Diogo Merguizo Sanchez

Some Initial Conditions for Disposed Satellites of the Systems GPS and Galileo Constellations

Through the averaged equations we revisit theoretical and numerical aspects of the strong resonance that increases the eccentricity of the disposed objects of GPS and Galileo Systems. A simple view of the phase space of the problem shows that the resonance does not depend on the semi-major axis. Therefore, usual strategies of changing altitude (raising perigee) do not work. In this problem we search for a set of initial conditions such that the deactivated satellites or upper-stages remain at least for 250 years without penetrating in the orbits of the operational satellites. In the case that Moons perturbation is not significant, we can identify, in the phase space, the regions where eccentricity reaches maximum and minimum values so that possible risks of collision can be avoided. This is done semi-analytically through the averaged system of the problem. Guided by this idea, we numerically found the (𝜔,Ω) values of the real unaveraged problem. In particular, for the Galileo case, the theoretical results predicted in the averaged system are in good agreement with numerical results. We also show that initial inclination of the Moon plays an important role in the search of these conditions.

Study of Some Strategies for Disposal of the GNSS Satellites

The complexity of the GNSS and the several types of satellites in the MEO region turns the creation of a definitive strategy to dispose the satellites of this system into a hard task. Each constellation of the system adopts its own disposal strategy; for example, in the American GPS, the disposal strategy consists in changing the altitude of the nonoperational satellites to 500 km above or below their nominal orbits. In this work, we propose simple but efficient techniques to discard satellites of the GNSS by exploiting Hohmann type maneuvers combined with the use of the resonance to increase its orbital eccentricity, thus promoting atmospheric reentry. The results are shown in terms of the increment of velocity required to transfer the satellites to the new orbits. Some comparisons with direct disposal maneuvers (Hohmann type) are also presented. We use the exact equations of motion, considering the perturbations of the Sun, the Moon, and the solar radiation pressure. The geopotential model was considered up to order and degree eight. We showed the quantitative influence of the sun and the moon on the orbit of these satellites by using the method of the integral of the forces over the time.

On the Evection Resonance and Its Connection to the Stability of Outer Satellites

In terms of stability around the primary, it is widely known that the semimajor axis of the retrograde satellites is much larger than the corresponding semimajor axis of the prograde satellites. Usually this conclusion is obtained numerically, since precise analytical derivation is far from being easy, especially, in the case of two or more disturbers. Following the seminal idea that what is unstable in the restricted three-body problem is also unstable in the general N-body problem, we present a simplified model which allows us to derive interesting resonant configurations. These configurations are responsible for cumulative perturbations which can give birth to strong instability that may cause the ejection of the satellite. Then we obtain, analytically, approximate bounds of the stability of prograde and retrograde satellites. Although we recover quite well previous results of other authors, we comment very briefly some weakness of these bounds.

Equilibrium points in the restricted synchronous three-body problem using a mass dipole model

The objective of the present paper is to investigate the zero velocity curves, using the Jacobi constantC

Close approach maneuvers around an oblate planet

C

On the effects of each term of the geopotential perturbation along the time I: Quasi-circular orbits

, and to determine the positions of the libration points in the restricted synchronous three-body problem. To perform this task, it is necessary to obtain the equations of motion of a negligible mass traveling in a system composed of two other massive bodies. One of them is assumed to have a spherical shape, while the other one is irregular shaped and modeled as a rotating mass dipole. The locations of the equilibrium points are determined and then, for several values C

Lifetime of a spacecraft around a synchronous system of asteroids using a dipole model

C

Orbital transfers in an asteroid system considering the solar radiation pressure

of the Jacobi constant, the boundary regions are obtained where the motion of the particle is allowed. The zero velocity curves are plotted. Next, the stability of these equilibrium points examined, including the collinear and non-collinear ones. It is found that the collinear points are unstable and the non-collinear ones are linearly stable for lower values of the mass parameter. A comparison with the equivalent results for the dynamics considering three points of mass is made, to emphasize the influence of the elongation of one of the bodies.

Traveling Between the Earth-Moon Lagrangian Points and the Earth

There are many applications of the close approach maneuvers in astronautics, and several missions used this technique in the last decades. In the present work, those close approach maneuvers are revisited, but now considering that the spacecraft passes around an oblate planet. This fact changes the distribution of mass of the planet, increasing the mass in the region of the equator, so increasing the gravitational forces in the equatorial plane. Since the present study is limited to planar trajectories, there is an increase in the variation of energy given by the maneuver. The planet Jupiter is used as the body for the close approach, but the value of J2 is varied in a large range to simulate situations of other celestial bodies that have larger oblateness, but the same mass ratio. This is particularly true in recent discovered exoplanets, and this first study can help the study of the dynamics around those bodies.