A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. the disturbing function is expanded in Legendre polynomials up to the second order in both cases. the equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. the results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Inst Nacl Pesquisas Espaciais, BR-12227010 Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, BR-12231280 Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, BR-12231280 Sao Jose Dos Campos, SP, BrazilCNPq: 150195/2012-5CNPq: 304700/2009-6FAPESP: 2011/09310-7FAPESP: 2011/08171-3Web of Scienc

Resonant Orbital Dynamics in LEO Region: Space Debris in Focus

The increasing number of objects orbiting the earth justifies the great attention and interest in the observation, spacecraft protection, and collision avoidance. These studies involve different disturbances and resonances in the orbital motions of these objects distributed by the distinct altitudes. in this work, objects in resonant orbital motions are studied in low earth orbits. Using the two-line elements (TLE) of the NORAD, resonant angles and resonant periods associated with real motions are described, providing more accurate information to develop an analytical model that describes a certain resonance. the time behaviors of the semimajor axis, eccentricity, and inclination of some space debris are studied. Possible irregular motions are observed by the frequency analysis and by the presence of different resonant angles describing the orbital dynamics of these objects.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, BR-12231280 Sao Jose Dos Campos, SP, BrazilAstron Observ, AMU, PL-60286 Poznan, PolandITA, BR-12228900 Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, BR-12231280 Sao Jose Dos Campos, SP, BrazilFAPESP: 2012/24369-0FAPESP: 2012/21023-6CNPq: 303070/2011-0Web of Scienc

Searching Less Perturbed Circular Orbits for a Spacecraft Travelling around Europa

Space missions to visit the natural satellite of Jupiter, Europa, constitute an important topic in space activities today, because missions to this moon are under study now. Several considerations have to be made for these missions. the present paper searches for less perturbed circular orbits around Europa. This search is made based on the total effects of the perturbing forces over the time, evaluated by the integral of those forces over the time. This value depends on the dynamical model and on the orbit of the spacecraft. the perturbing forces considered are the third-body perturbation that comes from Jupiter and the J(2), J(3,) and C-22 terms of the gravitational potential of Europa. Several numerical studies are performed and the results show the locations of the less perturbed orbits. Using those results, it is possible to find near-circular frozen orbits with smaller amplitudes of variations of the orbital elements.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Universidade Federal de São Paulo UNIFESP, Inst Ciencia & Tecnol, BR-12231280 Sao Jose Dos Campos, SP, BrazilInst Nacl Pesquisas Espaciais, BR-12243750 Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, Inst Ciencia & Tecnol, BR-12231280 Sao Jose Dos Campos, SP, BrazilCNPq: 303070/2011-0CNPq: 473387/2012-3CNPq: 304700/2009-6FAPESP: 2011/05671-5FAPESP: 2011/09310-7FAPESP: 2011/08171-3FAPESP: 2012/21023-6Web of Scienc

Signal Transceiver Transit Times and Propagation Delay Corrections for Ranging and Georeferencing Applications

The accuracy of ranging measurements depends critically on the knowledge of time delays undergone by signals when retransmitted by a remote transponder and due to propagation effects. A new method determines these delays for every single pulsed signal transmission. It utilizes four ground-based reference stations, synchronized in time and installed at well-known geodesic coordinates and a repeater in space, carried by a satellite, balloon, aircraft, and so forth. Signal transmitted by one of the reference bases is retransmitted by the transponder, received back by the four bases, producing four ranging measurements which are processed to determine uniquely the time delays undergone in every retransmission process. A minimization function is derived comparing repeater's positions referred to at least two groups of three reference bases, providing the signal transit time at the repeater and propagation delays, providing the correct repeater position. The method is applicable to the transponder platform positioning and navigation, time synchronization of remote clocks, and location of targets. The algorithm has been demonstrated by simulations adopting a practical example with the transponder carried by an aircraft moving over bases on the ground.CNPq Agency (Brazil)Brazil agency CNPqBrazil agency CAPESBrazil agency CAPE

Nonrecursive algorithm for remote geolocation using ranging measurements

The objective of this work is to present a new algebraic solution for the problem of remote determination of geographic coordinates of a target, using a new remote geopositioning system being developed in Brazil. It can be useful for double-check measurements obtained with other methods, for certain critical applications, being capable to perform independently from them. This system requires three-reference bases on the surface of the earth with synchronized clocks and a repeater in space. Calculations are derived from measurements of propagation time of clock signal transmitted by one base to all bases and target, via a transponder in space. The algorithm also provides the “instantaneous” determination of the repeater position in space and brings other applications in navigation and remote clock synchronization. The algorithm has been successfully tested through computational software

A semi-analytical approach using the single and double averaged methods and the Lidov–Kozai mechanism

An analysis of the orbital motion of artificial satellites around Mercury is presented taking into account its non-sphericity (J2, J3, C22) and the perturbation of the third body. The disturbing potential due to the third body is developed in circular and inclined orbit. The double-averaged method should be used with caution in some situations where the averaging is applied at different timescales. In this work, a study is presented considering this observation for orbits around Mercury. When the mean anomaly of the Sun is eliminated, the idea is that all effects whose periods below 88 days are neglected. As the rotation of Mercury is about 58.6 days, this means that the perturbation due to the C22 term must also be neglected. However, since the C22 term is important and should be taken into account, then terms longer than 58.6 days should also be preserved. In other words, keeping the C22 term with a period of 58.6 days means that the solar terms with the longest period (88 days) will be maintained here. The single-averaged method is applied to eliminate only the mean anomaly of the spacecraft. A comparison between the single and double averaged models is presented. We found that for the case of Mercury the two models are in agreement, but the single-averaged model is more realistic because it keeps more terms in the disturbing potential. Several types of resonances can be analyzed starting of the single-averaged potential. Considering our single-averaged disturbing potential, the terms due to Lidov–Kozai resonance were isolated to make a qualitative analysis considering the libration and circulation regions in the diagram, eccentricity versus argument of the pericenter

Influence of Earth's shadow on the rotational motion of an artificial satellite perturbed by solar radiation torque

A semi-analytical approach is proposed to study the rotational motion of an artificial satellite under the influence of the torque due to the solar radiation pressure and taking into account the influence of Earth's shadow. The Earth's shadow is introduced in the equations for the rotational motion as a function depending on the longitude of the Sun, on the ecliptic's obliquity and on the orbital parameters of the satellite. By mapping and computing this function, we can get the periods in which the satellite is not illuminated and the torque due to the solar radiation pressure is zero. When the satellite is illuminated, a known analytical solution is used to predict the satellite's attitude. This analytical solution is expressed in terms of Andoyer's variables and depends on the physical and geometrical properties of the satellite and on the direction of the Sun radiation flux. By simulating a hypothetical circular cylindrical type satellite, an example is exhibited and the results agree quite well when compared with a numerical integration. © 1997 COSPAR. Published by Elsevier Science Ltd