Gravitational interaction of two planetesimals moving in close orbits
Abstract
Studies of the orbital evolution of two gravitationally interacting material  point objects moving around the sun are reported. The work was done basically by numerical integration of the plane threebody problem. The following types of orbital evolution were considered: motion about triangular libration points on tadpole and horseshoe synodic orbits (types M and N), the case of close approaches of the objects (type A), and chaotic variations of the orbital elements during which close approaches of the objects are impossible (type C). In the case of initially circular orbits with an initial angle \varphi_{°} = 60° between the lines to the objects from the sun vertex and 10^{9} ≤ μ ≤ 2 \cdot 10^{4}, the maximum values of \varepsilon_{°} = (a_2°  a_{1°})/ a_{1°} that correspond to types N, M, A, and C were found to be equal respectively to α =1.631.64 μ^{1/2}, β = 0.770.81 μ^{1/3}, γ = 2.12.45 &mu^{1/3} and δ = 1.451.64 μ^{2/7}, where a_{1°} and a_{2°} are the initial values of the semimajor axes and μ is the ratio of the sum of the masses of the objects to the mass of the sun. The values of α, β, and δ are generally smaller for other values of \varphi_{°}. When ∊_{°} =0, the smallest values of \varphi_{°}, which correspond to types N and M, are near 0.4 and 4 μ^{1/3} rad. The maximum eccentricities at μ_{1} ≤ 10^{5} did not usually exceed (78) \cdot μ_{1}^{1/3} for type A or (46) \cdot μ_{1}^{1/3} for type C, where μ_{1} is the mass of the larger object in sun masses.
 Publication:

Astronomicheskii Vestnik
 Pub Date:
 1994
 Bibcode:
 1994AVest..28...10I
 Keywords:

 THREEBODY PROBLEM;
 ORBITAL EVOLUTION;
 TADPOLE AND HORSESHOE ORBITS;
 CHAOTIC VARIATIONS;
 TYPES OF EVOLUTION