Antonio F. B. A. Prado

Third-Body Perturbation in Orbits Around Natural Satellites

An analytical and a numerical study of the perturbation imparted to a spacecraft by a third body is developed. There are several important applications of the present research, such as calculation of the effect of lunar and solar perturbations on high-altitude Earth satellites. The goal is to study the evolution of orbits around some important natural satellites of the solar system, such as the moon, the Galilean satellites of Jupiter, Titan, Titania, Triton, and Charon. There is special interest in learning under which conditions a near-circular orbit remains near circular. The existence of circular, equatorial, and frozen orbits are also considered for a lunar satellite, but the results are valid for any system of primaries by making a time transformation that depends on the masses of the bodies involved. Several plots will show the time histories of the Keplerian elements of the orbits involved. Then, a study is performed to estimate the lifetime of orbits around those natural satellites.

Mathematical methods applied to the celestial mechanics of artificial satellites

1 INPE-DMC, Avenida dos Astronautas 1758, 12227-010 Sao Jose dos Campos, SP, Brazil 2 IEEC and Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain 3 Universidade Estadual Paulista, UNESP, CEP 12516-410, Campus de Guaratingueta, Guaratingueta, SP, Brazil 4Universidade Estadual Paulista, UNESP, Caixa Postal 178, CEP 13500-970, Campus de Rio Claro, Rio Claro, SP, Brazil

Stability regions around the components of the triple system 2001 SN263

The space missions are an unquestionable way to increase our knowledge about asteroids. The NEAs (Near-Earth Asteroids) arise as good targets for such missions, since they periodically approach the orbit of the Earth. Due to these advantages, a growing number of missions to NEAs are being planned around the world. Recently, the NEA (153591) 2001 SN263 was chosen as the target of the ASTER MISSION- First Brazilian Deep Space Mission, planned to be launched in 2015. The NEA (153591) 2001 SN263 was discovered in 2001. In February 2008, the radio astronomers from Arecibo-Puerto Rico concluded that (153591) 2001 SN263 is actually a triple system (Nolan et al., 2008). The announcement of the ASTER MISSION has motivated the development of the present work, whose goal is to characterize regions of stability and instability of the triple system (153591) 2001 SN263. Understanding and characterizing the stability of such system is an important information to design the mission aimed to explore it. The method adopted consisted in dividing the region around the system into four distinct regions (three of them internal to the system and one external). We have performed numerical integrations of systems composed by seven bodies: Sun, Earth, Mars, Jupiter and the three components of the system (being Alpha the most massive body, Beta the second most massive body, and Gamma, the least massive body), and by thousands of particles randomly distributed within the demarcated regions, for the planar and inclined prograde cases. The results are diagrams of semi-major axis versus eccentricity, where it is shown the percentage of particles that survive for each set of initial conditions. The regions where 100% of the particles survive is dened as stable regions. We found that the stable regions are in the neighborhood of Alpha and Beta, and in the external region. It was identied resonant motion of the particles with Beta and Gamma in the internal regions, which lead to instability. For particles with I > 45 in the internal region, where I is the inclination with respect to Alpha’s equator, there is no stable region, except for the particles placed really close to Alpha. The stability in the external region is not aected by the variation of inclination. We also present a discussion on the long-term stability in the internal region, for the planar and circular cases, with comparisons with the short-term stability.

Traveling between the Lagrangian points and the Earth

Abstract This paper is concerned with minimum energy trajectories to transfer a spacecraft between the five Lagrangian points and Earth. The planar circular restricted three-body problem in two dimensions is used as the model for the Earth-Moon system, and Lemaitre regularization is used to avoid singularities.

Single frequency GPS measurements in real-time artificial satellite orbit determination ☆

Abstract A simplified and compact algorithm with low computational cost providing an accuracy around tens of meters for artificial satellite orbit determination in real-time and on-board is developed in this work. The state estimation method is the extended Kalman filter. The Cowells method is used to propagate the state vector, through a simple Runge–Kutta numerical integrator of fourth order with fixed step size. The modeled forces are due to the geopotential up to 50th order and degree of JGM-2 model. To time-update the state error covariance matrix, it is considered a simplified force model. In other words, in computing the state transition matrix, the effect of J2 (Earth flattening) is analytically considered, which unloads dramatically the processing time. In the measurement model, the single frequency GPS pseudorange is used, considering the effects of the ionospheric delay, clock offsets of the GPS and user satellites, and relativistic effects. To validate this model, real live data are used from Topex/Poseidon satellite and the results are compared with the Topex/Poseidon Precision Orbit Ephemeris (POE) generated by NASA/JPL, for several test cases. It is concluded that this compact algorithm enables accuracies of tens of meters with such simplified force model, analytical approach for computing the transition matrix, and a cheap GPS receiver providing single frequency pseudorange measurements.

Transfer orbits in the Earth-moon system using a regularized model

In a continuation of previous research where the problem was studied for the Earth-sun system, we search for transfer orbits from one body back to the same body (known in the literature as Henons problem) in the Earth-moon system. In particular, we are searching for orbits that can be used in three situations: 1) to transfer a spacecraft from the moon back to the moon (passing close to the Lagrangian point L

Effects of atmospheric drag in swing-by trajectory

in most of the cases); 2) to transfer a spacecraft from the moon to the respective Lagrangian points L

Planetary Satellite Orbiters: Applications for the Moon

, L^ and LS; and 3) to transfer a spacecraft to an orbit that passes close to the moon and to the Earth several times, with the goal of building a transportation system between these two celestial bodies. The model used for the dynamics is the planar and circular restricted three-body problem. The global Lemaltre regularization is used to avoid numerical problems during close approaches. An interesting result that was obtained in this research is a family of transfer orbits from the moon back to the moon that requires an impulse with magnitude lower than the escape velocity from the

Study of the gravitational capture in the elliptical restricted three-body problem

Abstract In this paper, we study the effects of the atmospheric drag in swing-by maneuvers. Our goal is to simulate a large variety of initial conditions for those orbits and study them according to the effects caused by this close approach. The practical importance of this topic is to allow mission designers to explore close approaches with planets, as well as to take advantage of the atmospheric effects, when it is possible. We use the well-known planar restricted circular three-body problem plus atmospheric drag as our model. We integrate numerically the equations of motion forward and backward in time, until the spacecraft is in a distance that we can neglect the planets effect and consider the system formed by the Sun and the spacecraft as a two-body system. At these two points we can use the two body celestial mechanics to compute energy, angular momentum and the Jacobian constant before and after the close approach.

Study of Some Strategies for Disposal of the GNSS Satellites

Low-altitude, near-polar orbits are very desirable as science orbits for missions to planetary satellites, such as the Earths Moon. In this paper, we present an analytical theory with numerical simulations to study the orbital motion of lunar low-altitude artificial satellite. We consider the problem of an artificial satellite perturbed by the nonuniform distribution of the mass of the Moon (𝐽2–𝐽5, 𝐽7, and 𝐶22). The conditions to get frozen orbits are presented. Using an approach that considers the single-averaged problem, we found families of periodic orbits for the problem of an orbiter travelling around the Moon, where frozen orbits valid for long periods of time are found. A comparison between the models for the zonal and tesseral harmonics coefficients is presented.