The swing-by effect in the Vesta-Magnya case. Single and multiple encounters.

It was verified that the asteroid Magnya has some physical and chemical characteristics similar to the bodies from Vesta family. However, astronomical observations revealed that Magnya is distant from these bodies. In the present work, we assumed that Magnya originated from Vesta and we try to justify its current distant orbital location taking into account the effects of close encounters between Magnya and Vesta. The methodology adopted involved an analytical approach considering the technique of the gravity assisted maneuver, also known as swing-by. We found that the energy variation achieved through a single swing-by between Vesta and Magnya are very small when compared to the variation that would be required to change the orbit of Magnya. The effects of multiple close encounters were also considered and discussed. We concluded that the possibility of multiple encounters is limited, and therefore, that Magnya should suffer other perturbations (such as resonances, collisions or close encounters with other bodies, for instance) that would provide the supposed change in its orbit.

Optimal impulsive control in a powered Swing-By

This paper studies the problem of applying an impulsive control in a spacecraft that is performing a Swing-By maneuver. The objective is to study the changes in velocity, energy and angular momentum for this maneuver as a function of the three usual parameters of the standard Swing-By plus the three parameters (the magnitude of the impulse, the point of its application and the angle between the impulse and the velocity of the spacecraft) that specify the impulse applied. The dynamics used is the restricted three body problem under the regularization of Lemaitre, made to increase the accuracy of the numerical integration near the primaries. The present research develops an algorithm to calculate the variation of energy and angular momentum in a maneuver where the application of the impulsive control occurs before or after the passage of the spacecraft by the periapsis, but within the sphere of influence of the secondary body and in a non-tangential direction. Using this approach, it is possible to find the best position and direction to apply the impulse to maximize the energy change of the total maneuver. The results showed that the application of the impulse at the periapsis and in the direction of motion of the spacecraft is usually not the optimal solution.

Ideal golf swing : an evaluation of its characteristics and the assumptions underlying its acquisition during coaching

The game of golf requires hitting a ball from a range of lies over a range of distances in environments that include many obstacles to be avoided. Each of these different golf shots arc designed to move the ball from the tee to the hole in the least number of strokes. However, the fundamental assumption that seems to underlie the coaching of golf, particularly to novice players, is that acquisition of an ideal basic golf swing is the most important outcome of coaching. Implicit in this view are three further assumptions. The first is that once this ideal basic golf swing is acquired by players, they are able to complete a game of golf in a competent manner even though this requires a range of different shots. The second is that there is a close correspondence between the quality of execution of any golf swing as judged in terms of this ideal swing, and the quality of outcome of the golf shot of which the swing is a part, as judged by where the ball comes to rest. The third assumption is that visual inspection of the golf swing by a coach can reveal inadequacies which can be remedied leading lo improved performance in the game of golf. The research reported in this thesis is an investigation of these assumptions. The rationale underlying coaching of golf was examined by reviewing the golf coaching literature (Chapter 1) and conducting a survey of professional golf coaches (Chapter 2). Results of the literature review and the survey indicated that the major emphasis of golf coaching of novices was on their acquiring what might be described as an ideal basic golf swing. This typically involved identifying components in sequence. Little emphasis was placed during this stage of coaching on what might be described as the complete action of a golf shot which involves hitting a ball to some target location. To examine the assumption that there was a close correspondence between the quality of execution of the golf swing and the quality of the outcome of a golf shot, two studies were conducted. In Chapter 3 the development of a 70-item checklist to be used to evaluate the quality of execution of a golf swing is reported. This checklist was based on a detailed behavioural analysis of the golf swing involving collaboration with relevant experts (i.e., golf coaches, biomechanist, kinesiologist), and information derived from a review of golf coaching materials. Development of the checklist was an iterative process in which earlier versions were used to evaluate sample golf swings, and problems identified during this lest process were used to improve the checklist. The final 70-item checklist comprised of a static component with three parts (left-hand grip; right-hand grip; stance) and a dynamic component with six parts (half backswing; full backswing; half downswing; ball contact; half followthrough; finish position). This version of the checklist was used in a study (reported in Chapter 4) of the relationship between the judged quality of execution of a golf swing and the outcome accuracy of a golf shot. Three groups of golfers with varying ability and experience were required to hit 50 balls with a 9-iron club to a target. Outcome accuracy for each shot was assessed in terms of the distance between the target and the resting location of the ball. Edited videotapes (showing only execution of the golf swing) of the five most, and five least accurate shots produced a sub-sample of these golfers (four professional players; four novice players) were subsequently viewed by three expert coaches. They independently rated using the checklist, the quality of execution of the 80 golf swings in random order without having information about the accuracy of any shot. As expected, the professional golfers completed more accurate golf shots than did the novices, and the golf swings completed by the professionals were rated more highly than those completed by the novices. However, for both groups of golfers the results indicated that there was no clear relationship between the rated quality of execution of golf swings and the outcome accuracy of the shots of which the swing were the initial part. Chapter 5 provides a summary and overview of the research reported in Chapter 1 to 4. It is argued that this research suggests a need for a change of emphasis in golf coaching away from consideration of the golf swing in isolation to consideration of the golf swing as part of a complete action. That is, the quality of execution of a golf swing should not be judged simply in relation to some ideal set of golf-swing components, but rather in relation to how well the completed swing (i.e., the golf shot) achieves the desired aim of propelling the ball from its present location to the target location.

On the scattering of comets by a planet

In this paper, numerical simulations are made, using the three-dimensional restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Saturn in the orbit of a comet. To show the results, the orbit of the comet is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct and hyperbolic retrograde. Then, the modification in the orbit of the comet due to the close approach is shown in plots that specify from which group the comet's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters (position and velocity at the periapse) vary is performed and the influence of each of them is shown and explained. The result is a collection of maps that describe the evolution of the trajectory of the comet due to the close approach. Those maps can be used to estimate the probability of some events, like the capture or escape of a comet. An example of this technique is shown in the paper. (C) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

A numerical study of powered Swing-Bys around the Moon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Alternative Transfers to the NEOs 99942 Apophis, 1994 WR12, and 2007 UW1 via Derived Trajectories from Periodic Orbits of Family G

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Interplanetary natural routes via Moon and Lagrangiam points L1 and L2

Swing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spaceships. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct links between low Earth orbits and the lunar sphere of influence, to obtain low-energy interplanetary trajectories through swing-bys with the Moon and the Earth. The existence of these links are related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in these links are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow us a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. On the other hand, still within the Earth sphere of influence, and taking advantage of the sensitivity of the trajectories, is possible to design other swing-bys with the Earth or Moon. This allows the trajectories to have larger reach, until they can reach the orbit of other planets as Venus and Mars.(3σ)Broucke, R.A., Periodic Orbits in the Restricted Three-Body Problem with Earth-Moon Masses, JPL Technical Report 32-1168, 1968.

Optimal low cost transfer to L4 and L5 lagrangian points

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. In this work, we introduce a new low-cost orbital transfer strategy that opportunistically combine chaotic and swing-by transfers to get a very efficient strategy that can be used for servicing mission on astronomical mission placed on Lagrangian points L4 or L5. This strategy is not only efficient with respect to thrust requirement, but also its time transfer is comparable to others known transfer techniques based on time optimization. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Encontros próximos: captura gravitacional temporária e esfera de influência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Alternative transfer to the Earth-Moon Lagrangian points L4 and L5 using lunar gravity assist

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Searching for capture and escape trajectories around Jupiter using its Galilean satellites

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

Optimum switching point assessment of parallel braking resistor and serial current limiter for power system stability enhancement

A new control algorithm using parallel braking resistor (BR) and serial fault current limiter (FCL) for power system transient stability enhancement is presented in this paper. The proposed control algorithm can prevent transient instability during first swing by immediately taking away the transient energy gained in faulted period. It can also reduce generator oscillation time and efficiently make system back to the post-fault equilibrium. The algorithm is based on a new system energy function based method to choose optimal switching point. The parallel BR and serial FCL resistor can be switched at the calculated optimal point to get the best control result. This method allows optimum dissipation of the transient energy caused by disturbance so to make system back to equilibrium in minimum time. Case studies are given to verify the efficiency and effectiveness of this new control algorithm.