Effects of the eccentricity of the primaries in powered Swing-By maneuvers

Abstract

The present paper studies the powered Swing-By maneuver when performed in an elliptical system of primaries. It means that there is a spacecraft travelling in a system governed by the gravity fields of two bodies that are in elliptical orbits around their center of mass. The paper particularly analyzes the effects of the parameters relative to the Swing-By (V inf À ; r p ; w), the orbit of the secondary body around the primary one (e; m) and the elements that specify the impulse applied (dV ; a) to the spacecraft. The impulse is applied when the spacecraft passes by the periapsis of its orbit around the body, where it performs the Swing-By, with different magnitudes and directions. The inclusion of the orbital eccentricity of the primaries in this problem makes it closer to reality, considering that there are many known systems with eccentricities different from zero. In particular, there are several moons in the Solar System which orbits are not circular, as well as some smaller bodies, like the dwarf planet Haumea and its moons, which have eccentricities of 0.25 or even larger. The behavior of the energy variation of the spacecraft is shown in details, as well as the cases where captures and collisions occur. The results show the conditions that optimize this maneuver, according to some given parameters, and how much can be obtained in terms of gains or losses of energy using the best conditions found by the algorithm developed here.

Analytical study of the swing-by maneuver in an elliptical system

“…In a sequence, Casalino et al (1999a) expanded this analytical study to cover the situation where the impulse is applied in different points of the trajectory. There are several other works considering the study of the swing-by maneuver combined with an impulse in the spacecraft based on numerical integration (Prado 1997;Casalino et al 1999b;Santos et al 2008;Silva et al 2013;Ferreira et al 2015Ferreira et al , 2017aFerreira et al , 2017bFerreira et al , 2017cPiñeros and Prado 2017).…”

“…Then, the objective of the present paper is to make an analytical study of the pure gravity swing-by maneuver (without impulse), presenting the equations for the velocity, energy and angular momentum variation as functions of the basic parameters of the swing-by, for systems where the primary bodies are in elliptical orbits. Prado (1997) and Ferreira et al (2017a) performed numerical studies for systems in elliptical orbits, using the elliptic restricted three body problem, but in both cases considering also an impulsive maneuver. Those studies showed interesting aspects of the problem, indicating the necessity of making analytical studies for the elliptical case, similar to those available for the circular problem.…”

Analytical study of the powered Swing-By maneuver for elliptical systems and analysis of its efficiency

“…An example of an even higher eccentric system in the Solar System is the dwarf planet Haumea, which has a moon with an eccentricity close to 0.25 (Sanchez et al 2016). A first study of maneuvers in eccentric systems is shown in Prado (1997), which studied the pure gravity Swing-By maneuver (without impulses) for the elliptic case and Ferreira et al (2017cFerreira et al ( , 2017a, which made a numerical study of the powered Swing-By maneuver, with the impulse applied at the periapsis of the orbit of the spacecraft around the secondary body of the system and in different directions, considering the two main bodies in elliptical orbits. An analysis of the effect of the eccentricity was presented in these papers, besides the study of the maximum gains and losses of energy obtained from the maneuver.…”

Effects of Bank Angle During Powered Aerogravity-Assist Maneuver

“…If an impulsive maneuver is applied during the GAM, the direction of the impulse works as one more control for the maneuver, changing the effects of the GA. As a negative point, this powered maneuver requires the use of a space propulsion system, resulting in fuel consumption, and so increasing the cost of the mission. The possible uses of this powered maneuver have been analyzed for planets and moons of the solar system [17][18][19][20][21][22][23][24]. When the maneuver is made close to planets that have significant atmosphere and using a spacecraft with wing-body shape (waverider), the AGAM could also be controlled by the direction and/or magnitude of the aerodynamic forces generated during atmospheric flight [2][3][4][25][26][27][28][29][30][31][32].…”

“…In that sense, the present paper has the goal of studying a new version of this maneuver, where the bank angle is assumed to be variable and constituting in a new form to control the AGAM and PAGAM, which was not used before. The mathematical model selected to analyze the applications of the maneuvers and the resulting trajectories around the center of mass of the orbital system is the circular restricted three-body problem (CRTBP) [36], which is highly accepted in this kind of problems [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The choice of this model is based on our solar system, where the massive body is the sun, the secondary body is a planet with atmosphere used for the maneuver, and the third body is the spacecraft, represented as a massless waverider.…”