Non-collinear libration points in ER3BP with albedo effect and oblateness

Abstract

In this paper we establish a relation between direct radiations (generally called radiation factor) and reflected radiations (albedo) to show their effects on the existence and stability of non-collinear libration points in the elliptic restricted three-body problem taking into account the oblateness of smaller primary. It is discussed briefly when \(\alpha =0\) and \(\sigma =0\), the non-collinear libration points form an isosceles triangle with the primaries and as e increases the libration points \(L_{4,5}\) move vertically downward (\(\alpha \), \(\sigma \) and e represents the radiation factor, oblateness factor and eccentricity of the primaries respectively). If \(\alpha = 0\) but \(\sigma \ne 0\), the libration points slightly displaced to the right-side from its previous location and form scalene triangle with the primaries and go vertically downward as e increases. If \(\alpha \ne 0\) and \(\sigma \ne 0\), the libration points \(L_{4,5}\) form scalene triangle with the primaries and as e increases \(L_{4,5}\) move downward and displaced to the left-side. Also, the libration points \(L_{4,5}\) are stable for the critical mass parameter \(\mu \le \mu _{c}\).