Rodolpho Vilhena de Moraes

Studying Close Approaches for a Cloud of Particles Considering Atmospheric Drag

The present paper has the goal of studying close approaches between a planet and a group of particles. The mathematical model includes the presence of the atmosphere of the planet. This cloud is assumed to be created by the passage of the spacecraft in the atmosphere of the planet, which can cause the explosion of the spacecraft. The system is assumed to be formed by the Sun, the planet, and the spacecraft that explodes and becomes a cloud of particles. The Sun and the planet are assumed to be in circular orbits and the motion is planar. The equations of motion are the ones given by the circular planar restricted three-body problem combined with the forces given by the atmospheric drag. In the numerical simulations, the planet Jupiter is the celestial body used for the close approaches. The initial positions and velocities of the spacecraft and the particles are specified at the periapsis, because it is assumed that this is the point where the explosion occurs.

Planetary Satellite Orbiters: Applications for the Moon

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.

The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance

The orbital dynamics of synchronous satellites is studied. The 2 : 1 resonance is considered; in other words, the satellite completes two revolutions while the Earth completes one. In the development of the geopotential, the zonal harmonics 𝐽20 and 𝐽40 and the tesseral harmonics 𝐽22 and 𝐽42 are considered. The order of the dynamical system is reduced through successive Mathieu transformations, and the final system is solved by numerical integration. The Lyapunov exponents are used as tool to analyze the chaotic orbits.

Nonsphericity of the Moon and Near Sun-Synchronous Polar Lunar Orbits

Herein, we consider the problem of a lunar artificial satellite perturbed by the nonuniform distribution of mass of the Moon taking into account the oblateness () and the equatorial ellipticity (sectorial term ). Using Lie-Hori method up to the second order short-period terms of the Hamiltonian are eliminated. A study is done for the critical inclination in first and second order of the disturbing potential. Coupling terms due to the nonuniform distribution of mass of the Moon are analyzed. Numerical simulations are presented with the disturbing potential of first and second order is. It an approach for the behavior of the longitude of the ascending node of a near Sun-synchronous polar lunar orbit is presented.

A Discussion Related to Orbit Determination Using Nonlinear Sigma Point Kalman Filter

Herein, the purpose is to present a Kalman filter based on the sigma point unscented transformation development, aiming at real-time satellite orbit determination using GPS measurements. First, a brief review of the extended Kalman filter will be done. After, the sigma point Kalman filter will be introduced as well as the basic idea of the unscented transformation, in which this filter is based. Following, the unscented Kalman filter applied to orbit determination will be explained. Such explanation encloses formulations about the orbit determination through GPS; the dynamic model; the observation model; the unmodeled acceleration estimation; also an application of this new filter approaches on orbit determination using GPS measurements discussion.

GPS Satellites Orbits: Resonance

The effects of perturbations due to resonant geopotential harmonics on the semimajor axis of GPS satellites are analyzed. For some GPS satellites, secular perturbations of about 4 m/day can be obtained by numerical integration of the Lagrange planetary equations considering in the disturbing potential the main secular resonant coefficients. Amplitudes for long-period terms due to resonant coefficients are also exhibited for some hypothetical satellites orbiting in the neighborhood of the GPS satellites orbits. The results are important to perform orbital maneuvers of GPS satellites such that they stay in their nominal orbits. Also, for the GPS satellites that are not active, the long-period effects due to the resonance must be taken into account in the surveillance of the orbital evolutions of such debris.

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.

Simulations under Ideal and Nonideal Conditions for Characterization of a Passive Doppler Geographical Location System Using Extension of Data Reception Network

This work presents a (Data Reception Network) DRN software investigation considering simulated conditions inserting purposely errors into the Doppler measurements, satellites ephemeris, and time stamp, to characterize the geographical location software (GEOLOC) developed by Sousa (2000) and Sousa et al. (2003). The extension of reception stations in Brazilian territory can result in more precise locations if the network is considered in the GEOLOC. The results and analyses were first obtained considering the ground stations separately, to characterize their effects in the geographical location (GL) result. Six conditions were investigated: ideal simulated conditions, random and bias errors in the Doppler measurements, errors in the satellite ephemeris, and errors in the time stamp in order to investigate the DRN importance to get more accurate locations; an analysis was performed considering the random errors of 1 Hz in the Doppler measurements. The results are quite satisfactory and also show good compatibility between the simulator and the GEOLOC using the DRN.

Simple orbit determination using GPS based on a least-squares algorithm employing sequential givens rotations

A low-cost computer procedure to determine the orbit of an artificial satellite by using short arc data from an onboard GPS receiver is proposed. Pseudoranges are used as measurements to estimate the orbit via recursive least squares method. The algorithm applies orthogonal Givens rotations for solving recursive and sequential orbit determination problems. To assess the procedure, it was applied to the TOPEX/POSEIDON satellite for data batches of one orbital period (approximately two hours), and force modelling, due to the full JGM-2 gravity field model, was considered. When compared with the reference Precision Orbit Ephemeris (POE) of JPL/NASA, the results have indicated that precision better than 9 m is easily obtained, even when short batches of data are used.

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.