Searching for Orbits with Minimum Fuel Consumption for Station-Keeping Maneuvers: An Application to Lunisolar Perturbations

The present paper has the goal of developing a new criterion to search for orbits that minimize the fuel consumption for station-keeping maneuvers. This approach is based on the integral over the time of the perturbing forces. This integral measures the total variation of velocity caused by the perturbations in the spacecraft, which corresponds to the equivalent variation of velocity that an engine should deliver to the spacecraft to compensate the perturbations and to keep its orbit Keplerian all the time. This integral is a characteristic of the orbit and the set of perturbations considered and does not depend on the type of engine used. In this sense, this integral can be seen as a criterion to select the orbit of the spacecraft. When this value becomes larger, more consumption of fuel is required for the station keeping, and, in this sense, less interesting is the orbit. This concept can be applied to any perturbation. In the present research, as an example, the perturbation caused by a third body is considered. Then, numerical simulations considering the effects of the Sun and the Moon in a satellite around the Earth are shown to exemplify the method

Parametric Optimization of Low Thrust Orbital Maneuvers

The goal of the present paper is to make a numerical analysis of parametric optimization of low thrust orbital maneuver. An orbital maneuver occurs when it is necessary to modify the orbit a space vehicle to change its function or to correct effects of perturbations. A parametric optimization is made when the thrust is not free to point to any direction, but has to follow some prescribed law, like a linear or quadratic relation with time

A Circular Restricted n-body Problem

This paper introduces the Circular Restricted n-Body Problem (CRNBP), an extension of the bicircular restricted four-body problem (BCR4BP) designed to describe the dynamics of an n-body system. In the CRNBP, each massive body in the system is constrained to follow a Keplerian motion, similar to the BCR4BP's artificial constraint. The CRNBP is an efficient alternative for trajectory design in multiple-body systems, particularly for outer planetary systems, as it requires integrating only six first-order ordinary differential equations compared to the 6N equations in an ephemerides model. By reproducing complex dynamical behaviors observed in ephemerides n-body problems, we demonstrate the structural stability of the CRNBP. Additionally, we propose a straightforward approach to relate the CRNBP with ephemerides, enabling the exploration of trajectory design possibilities before committing to a dedicated ephemerides analysis. This allows for the identification of general dynamical behaviors and provides valuable insights into the dynamics of multiple body systems. Finally, illustrative examples highlight the richness of trajectories and potential advantages of using the CRNBP for designing complex trajectories in outer planetary systems. The CRNBP proves to be a valuable tool for preliminary trajectory design, facilitating the identification of low-energy trajectories and providing a foundation for further exploration in future dedicated studies.Comment: Draft version of the article published in the JGC

Autonomous and Robust Orbit-keeping for Small Body Missions

This article presents a path-following control law for autonomous orbital maintenance of small body missions. The control law is robust, stable, and capable of controlling only the orbital geometry, allowing the spacecraft to operate with idle-thruster periods. It is entirely analytical and suitable for real-time operations. The control law is inspired by the two-body problem and uses sliding mode control theory to ensure robustness against bounded disturbances. Practical considerations, such as measurement noise, thruster limitations, and hysteresis-based control switching, are taken into account. The proposed control law is demonstrated and validated through several examples, including orbit-keeping around the asteroid Bennu, showing its feasibility and efficiency for small body missions. The results indicate that the control law can achieve precise and safe orbit maintenance with minimal fuel consumption, making it a valuable asset for autonomous space missions.Comment: Draft of the paper published by the JGC

A Comparison of Averaged and Full Models to Study the Third-Body Perturbation

The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made

Outer Planet Missions with Electric Propulsion Systems—Part I

For interplanetary missions, efficient electric propulsion systems can be used to increase the mass delivered to the destination. Outer planet exploration has experienced new interest with the launch of the Cassini and New Horizons Missions. At the present, new technologies are studied for better use of electric propulsion systems in missions to the outer planets. This paper presents low-thrust trajectories using the method of the transporting trajectory to Uranus, Neptune, and Pluto. They use nuclear and radio isotopic electric propulsion. These direct transfers have continuous electric propulsion of low power along the entire trajectory. The main goal of the paper is to optimize the transfers, that is, to provide maximum mass to be delivered to the outer planets

Dynamics of Artificial Satellites around Europa

A planetary satellite of interest at the present moment for the scientific community is Europa, one of the four largest moons of Jupiter. There are some missions planned to visit Europa in the next years, for example, Jupiter Europa Orbiter (JEO, NASA) and Jupiter Icy Moon Explorer (JUICE, ESA). in this paper, we search for orbits around Europa with long lifetimes. Here, we develop the disturbing potential in closed form up to the second order to analyze the effects caused on the orbital elements of an artificial satellite around Europa. the equations of motion are developed in closed form to avoid expansions in power series of the eccentricity and inclination. We found polar orbits with long lifetimes. This type of orbits reduces considerably the maintenance cost of the orbit. We show a formula to calculate the critical inclination of orbits around Europa taking into account the disturbing potential due to the nonspherical shape of the central body and the perturbation of the third body.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Universidade Federal de São Paulo UNIFESP, Inst Ciencia & Tecnol, BR-12331280 Sao Jose Dos Campos, SP, BrazilINPE, Div Space Mech & Control, BR-12227010 Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, Inst Ciencia & Tecnol, BR-12331280 Sao Jose Dos Campos, SP, BrazilFAPESP: 2011/05671-5FAPESP: 2011/09310-7FAPESP: 2011/08171-3CNPq: 304700/2009-6CNPq: 3003070/2011-0Web of Scienc

Special Issue: Advances in Mechanics and Control

The topic of mechanics and control is very important nowadays, with many applications in several fields, such as space research and the modeling of viruses [...

Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth

Determination of onboard coplanar orbital maneuvers with orbits determined using GPS WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS

Abstract -In the present paper a study is made in order to find an algorithm that can calculate coplanar orbital maneuvers for an artificial satellite. The idea is to find a method that is fast enough to be combined with onboard orbit determination using GPS data collected from a receiver that is located in the satellite. After a search in the literature, three algorithms are selected to be tested. Preliminary studies show that one of them (the so called "Minimum Delta-V Lambert Problem") has several advantages over the two others, both in terms of accuracy and time required for processing. So, this algorithm is implemented and tested numerically combined with the orbit determination procedure. Some adjustments are performed in this algorithm in the present paper to allow its use in real-time onboard applications. Considering the whole maneuver, first of all a simplified and compact algorithm is used to estimate in real-time and onboard the artificial satellite orbit using the GPS measurements. By using the estimated orbit as the initial one and the information of the final desired orbit (from the specification of the mission) as the final one, a coplanar bi-impulsive maneuver is calculated. This maneuver searches for the minimum fuel consumption. Two kinds of maneuvers are performed, one varying only the semi major axis and the other varying the semi major axis and the eccentricity of the orbit, simultaneously. The possibilities of restrictions in the locations to apply the impulses are included, as well as the possibility to control the relation between the processing time and the solution accuracy. Those are the two main reasons to recommend this method for use in the proposed application