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In this paper, the feasibility of exploiting the Sun's gravitational force to design the final phase (capture and orbit circularisation) to Mercury with a low propellant consumption has been investigated. The initial conditions, on the eccentricity and argument of pericentre, for the circularisation phase are obtained from a prime integral of motion, which takes place when the probe moves over a polar orbit. A numerical analysis has highlighted how these initial conditions allow, under the third-body effect, an optimal reduction of eccentricity (circularisation phase) with limited variations of the other orbit elements, without requiring orbital manoeuvres. Then, by introducing a small velocity variation, the phase of ballistic capture has been joined to the circularisation phase. The obtained results can encourage the exploitation of this phenomenon in future missions for the exploration of Mercury. [ABSTRACT FROM AUTHOR]

The determination of analytical expressions which, including the main perturbative effects, allow the retrieval of the orbit elements of a probe represents an important requirement in designing science trajectories. One of these perturbations is given by the third body attraction. The case in which the perturbing body moves on a plane coincident with the equatorial plane of the primary body has been investigated in previous studies and equations able to provide the temporal evolution of the orbit elements have been determined and applied to the main moons of the Solar System. In this paper an extension of this topic has been carried out and equations which allow the determination of the orbit evolution have been analytically retrieved in the general case in which one or more perturbing bodies describe elliptical and inclined orbits with respect to the equatorial plane of the primary. Then, introducing these equations into the periodicity condition for the probe ground track, and considering the $$J_{2}$$ and $$J_{4}$$ effects coming from the primary body, an equation able to provide repeating ground track orbits has been determined. [ABSTRACT FROM AUTHOR]

In this paper, the design of science orbits for the observation of a celestial body has been carried out using polynomial equations. The effects related to the main zonal harmonics of the celestial body and the perturbation deriving from the presence of a third celestial body have been taken into account. The third body describes a circular and equatorial orbit with respect to the primary body and, for its disturbing potential, an expansion in Legendre polynomials up to the second order has been considered. These polynomial equations allow the determination of science orbits around Jupiter's satellite Europa, where the third body gravitational attraction represents one of the main forces influencing the motion of an orbiting probe. Thus, the retrieved relationships have been applied to this moon and periodic sun-synchronous and multi-sun-synchronous orbits have been determined. Finally, numerical simulations have been carried out to validate the analytical results. [ABSTRACT FROM AUTHOR]