Long-term perturbations due to a disturbing body in elliptic inclined orbit

In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body's inclination, and illustrate that the lunar obliquity with the value 6.68\degree is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure

Algorithms for On-Board Orbit Determination using GPS OBODE-GPS

In the framework of GPS-based onboard orbit determination in real-time, a prototype implementation of an orbit determination software (OBODE-GPS) has been developed. The main goal of the OBODE-GPS aims to achieve an accuracy of 10 m along with minimum computational cost and usage of a taylored force model. For this sake, only the GPS code pseudo-range at the L1 frequency is applied, considering the effects of the clock offsets of the GPS and user satellites. The dynamic model considers a complex geopotential, while the state covariance matrix is propagated based on a simplified model. The Cowell`s method is used to propagate the orbit state vector; and a simple 4th order Runge-Kuta (RK 4) algorithm is used. Based on a conventional extended Kalman Filter, the spacecraft position and velocity state vectors as well as the user clock offset is extimated. To validate this model, real data from Topex/Poseidon satellite, which makes use of a dual frequency GPS receiver onboard, are apllied, and the results are compared with the Topex/Poseidon Precision Orbit Eqhemeris (POE) generated by NASA/JPL. In the analysis, emphasis is given to the determintion of an appropriate order of the gravity field and the step-size of the RK4 integrator. Furthermore, the consequences of including or excluding the J2 effects in the computation of the transition matrix are evaluated. Finally, the GPS broadcast ephemeris are comared with the GPS precise ephemeris

An optimization approach to search for quasi-critical inclinations for direct and retrograde orbits

When only the secular terms due to the central body oblateness are considered in the gravitational potential, the critical inclination classical values are about 63.43° and 116.56° for the direct and retrograde orbits, respectively. If sectoral terms are included into disturbing function, the equations of motion become coupled, then searching for critical inclinations is not a trivial problem. Thus, for the purpose of overcoming this difficulty and to shed light on the effect of inserting the C22 sectoral hamornic in the Hamiltonian function, the quasi-critical inclinations concept is revised and its solution is proposed as an optimization problem. In this sense, the present article makes the following contributions to the quasi-critical inclination problem: (i) applying the nonlinear optimization tools to solve this problem; (ii) through this technique, obtaining quasi-critical inclinations for the retrograde case for the first time; (iii) using this technique to find direct and retrograde orbits around Io, a very important body to be studied in the future

Swing-By Applications and Estimation of the Van Allen Belts’ Radiation Exposure for a Spacecraft in a Low Thrust Transfer to the Moon

This paper presents a handful of the underlying properties of a spacecraft’s transfer from a low Earth orbit (LEO) to the moon’s orbit using an electric propulsion (low-thrust) system. The use of analytical and numerical-analytical modeling in complex natural and technical processes is a key factor in this issue of Symmetry, which has been thoroughly explored in this paper. First, an optimization problem was considered to find the locations and lengths of the thrust arcs that maximizes the final mass of the spacecraft for a number of transfer orbits, thereby limiting the scope of trajectories to the most fuel-efficient ones. In addition to this, the Van Allen belts were modelled according to the density of electrons and protons in each point of space, in order to measure the total radiation absorbed by the spacecraft through an integration of the density of particles over the corresponding time. The simulations were then able to predict the relationship between the fluence of the particles and several initial parameters, such as the initial orbit’s eccentricity and the propulsion system’s characteristics. Then, a multi-linear regression and an artificial neural network were fitted to the data through a regression that related the fluence of protons and electrons as a function of the following parameters: mission time, specific impulse, thrust, final mass (i.e., propellant consumption) and the initial height of the perigee, eccentricity and inclination. This analysis was proven to be powerful due to the expressive values from statistical tests, showing underlying positive correlations between thrust, mission time and final spacecraft mass with the fluence of particles, and negative correlations between specific impulse, initial orbit eccentricity, inclination and the height of the perigee with the fluence of particles. Finally, an analysis of a swing-by maneuver was also carried out, together with the radiation incidence, revealing hidden dependencies of the increments in energy and velocity with respect to the fuel consumption, radiation absorption, propulsion system and initial orbit parameters. © 2022 by the authors. Licensee MDPI, Basel, Switzerland

On the effects of solar radiation pressure on the deviation of asteroids

In this work, we study the effects of solar radiation pressure (SRP) on the problem of changing the orbit of an asteroid to support planetary defense, scientific research, or exploitation of materials. This alternative considers a tethered reflective balloon (or a set of reflective balloons) attached to the asteroid, with a high area-to-mass ratio, to use the SRP to deflect a potentially hazardous asteroid (PHA) or to approximate the target asteroid to Earth. The tether is assumed to be inextensible and massless, and the motion is described only in the orbital plane of the asteroid around the Sun. The model is then used to study the effects that the tether length, the reflectivity coefficient, and the area-to-mass ratio have on the deviation of the trajectory of the asteroid. © 2021: Instituto de Astronomía, Universidad Nacional Autónoma de Méxic

A survey on extensions of the pure gravity swing-by maneuver

The present paper surveys the more recent techniques related to the swing-by maneuver, where a spacecraft changes its energy and angular momentum by passing close to celestial bodies. It is focused on the literature related to extensions of this maneuver, with emphasis in the powered version, where an impulse is applied to the spacecraft near the closest approach. Several mathematical models are considered, including the patched-conics approximation for analytical studies, and the restricted three-body problem for the numerical simulations. The main goal is to show the models and the main conclusions available in the literature for those maneuvers. Some key results are shown to discuss important aspects of this maneuver, including the analysis of the energy variation of the spacecraft, the behavior of the trajectories and other applications. © 2021: Instituto de Astronomía, Universidad Nacional Autónoma de Méxic

Analysis of the dynamics of a spacecraft in the vicinity of an asteroid binary system with equal masses

In this work, we performed a dynamical analysis of a spacecraft around a nearly equal-mass binary near-Earth asteroid with application to the asteroid 2017 YE5, which is also a possible dormant Jupiter-family comet. Thus, we investigated the motion of a particle around this binary system using the circular restricted three-body problem. We calculated the locations of the Lagrangian points of the system and their Jacobi constant. Through numerical simulations, using the Poincaré Surface of Sections, it was possible to find several prograde and retrograde periodic orbits around each binary system's primary, some exhibiting significantly-sized higher-order behavior. We also calculated the stability of these orbits. After finding the periodic orbits, we investigated the influence of solar radiation pressure on these orbits. For this analysis, we considered that the area-to-mass ratio equals 0.01 and 0.1. We also performed a spacecraft lifetime analysis considering the physical and orbital characteristics of the 2017YE5 system and investigated the behavior of a spacecraft in the vicinity of this system. We analyzed direct and retrograde orbits for different values of Jacobi's constant. This study investigated orbits that survive for at least six months, not colliding or escaping the system during that time. We also analyze the initial conditions that cause the spacecraft to collide with M1 or M2, or escape from the system. In this work, we take into account the gravitational forces of the binary asteroid system and the solar radiation pressure (SRP). Finally, we calculated optimal bi-impulsive orbital maneuvers between the collinear Lagrangian points. We found a family of possible orbital transfers considering times of flight between 0.1 and 1 day.publishe