Quantification of relativistic perturbation forces on spacecraft trajectories

The intent of the work presented in this thesis is to show that relativistic perturbations should be considered in the same manner as well known perturbations currently taken into account in planet-satellite systems. It is also the aim of this research to show that relativistic perturbations are comparable to standard perturbations in speciffc force magnitude and effects. This work would have been regarded as little more then a curiosity to most engineers until recent advancements in space propulsion methods { e.g. the creation of a artiffcial neutron stars, light sails, and continuous propulsion techniques. These cutting-edge technologies have the potential to thrust the human race into interstellar, and hopefully intergalactic, travel in the not so distant future. The relativistic perturbations were simulated on two orbit cases: (1) a general orbit and (2) a Molniya type orbit. The simulations were completed using Matlab's ODE45 integration scheme. The methods used to organize, execute, and analyze these simulations are explained in detail. The results of the simulations are presented in graphical and statistical form. The simulation data reveals that the speciffc forces that arise from the relativistic perturbations do manifest as variations in the classical orbital elements. It is also apparent from the simulated data that the speciffc forces do exhibit similar magnitudes and effects that materialize from commonly considered perturbations that are used in trajectory design, optimization, and maintenance. Due to the similarities in behavior of relativistic versus non-relativistic perturbations, a case is made for the development of a fully relativistic formulation for the trajectory design and trajectory optimization problems. This new framework would afford the possibility of illuminating new more optimal solutions to the aforementioned problems that do not arise in current formulations. This type of reformulation has already showed promise when the previously unknown Space Superhighways arose as a optimal solution when classical astrodynamics was reformulated using geometric mechanics.

A new approach on the long term dynamics of neo's under Yarkorsky effect

To calculate the force associated with the Yarkovsky effect the temperature distribution on the surface of the asteroid should be determined; it depends on the asteroid orbit, size and shape, spin axis orientation and period, mass, density of surface layers, albedo, thermal conductivity, capacity and IR emissivity of the material. The uncertainty of many of these parameters invites to develop simplified methods to calculate the influence of the Yarkovsky effect on long term dynamics of asteroids. In this paper we present one of this method based in a special perturbation procedure developed in our group.

EDROMO: An accurate propagator for elliptical orbits in the perturbed two-body problem

EDROMO is a special perturbation method for the propagation of elliptical orbits in the perturbed two-body problem. The state vector consists of a time-element and seven spatial elements, and the independent variable is a generalized eccentric anomaly introduced through a Sundman time transformation. The key role in the derivation of the method is played by an intermediate reference frame which enjoys the property of remaining fixed in space as long as perturbations are absent. Three elements of EDROMO characterize the dynamics in the orbital frame and its orientation with respect to the intermediate frame, and the Euler parameters associated to the intermediate frame represent the other four spatial elements. The performance of EDromo has been analyzed by considering some typical problems in astrodynamics. In almost all our tests the method is the best among other popular formulations based on elements.

An asymptotic solution for the main problem

In this paper, an analytical solution of the main problem, a satellite only perturbed by the J2 harmonic, is derived with the aid of perturbation theory and by using DROMO variables. The solution, which is valid for circular and elliptic orbits with generic eccentricity and inclination, describes the instantaneous time variation of all orbital elements, that is, the actual values of the osculating elements

A new regularization method for fast and accurate propagation of roto-translationally coupled asteroids

There is a well-distinguished group of asteroids for which the roto-translational cou-pling is known to have a non-negligible e�ect in the long-term. The study of such asteroids suggests the use of specialized propagation techniques, where perturbation methods make their best. The techniques from which the special regularization method DROMO is derived, have now been extended to the attitude dynamics, with equally remarkable results in terms of speed and accuracy, thus making the combination of these algorithms specially. well-suited to deal with the propagation of bodies with strong attitude coupling.

Technology diffusion and its effects on social inequalities

We develop a dynamic general-equilibrium framework in which growth is driven by skill-biased technology diffusion. The model incorporates leisure–labor decisions and human capital accumulation through education. We are able to reproduce the trends in income inequality and labor and skills supplies observed in the United States between 1969 and 1996. The paper also provides an explanation for why more individuals invest in human capital when the investment premium is going down, and why the skill-premium goes up when the skills supply is increasing.

Gravity fields of the solar system /

Cover title.

A study of the effect of man's motion on the attitude and orbital motion of a satellite.

Technical report SEG-TR-65-41

Orbital dynamics of space vehicles.

Bibliography: p. 392-401.

Flight Mechanics/Estimation Theory Symposium 1992 : proceedings of a symposium sponsored by NASA Goddard Space Flight Center and held at Goddard Space Flight Center, Greenbelt, Maryland, May 5-7, 1992 /

Includes bibliographical references.