Effects of Geopotential and Atmospheric Drag Effects on Frozen Orbits Using Nonsingular Variables

The concept of frozen orbit has been applied in space missions mainly for orbital tracking and control purposes. This type of orbit is important for orbit design because it is characterized by keeping the argument of perigee and eccentricity constant on average, so that, for a given latitude, the satellite always passes at the same altitude, benefiting the users through this regularity. Here, the system of nonlinear differential equations describing the motion is studied, and the effects of geopotential and atmospheric drag perturbations on frozen orbits are taken into account. Explicit analytical expressions for secular and long period perturbations terms are obtained for the eccentricity and the argument of perigee. the classical equations of Brouwer and Brouwer and Hori theories are used. Nonsingular variables approach is used, which allows obtaining more precise previsions for CBERS (China Brazil Earth Resources Satellite) satellites family and similar satellites (SPOT, Landsat, ERS, and IRS) orbital evolution.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)EEL USP LOB, Engn Sch Lorena, BR-12602810 Lorena, SP, BrazilUniversidade Federal de São Paulo UNIFESP, ICT, BR-12231280 Sao Jose Dos Campos, SP, BrazilNatl Inst Space Res INPE DMC, Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, ICT, BR-12231280 Sao Jose Dos Campos, SP, BrazilFAPESP: 2012/21023-6Web of Scienc

Efeitos de Forças Gravitacionais e Não-Gravitacionais sobre o Movimento Orbital de Satélites Artificiais

Uma teoria para estudar o movimento orbital de satélites artificiais sobre efeitos do arrasto atmosférico e da pressão de radiação solar direta - considerando a sombra da Terra e alguns termos do geopotencial - é desenvolvida analiticamente. A sombra da Terra é modelada utilizando a função sombra (psi), como introduzida por Ferraz Mello: psi igual zero quando o satélite está na região de sombra e igual a um quando é iluminado pelo Sol. As componentes do arrasto são dadas por Vilhena de Moraes baseado no modelo atmosférico TD-88. O método de Hori para sistemas não-canônicos é aplicado para resolver as equações de movimento. Um software para manipulação algébrica é fundamental para fazer os cálculos necessários. Efeitos seculares e periódicos que influenciam no movimento orbital de satélites artificiais são analisados. É dada ênfase aos termos de acoplamento que surgem na solução do sistema de equações diferenciais. Utilizando dados orbitais do satélite CBERS-1 é feito um estudo para analisar ordens de grandeza da variação do semi-eixo maior devidas às perturbações consideradas

Using low Lift-to-Drag spacecraft to perform upper atmospheric Aero-Gravity Assisted Maneuvers

The Gravity Assisted Maneuver has been applied in lots of space missions, to change the spacecraft heliocentric velocity vector and the geometry of the orbit, after the close approach to a celestial body, saving propellant consumption. It is possible to take advantage of additional forces to improve the maneuver, like the forces generated by the spacecraft-atmosphere interaction and/or propulsion systems; reducing the time of flight and the need for multiple passages around secondary bodies. However, these applications require improvements in critical subsystems, which are necessary to accomplish the mission. In this paper, a few combinations of the Gravity-Assist were classified, including maneuvers with thrust and aerodynamic forces; presenting the advantages and limitations of these variations. There are analyzed the effects of implementing low Lift-to-Drag ratios at high altitudes for Aero-gravity Assist maneuvers, with and without propulsion. The maneuvers were simulated for Venus and Mars, due to their relevance in interplanetary missions, the interest in exploration, and the knowledge about their atmospheres. The Aero-gravity Assist maneuver with low Lift-to-Drag ratios at high altitudes shows an increase of more than 10{\deg} in the turn angle for Venus and 2.5{\deg} for Mars. The maneuvers increase the energy gains by more than 15% when compared to the Gravity-Assist. From the Technology Readiness Levels, it was observed that the current level of development of the space technology makes feasible the application of Aero-gravity Assisted Maneuvers at high altitudes in short term

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

Analysis of the orbital evolution of space debris using a solar sail and natural forces

In this work, the orbital evolution of these objects that are located in the geostationary orbit (GEO) is analyzed. Knowing this, the possibility of using a solar sail is considered to help to clean the space environment. The main natural environmental perturbations that act in the orbit of the debris are considered in the dynamics. Such forces acting in the solar sail can force the growth of the eccentricity of these objects in the GEO orbit. Several authors have presented models of the solar radiation pressure considering the single-averaged model. But, doing a literature research, we found that the authors consider the Earth around the Sun in a circular and inclined orbit. Our contribution to the SRP model is in developing a different approach from other authors, where we consider the Sun in an elliptical and inclined orbit, which is valid for other bodies in the solar system when the eccentricity cannot be neglected. The expression of the SRP is developed up to the second order. We found that the first-order term is much superior to the second-order term, so the quadrupole term can be neglected. Another contribution is the approach to identify the initial conditions of the perigee argument (g) and the longitude of the ascending node (h), where some values of the (g, h) plane contribute to amplify the eccentricity growth. In the numerical simulations we consider real data from space debris removed from the site Stuff in Space. The solar sail helps to clean up the space environment using a propulsion system that uses the Sun itself, a clean and abundant energy source, unlike chemical propellants, to contribute to the sustainability of space exploration

Autonomous Rapid Exploration in Close-Proximity of an Asteroid

The increasing number of space missions may overwhelm ground support infrastructure, prompting the need for autonomous deep-space guidance, navigation, and control (GN\&C) systems. These systems offer sustainable and cost-effective solutions, particularly for asteroid missions that deal with uncertain environments. This study proposes a paradigm shift from the proposals currently found in the literature for autonomous asteroid exploration, which inherit the conservative architecture from the ground-in-the-loop approach that relies heavily on reducing uncertainties before close-proximity operations. Instead, it advocates for robust guidance and control to handle uncertainties directly, without extensive navigation campaigns. From a series of conservative assumptions, we demonstrate the feasibility of this autonomous GN\&C for robotic spacecraft by using existing technology. It is shown that a bolder operational approach enables autonomous spacecraft to significantly reduce exploration time by weeks or months. This paradigm shift holds great potential for reducing costs and saving time in autonomous missions of the future.Comment: Published in the AIAA's Journal of Guidance, Control, and Dynamics. DOI: 10.2514/1.G00718

Applying the perturbative integral in aeromaneuvers around Mars to calculate the cost

The perturbative integral method was applied to quantify the contribution of external forces during a specific interval of time in trajectories of spacecraft around asteroids and under the Luni-solar influence. However, this method has not been used to quantify the contributions of drag in aerocapture and aerobraking. For this reason, the planet Mars is selected to apply this method during an aerogravity-assisted maneuver. Several trajectories are analyzed, making use of a drag device with area to mass ratios varying from 0.0 to 20.0 m2/kg, simulating solar sails or de-orbit devices. The mathematical model is based in the restricted three-body problem. The use of this maneuver makes it possible to obtain the variations of energy in the trajectory, replacing expensive maneuvers based on fuel consumption. To observe the effects of the maneuvers, different values of pericenter velocity and altitude were selected for prograde and retrograde orbits. The innovation of this research is the application of an integral method to quantify the delta-V of the aero gravity maneuver, comparing the cost of the maneuver with the traditional methods of space propulsion. The results allow the identification of orbits with conditions to capture, and the perturbative maps show the velocity variations

Optimization of Aero-gravity assisted maneuvers for spaceplanes at high atmospheric flight on Earth

Gravity assists are impulse maneuvers that save costs for interplanetary missions, resulting from close approaches to celestial bodies. Aero-Gravity Assist maneuvers offer another solution to reduce mission cost by taking advantage of aerodynamic forces through cruise flights over the atmospheres of minor planets, like the Earth, which is selected because has been used on multiple gravity assist maneuvers. Despite their theoretical feasibility, the technological requirements make them impossible at low altitudes. Therefore, this work focuses on a spaceplane aeromaneuvering at high atmospheric altitudes and in continuum hypersonic flow, with Knudsen Numbers between 10-3 and 10-2. It is formulated as an optimal control problem with the dynamic optimization suite GEKKO, and solved via nonlinear programming. Nine different cost functions are analyzed separately: the maximization of longitude, latitude, and velocity at the end of the atmospheric flight; minimization of heat transfer, dynamic pressure, and load factor along the trajectory; minimization of flight time; and maximization of plane inclination and range angle. The results show a successful outcome in all cases, with a conclusive Monte Carlo analysis further demonstrating the robustness of the controller to support uncertainties in the initial conditions and atmospheric densityFAPESP grants number 2022/15564-6FAPESP 2019/26605-

Analysis of the secular problem for triple star systems

The long-term dynamics of the three-body problem is studied. the goal is to study the motion of a planet (m(1)) around a star (m(0)) that is perturbed by a third-body (m(2)) (a planet or a brown dwarf star). the gravitational potential is developed in closed form up to the fourth order. Taking into account the triple system, it is shown here the evolution of some orbital parameters of the planet (m(1)). A comparison considering models with different orders for the disturbing potential is presented. We show that the behavior of the orbit of the inner planet can flip from prograde to retrograde trajectories. This is due to the third-order term, which strongly affects the eccentricity and inclination. We show that the effect of the fourth order term is to change the times when the phenomenon occurs.Universidade Federal de São Paulo, UNIFESP ICT, Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo, UNIFESP ICT, Sao Jose Dos Campos, SP, BrazilWeb of Scienc