On the elliptic restricted problem of three bodies

Abstract

Allowing nonzero eccentricity for Jupiter's orbit, the differential equations of motion of the restricted problem are presented. The simple form of the equations is obtained by using the true anomaly of the pri- maries as the independent variable and by introducing a special set of dimensionless variables describing the position of the third body. The short- and long-time effe ts of the eccentricity of the orbits of the pri- maries are discussed in connection with the generalized Jacobi integral. The similarity between the equations for the circular and for the elliptic case permits the introduction of regularizing transformations following methods applicable for the circular case. The major effect of the ec- centricity is that the regularized equations are in the form of integro-differential equations.