Close approach maneuvers around an oblate planet

Abstract

Abstract. 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. IntroductionSeveral papers in the literature describe the close approach maneuvers, like the ones shown in references [1] to [20]. Using the model given by the "patched conics" to explain the close approach maneuvers, it is assumed that the mission can be divided in three stages, all of them studied under Keplerian motion. It is also considered that the system consists of three bodies: M 1 , a massive body in the center of the Cartesian system; M 2 , a smaller body in a Keplerian orbit around M 1 ; and M 3 , a spacecraft that is traveling in an orbit around M 1 when it passes close to M 2 . This passage changes the orbit of M 3 , which leads to a variation of eccentricity, semi-major axis, velocity, energy and angular momentum of M 3 . This phenomenon is also called a swing-by maneuver. The advantages of this maneuver are the savings of time and fuel for a particular mission. According to these assumptions, the orbits of M 1 and M 2 remain unchanged. For the motion of the spacecraft, the model of two bodies is used in the initial phase, for the spacecraft-central body system. In the second stage, it is assumed that the spacecraft passes through the secondary body in an open trajectory. The third step is again assumed to be a system formed by two bodies, spacecraft-central body. The goal of this maneuver is to modify the Keplerian trajectories spacecraft-central body from the first to the third stage. Figure 1 illustrates this sequence. In this figure, A and B are the initial and final points of the trajectory during the close approach,  is the angle of curvature of the spacecraft,  is the angle between the periapsis line and the line connecting M 1 and M 2 , V 2 is the velocity of M 2 with respect to M 1 , and are the velocities of M 3 with respect to M 2 , when approaching and leaving M 2 , respectively, and rp is the periapsis distance of the close approach.