Studying the errors in the estimation of the variation of energy by the “patched-conics” model in the three-dimensional swing-by

Winter

et al. 2018

Astrophys Space Sci

The objective of the present paper is to derive a set of analytical equations that describe a swing-by maneuver realized in a system of primaries that are in elliptical orbits. The goal is to calculate the variations of energy, velocity and angular momentum as a function of the usual basic parameters that describe the swing-by maneuver, as done before for the case of circular orbits. In elliptical orbits the velocity of the secondary body is no longer constant, as in the circular case, but it varies with the position of the secondary body in its orbit. As a consequence, the variations of energy, velocity and angular momentum become functions of the magnitude and the angle between the velocity vector of the secondary body and the line connecting the primaries. The "patched-conics" approach is used to obtain these equations. The configurations that result in maximum gains and losses of energy for the spacecraft are shown next, and a comparison between the results obtained using the analytical equations and numerical simulations are made to validate the method developed here.

Section: Comparison Between the Results Obtained By The Analytical Anmentioning

confidence: 77%

Section: Comparison Between the Results Obtained By The Analytical Anmentioning

confidence: 85%

See 1 more Smart Citation

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

Ferreira

Winter

et al. 2018

Astrophys Space Sci

“…Earth-Moon system), a three-body problem is needed. Further considerations about the limitation of the patched-conics can be found in the literature [10,36,67,68,76,81,90,91].…”

Section: What Is a Gravity-assist?mentioning

confidence: 99%

A historical review of the theory of gravity-assists in the pre-spaceflight era

Negri

J Braz. Soc. Mech. Sci. Eng.

2020

Self Cite

The gravity-assist manoeuvre is a technique in which a spacecraft changes its orbital energy and angular momentum by a close-approach with a celestial body. The result is a great reduction in the use of fuel and flight time. Several interplanetary missions have applied it for this reason, like the famous Voyagers, Mariner, or Galileo. The astronomers knew the mechanics behind such concept for at least two centuries by noting the change in the orbits of the comets after passing close to Jupiter. The introduction of this phenomenon to spaceflight was a very successful story and motivated many claims that the proposal of the gravity-assist manoeuvres occurred in the early 60s. However, the idea of using such mechanism for interplanetary spaceflight can be traced back to the 20s. The dispute of being the first to have this idea contributed to throw shadow on these early pioneers. In that sense, the present paper has the goal of discussing some aspects related to the history of this manoeuvre in the pre-spaceflight era, trying to show some of the major steps made in its early history. It covers from the first studies found on this topic and goes up to the beginning of the space age, with the launching of the Sputnik satellite. This time period is chosen to bring light to these early works in which the astronomical phenomenon is introduced in the astronautics. Their importance is highlighted by putting these works under their historical context, as it shows how some of them were far ahead of their time. Among these, the work of Tsander, made in mid-20s, is outstanding.

“…Under this assumption, each body has its own sphere of influence (Bate et al 1971;Araujo et al 2008). A detailed study of the errors introduced by this assumption is shown in Negri et al (2017). When the spacecraft is within the sphere of influence of one of the bodies, only the gravitational force between the spacecraft and this body is considered, while the gravity field of the other body is neglected.…”

Section: Statement Of the Problemmentioning

confidence: 99%

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

Ferreira

Winter

et al. 2018

Astrophys Space Sci

Analytical equations describing the velocity and energy variation of a spacecraft in a Powered Swing-By maneuver in an elliptic system are presented. The spacecraft motion is limited to the orbital plane of the primaries. In addition to gravity, the spacecraft suffers the effect of an impulsive maneuver applied when it passes by the periapsis of its orbit around the secondary body of the system. This impulsive maneuver is defined by its magnitude δV and the angle that defines the direction of the impulse with respect to the velocity of the spacecraft (α). The maneuver occurs in a system of main bodies that are in elliptical orbits, where the velocity of the secondary body varies according to its position in the orbit following the rules of an elliptical orbit. The equations are dependent on this velocity. The study is done using the "patched-conics approximation", which is a method of simplifying the calculations of the trajectory of a spacecraft traveling around more than one celestial body. Solutions for the velocity and energy variations as a function of the parameters that define the maneuver are presented. An analysis of the efficiency of the powered Swing-By maneu-B A.F.S. Ferreira