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This paper presents analytical solutions for the estimation of the Δ V cost of the transfer of a spacecraft subject to a low-thrust action. The equations represent an extension of solutions already available in the literature. Moreover, the paper presents novel analytical solutions for low-thrust transfers under the effect of the second-order zonal harmonics of the Earth's gravitational potential. In particular, the paper is divided into two parts. The first part presents analytical expressions for the Δ V cost of transfers. All analytical equations were validated through numerical integration of the dynamics of the spacecraft. The second part of the paper introduces new analytical equations for low-thrust transfers between circular inclined orbits with different values of the right ascension of the ascending node, under the effect of the second-order zonal harmonic of the Earth's gravitational potential. Both in the first and second parts, analytic solutions for the variation with time of the orbital elements during the transfer are presented. The proposed equations are applicable to low-thrust transfer realised through a long spiral trajectory. [ABSTRACT FROM AUTHOR]

This paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators. [ABSTRACT FROM AUTHOR]

In this paper two strategies are proposed to de-orbit up to 10 non-cooperative objects per year from the region within 800 and 1400 km altitude in Low Earth Orbit (LEO). The underlying idea is to use a single servicing spacecraft to de-orbit several objects applying two different approaches. The first strategy is analogous to the Traveling Salesman Problem: the servicing spacecraft rendezvous with multiple objects in order to physically attach a de-orbiting kit that reduces the perigee of the orbit. The second strategy is analogous to the Vehicle Routing Problem: the servicing spacecraft rendezvous and docks with an object, spirals it down to a lower altitude orbit, undocks, and then spirals up to the next target. In order to maximise the number of de-orbited objects with minimum propellant consumption, an optimal sequence of targets is identified using a bio-inspired incremental automatic planning and scheduling discrete optimisation algorithm. The optimisation of the resulting sequence is realised using a direct transcription method based on an asymptotic analytical solution of the perturbed Keplerian motion. The analytical model takes into account the perturbations deriving from the J 2 gravitational effect and the atmospheric drag. [ABSTRACT FROM AUTHOR]