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This dataset accompanies the paper "Extended Analytical Formulae for the Perturbed Keplerian Motion Under Low-Thrust Acceleration and Orbital Perturbations", submitted to Celestial Mechanics and Dynamical Astronomy. It contains formulas used to obtain the osculating and averaged variations of the equinoctial elements for a spacecraft under the effect of J3, J4, J5 and third body perturbations. The J3, J4, and J5 integrals are contained in the Matlab files in "IntegralsJ3J4J5.zip" Their names indicate which perturbation and element is considered. The third body calculations are contained in "ThirdBody.zip" The Matlab code is contained in file "thirdbody_gauss.m" The sane formulas are also contained in two notebook files, which show their derivations: -"integrals.nb" contains the integrals mentioned in the paper -"Thirdbody_Legendre_coefficients.nb" contains the coefficients for the acceleration vector and for the VoP equations. Besides these files, two packages containing definitions for some of these formulas are also included, to save running time: -"integrals.wl" contains full formulas for the integrals -"split_integrals.wl" has the same integrals split into secular and short-periodic forms. Secular terms were modified to not require complex algebra, and the short-periodic were modified to eliminate singularities.

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.

The number of visited asteroids is low compared to the total number that exists. Only a few missions have ever had a close approach or rendezvous with NEAs to better understand them. Additionally, as most observations are made from Earth, the uncertainties in their orbital elements could be greatly reduced with closer range measurements, while also allowing for other physical quantities to be determined such as mass, albedo, dimensions, and surface features. This concurrent design study acts as a feasibility study for a new concept of nanosatellite mission framework which is intended to allow reconnaissance of a large number of NEAs while minimizing cost. The presented mission framework consists of pairs of nanosatellites travelling together on multi-target flyby trajectories, and is designed to be flexible to suit many different target sets. One such set is presented in detail, however the methods used to find this set also generated many other possible multi flyby trajectories that could equally be launched.

This paper presents an analysis of new potential space missions to Near Earth Objects (NEOs) using nano-satellites and low-thrust propulsion. Both rendezvous and flyby scenarios are examined over a launch window that goes from 2024 to 2034. The paper first investigates the reachability of thousands of sample asteroids taken from the existing database of NEOs. Then, a sensitivity analysis is performed on a large number of transfers to study the effect of uncertainty on the initial mass at launch, thrust level and specific impulse of the engine. This second step provides information on the required spacecraft system and it is used to perform a more detailed trajectory optimisation on a selected scenario to study the effect of uncertain boundary conditions and disturbance on the control. Finally, an analysis is performed to assess how to improve our knowledge of some asteroid attributes during a flyby by using sensors that can be installed on board a nano-satellite.

The design and planning of space trajectories is a challenging problem in mission analysis. In the last years global optimisation techniques have proven to be a valuable tool for automating the design process that otherwise would mostly rely on engineers’ expertise. The paper presents the optimisation approach and problem formulation proposed by the team Strathclyde++ to address the problem of the 9th edition of the Global Trajectory Optimisation Competition. While the solution approach is introduced for the design of a set of multiple debris removal missions, the solution idea can be generalised to a wider set of trajectory design problems that have a similar structure.

The design and planning of space trajectories is a challenging problem in mission analysis. In the last years global optimisation techniques have proven to be a valuable tool for automating the design process that otherwise would mostly rely on engineers’ expertise. The paper presents the optimisation approach and problem formulation proposed by the team Strathclyde++ to address the problem of the 9th edition of the Global Trajectory Optimisation Competition. While the solution approach is introduced for the design of a set of multiple debris removal missions, the solution idea can be generalised to a wider set of trajectory design problems that have a similar structure.

This paper proposes a global optimisation of the low-thrust transfers from GTO to GEO incorporating different types of perturbation. The trajectory transcription method makes use of an analytical solution of the perturbed Keplerian motion together with a simple direct collocation of the thrust arcs. The paper will show that low-thrust GTO to GEO transfers exhibit a number of local minima with a small but not negligible difference. The paper presents different strategies to explore the set of local minima and shows a number of locally optimal solutions.

This paper presents the preliminary design of the international space mission HECATE (Human Exploration of Cis-lunar space via Assets Tele-operated from EML-2), aimed at exploring the far side of the Moon via tele-robotic activities during the 2020s. The exploration is realized by astronauts from HOPE (Human Orbiting Protected Environment), a space habitat in a halo orbit around the Earth-Moon Lagrange Point 2, a critical staging location for future robotic and human deep space missions. Inside the habitat, astronauts have access to tele-robotic hardware and instruments, used to tele-operate rovers and scientific equipment on the surface of the Moon. Plans to resupply and maintain HOPE for future missions, using a solar electric tug, are given. Ultimately, HOPE represents an energetically favorable intermediate locations for missions to Mars, Near-Earth Asteroids, and beyond. &nbsp

CAMELOT (Computational-Analytical Multi-fidelity Low-thrust Optimisation Toolbox) is a toolbox for the fast preliminary design and optimisation of low-thrust trajectories. It solves highly complex combinatorial problems to plan multi-target missions characterised by long spirals including different perturbations. In order to do so, CAMELOT implements a novel multi-fidelity approach combining analytical surrogate modelling and accurate computational estimations of the mission cost. Decisions are then made by using two pptimisation engines included in the toolbox, a single objective global optimiser and a combinatorial optimisation algorithm. CAMELOT has been applied to a variety of applications: from the design of interplanetary trajectories to the optimal deorbiting of space debris, from the deployment of constellations to on-orbit servicing. In this paper the main elements of CAMELOT are described and two space mission design problems solved using the toolbox are described.

In this paper two novel strategies to automatically design an optimized mission to de-orbit up to 10 non-cooperative objects per year are proposed, targeting the region within 800 and 1400 km altitude in 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 performs the re-entry. The second strategy is analogous to the Vehicle Routing Problem: The servicing spacecraft rendezvous with an object, spiral it down to a lower altitude orbit, and spiral up to the next target. In order to maximize the number of de-orbited non-operative objects with minimum propellant consumption, an optimal sequence of targets is identified using a bio-inspired incremental automatic planning and scheduling discrete optimization algorithm. The incremental planning and scheduling algorithm uses a model based on optimal low-Thrust transfer between objects. The optimization of the transfers is realized using a direct method and an analytical propagator based on a first-order solution of the perturbed Keplerian motion. The analytical model takes into account the perturbations deriving from the J2 gravitational effect and the atmospheric drag.

There is a demand for communications services at high latitudes that is not well served by conventional geostationary satellites. Alternatives using low-altitude orbits require too large constellations. Other options are the Molniya and Tundra families (critically-inclined, eccentric orbits with the apogee at high latitudes). In this work we have considered derivatives of the Tundra type with different inclinations and eccentricities. By means of a high-precision model of the terrestrial gravity field and the most relevant environmental perturbations, we have studied the evolution of these orbits during a period of two years. The effects of the different perturbations on the constellation ground track (which is more important for coverage than the orbital elements themselves) have been identified. We show that, in order to maintain the ground track unchanged, the most important parameters are the orbital period and the argument of the perigee. Very subtle changes in the orbital period (due mainly to lunar perturbations) cause a large east-west drift of the ground trace which dwarfs the displacement due to the regression of the ascending node. From these findings, a station-keeping strategy that minimizes propellant consumption has then been devised. Our results offer interesting guidelines for the design and operation of satellite constellations using these orbits.