Locations of L 4,5 of a dust grain type II comet tail in Solar-Jupiter system in the photogravitational relativistic R3BP

A calculating formula when q∈(−∞, 1] for the locations of the triangular points L 4,5 in the relativistic restricted three-body problem is proposed when the bigger primary is a source of radiation with a mass reduction factor q. As an application, we consider a dust grain in type II comet tail in Solar-Jupiter system with a mass reduction factor q∈(−1.2, 0.5). An investigation in this neighborhood reveals that the shifts due to the relativistic terms on the locations of a dust grain particle are very small with the shifts in ξ— coordinate smaller than those of η— coordinate. It is further observed that increasing negative values of q results in moving L 4,5 further away from the line joining the primaries and towards the smaller primary. Increasing positive values of q, however results in a shift of L 4,5 towards both the line joining both primaries and towards the smaller primary.