Ernesto Vieira Neto

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

Gravitational capture is the phenomenon where a particle, coming from outside the sphere of influence of another body, may have its velocity relative to the celestial body reduced and it can even stay in orbit around it temporarily, using only gravitational forces. This happens due to the change of the two-body energy of the massless body from positive to negative relative to one of the primaries of the restricted three-body problem. The two-body energy is constant in the two-body problem, but not in the three-body problem, where this energy is not conserved due to the perturbation of the third body. The importance of this study is that the results can be used to decrease the fuel expenditure for a mission going from one of the primaries to the other, like an Earth-Moon mission. This is performed by applying an impulse to the spacecraft during the temporary capture to accomplish a permanent capture. The application of this phenomenon in spacecraft trajectories is recent in the literature. The first demonstration of this was in 1987 (Belbruno [1]). Further studies include Belbruno [2, 3]; Krish [4]; Krish, Belbruno, and Hollister [5]; Miller and Belbruno [6]; Belbruno and Miller [7, 8]. They all studied missions in the Earth-Moon system that use this technique to save fuel during the insertion of the spacecraft in its final orbit around the Moon. Another set of papers that made fundamental contributions in this field, also with the main objective of constructing real trajectories in the Earth-Moon system, are those of Yamakawa, Kawaguchi, Ishii, and Matsuo (see references [9]–[12]). The first real application of a ballistic capture transfer was made during an emergency in a Japanese spacecraft [13]. After that, some studies that consider the time required for this transfer appeared in the literature. Examples of this approach can be found in the papers by Vieira-Neto and Prado [14, 15]. The references related to the gravitational capture for the elliptic case, like Bailey [16, 17, 18] and Heppenheimer [19], do not use the variation of the two-body energy as done in this paper. The Journal of the Astronautical Sciences, Vol. 54, Nos. 3 & 4, July–December 2006, pp. 567–582

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.

A study of low velocities regions near the Roche lobe during the gas giant planets formation

In this paper were studied regions close to the Roche lobe of a planet like Jupiter, in order to find regions with low velocities. We simulated a two dimensional and non-self-gravitating disk, where tidal and viscous torques are considered, using the hydrodynamic numerical integrator FARGO 2D. As stated earlier we are interested in find low velocities regions for in future works study the possibility of satellites formation in these regions.