Effects of the eccentricity on the primaries in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

Effects of the eccentricity on the primames in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

Satelites estabilizados por rotação e torque magnético residual

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A "Free-Lunch" tour of the Jovian System

An ED-tether mission to Jupiter is presented. A bare tether carrying cathodic devices at both ends but no power supply, and using no propellant, could move 'freely' among Jupiter's 4 great moons. The tour scheme would have current naturally driven throughout by the motional electric field, the Lorentz force switching direction with current around a 'drag' radius of 160,00 kms, where the speed of the jovian ionosphere equals the speed of a spacecraft in circular orbit. With plasma density and magnetic field decreasing rapidly with distance from Jupiter, drag/thrust would only be operated in the inner plasmasphere, current being near shut off conveniently in orbit by disconnecting cathodes or plugging in a very large resistance; the tether could serve as its own power supply by plugging in an electric load where convenient, with just some reduction in thrust or drag. The periapsis of the spacecraft in a heliocentric transfer orbit from Earth would lie inside the drag sphere; with tether deployed and current on around periapsis, magnetic drag allows Jupiter to capture the spacecraft into an elliptic orbit of high eccentricity. Current would be on at succesive perijove passes and off elsewhere, reducing the eccentricity by lowering the apoapsis progressively to allow visits of the giant moons. In a second phase, current is on around apoapsis outside the drag sphere, rising the periapsis until the full orbit lies outside that sphere. In a third phase, current is on at periapsis, increasing the eccentricity until a last push makes the orbit hyperbolic to escape Jupiter. Dynamical issues such as low gravity-gradient at Jupiter and tether orientation in elliptic orbits of high eccentricity are discussed.

Outreach Testing of Ancient Astronomy

This work is an outreach approach to an ubiquitous recent problem in secondary-school education: how to face back the decreasing interest in natural sciences shown by students under ‘pressure’ of convenient resources in digital devices/applications. The approach rests on two features. First, empowering of teen-age students to understand regular natural events around, as very few educated people they meet could do. Secondly, an understanding that rests on personal capability to test and verify experimental results from the oldest science, astronomy, with simple instruments as used from antiquity down to the Renaissance (a capability restricted to just solar and lunar motions). Because lengths in astronomy and daily life are so disparate, astronomy basically involved observing and registering values of angles (along with times), measurements being of two types, of angles on the ground and of angles in space, from the ground. First, the gnomon, a simple vertical stick introduced in Babylonia and Egypt, and then in Greece, is used to understand solar motion. The gnomon shadow turns around during any given day, varying in length and thus angle between solar ray and vertical as it turns, going through a minimum (noon time, at a meridian direction) while sweeping some angular range from sunrise to sunset. Further, the shadow minimum length varies through the year, with times when shortest and sun closest to vertical, at summer solstice, and times when longest, at winter solstice six months later. The extreme directions at sunset and sunrise correspond to the solstices, swept angular range greatest at summer, over 180 degrees, and the opposite at winter, with less daytime hours; in between, spring and fall equinoxes occur, marked by collinear shadow directions at sunrise and sunset. The gnomon allows students to determine, in addition to latitude (about 40.4° North at Madrid, say), the inclination of earth equator to plane of its orbit around the sun (ecliptic), this fundamental quantity being given by half the difference between solar distances to vertical at winter and summer solstices, with value about 23.5°. Day and year periods greatly differing by about 2 ½ orders of magnitude, 1 day against 365 days, helps students to correctly visualize and interpret the experimental measurements. Since the gnomon serves to observe at night the moon shadow too, students can also determine the inclination of the lunar orbital plane, as about 5 degrees away from the ecliptic, thus explaining why eclipses are infrequent. Independently, earth taking longer between spring and fall equinoxes than from fall to spring (the solar anomaly), as again verified by the students, was explained in ancient Greek science, which posited orbits universally as circles or their combination, by introducing the eccentric circle, with earth placed some distance away from the orbital centre when considering the relative motion of the sun, which would be closer to the earth in winter. In a sense, this can be seen as hint and approximation of the elliptic orbit proposed by Kepler many centuries later.

Third-body perturbation in the case of elliptic orbits for the disturbing body

This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed. Copyright (C) 2008 R. C. Domingos et al.

Third body perturbation using a single averaged model considering elliptic orbits for the disturbing body

In the present work, we expanded the study done by Solorzanol(1) including the eccentricity of the perturbing body. The assumptions used to develop the single-averaged analytical model are the same ones of the restricted elliptic three-body problem. The disturbing function was expanded in Legendre polynomials up to fourth-order. After that, the equations of motion are obtained from the planetary equations and we performed a set of numerical simulations. Different initial eccentricities for the perturbing and perturbed body are considered. The results obtained perform an analysis of the stability of a near-circular orbits and investigate under which conditions this orbit remain near-circular.

Third-body perturbation in the case of elliptic orbits for the disturbing body

In the present work it is presented a semi-analytical and a numerical study of the perturbation caused in a spacecraft by a third body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second-order. The important reason for this procedure is to eliminate the terms due to the short time periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. It is presented an analysis of the stability of a near-circular orbit and a study to know under which conditions this orbit remains near-circular. A study of the equatorial orbits is also performed.

Adaptive scheme for Accurate orbit propagation

Two extensions of the fast and accurate special perturbation method recently developed by Peláez et al. are presented for respectively elliptic and hyperbolic motion. A comparison with Peláez?s method and with the very efficient Stiefel- Scheifele?s method, for the problems of oblate Earth plus Moon and continuous radial thrust, shows that the new formulations can appreciably improve the accuracy of Peláez?s method and have a better performance of Stiefel-Scheifele?s method. Future work will be to include the two new formulations and the original one due to Peláez into an adaptive scheme for highly accurate orbit propagation

The elliptic rendezvous problem in DROMO formulation

The extension of DROMO formulation to relative motion is evaluated. The orbit of the follower spacecraft can be constructed through differences on the elements defining the orbit of the leader spacecraft. Assuming that the differences are small, the problemis linearized. Typical linearized solutions to relativemotion determine the relative state of the follower spacecraft at a certain time step. Because of the form of DROMO formulation, the performance of a frozen-anomaly transformation is explored. In this case, the relative state is computed for a certain value of the anomaly, equal for leader and follower. Since the time for leader and follower do not coincide, the implicit time delay needs to be corrected to recover the physical sense of the solution. When determining the relative orbit, numerical testing shows significant error reductions compared to previous linearized solutions.