Updated rotating mass dipole with oblateness of one primary (I): equilibria in the equator and their stability

The rotating mass dipole is possibly used to approximate the potential distribution of nearly axisymmetrical elongated celestial bodies. To increase the accuracy of the approximation, an updated dipole system is proposed by taking the oblateness of one primary into account. The system is composed with a point mass and a spheroid with oblateness connected with a massless rod. Dynamic equations of the updated dipole system in body-fixed frame are derived in canonical system units. The potential distribution is determined with three parameters, including the mass ratio, the force ratio and the oblateness of the primary. Equilibrium points along with zero-velocity curves are given in the equatorial plane. The influence of the above three parameters on the distribution of equilibria are illustrated via numerical simulations. The stability of the system equilibria is discussed under linearized dynamic equations around each equilibrium point.