Abstract
This study deals with the generalization of the Elliptic Restricted Three-Body Problem (ER3BP) by considering the effects of radiation and oblate spheroid primaries. This may illustrate a gas giant exoplanet orbiting its host star with eccentric orbit. In the three dimensional case, this generalization may possess two additional equilibrium points (<TEX>$L_{6,7}$</TEX>, out-of-plane). We determine the existence of <TEX>$L_{6,7}$</TEX> in ER3BP under the effects of radiation (bigger primary) and oblateness (small primary). We analytically derive the locations of <TEX>$L_{6,7}$</TEX> and assume initial approximations of (<TEX>${\mu}-1$</TEX>, <TEX>${\pm}\sqrt{3A_2}$</TEX>), where <TEX>${\mu}$</TEX> and <TEX>$A_2$</TEX> are the mass parameter and oblateness factor, respectively. The fixed locations are then determined. Our results show that the locations of <TEX>$L_{6,7}$</TEX> are periodic and affected by <TEX>$A_2$</TEX> and the radiation factor (<TEX>$q_1$</TEX>).
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