General configurations of the symmetric restricted 4-body problem (Q1764136)

The authors consider a symmetric four-body problem where the primaries \(m_1\), \(m_2\) and \(m_3\) are situated at the vertices of an equilateral triangle (the masses are \(m_1=m_2=1\), \(m_3=\mu\)), and the fourth infinitesimal mass \(m_4 = \varepsilon\) is situated on an axis of symmetry of the triangle. The authors examine the number of central configurations in the restricted case \(\varepsilon = 0\) when the primaries remain in the equilateral triangle configuration and the mass \(m_4=\mu\) is taken as bifurcation parameter. It is found that the number of central configurations varies from 1 to 4.