazardous Asteroid (PHA), it is of an essential importance to explore all circumstances under which these collisions and close approaches occur.

There are different approaches for the determination of the MOID between two confocal elliptical orbits. Most of these approaches includes the determination of all critical points of the distance function between two keplerian orbits, namely proximities (minima) among which the smallest one is the MOID, maxima and saddle points.

Generally, methods for determination of the critical points between two keplerian orbits can be divided in three groups: Numerical, analytical and combined. There are several analytical approaches to this problem. Two most frequently used are those by Gronchi (2002) which uses Fast Fourier Transform to obtain coefficients of the resultant of the two bivariate components of the gradient of d2 (squared distance) with respect to one variable, and by Kholshevnikov and Vassiliev (1999) which relies on determination of all real roots of a trigonometric polynomial of degree 8. There are also extensions of these methods to all types of conical sections (Gronchi, 2005, Baluyev and Kholshevnikov, 2005) which present algorithms for the determination of all critical points between any combination of circular, elliptic, parabolic or hyperbolic orbits. Pure numerical methods are very simple for application but they include too much calculation to be applied on a large number of orbital pairs. They consist of the calculation of the distance between every two points on the orbits and analyzing the numerically represented distance function. There is also a recent combined method (Milisavljević, 2010, Segan et al., 2011) which uses some analytical expressions (Lazović, 1993) to transform the distance function which is the function of two eccentric anomalies, E1 and E2, into two numerically represented minimal distance functions which are function of only one variable, E1 and E2 respectively. Using this method, a very rare configuration of orbits with 4 proximities was found between two asteroids in the main asteroidal belt.

The objectives here are: firstly, by using already developed algorithm (Milisavljević, 2010, Segan et al., 2011) to determine all proximities between every two orbits which belong to the three subgroups of the NEAs, secondly, to determine the MOIDs between these orbits, and finally, to investigate if there are some patterns in their distributions. The main goal of this analysis is to explore the circumstances of the close approaches and possible collisions of the NEAs and also to give some ideas for the development of faster algorithms for the determination of the MOIDs.

Section snippets

Analysis

We calculated the MOIDs between every two orbits from the three subgroups of the NEAs, Atens, Apollos and Amors, which is in total 8406 asteroids and 15,244,858 pairs of orbits. The characteristics of these subgroups of asteroids are summarized in Table 1 where one can see that these three subgroups have similar values of the average mutual inclination but quite different values of the average eccentricity.

In Fig. 1 is presented the mutual geometry of two keplerian orbits with elements which

Results

In order to estimate the possibility and circumstances of close approaches and possible collisions, we calculated the probability density functions of the different orbital parameters of the points corresponding to the MOIDs. In Fig. 2 is presented probability density function of the true longitudes of these points for all three subgroups of the NEAs together. This includes values for λ for both orbits in every analyzed pair and this is the case for each subsequent distribution in this paper.

Conclusions

The above analysis, made on over 15 millions of orbital pairs which is the largest number of the analyzed pairs up to date, can be summarized in three most important conclusions:

  • The probability for the MOID to occur in the vicinity of mutual nodes is an order of magnitude higher than that of occurring far enough from the mutual nodes.

  • The probability for the MOID to occur in the vicinity of the perihelion is higher than to occur in the vicinity of the aphelion.

  • Higher average eccentricity

References (7)

  • R.V. Baluyev et al.

    Distance between two arbitrary unperturbed orbits celest

    Mech. Dynam. Astron.

    (2005)
  • G.F. Gronchi

    On the stationary points of the squared distance between two ellipses with a common focus

    SIAM J. Sci. Comput.

    (2002)
  • G.F. Gronchi

    Algebraic method to compute the critical points of the distance function between two keplerian orbits celest

    Mech. Dynam. Astron.

    (2005)
There are more references available in the full text version of this article.

Cited by (3)

  • Meteoroid environment on the transfer trajectories to Mars

    2016, Aerospace Science and Technology
    Citation Excerpt :

    This method was chosen because it is highly efficient and allows fast calculation for a large number of orbits which is suitable for this analysis. There are also other parameters important for this analysis such as longitude of the points corresponding to MOIDs, with respect to the ascending node for every meteoroid orbit, which are shown in Fig. 4 [26]. The closest approach interface between the spacecraft on the transfer trajectory to Mars and the meteoroid is presented in Fig. 5.

  • SECULAR EVOLUTION OF THE MOID FOR NEAR-EARTH OBJECTS

    2021, Advances in the Astronautical Sciences
View full text