Changes In Semimajor Axis Research Articles

Control Laws for Minimum Orbital Change-The Satellite Retrieval Problem

Introduction I N a typical trajectory optimization problem the time of  ight or propellant consumed is minimized, resulting in signiŽ cant changes in one or more orbital elements. In situations where an upper-stage engine has failed to burn completely or a solid motor remains unŽ red, the optimization task is reversed; the goal is to expend as much propellant as possible, sometimes with little or no change in the orbital elements. In such cases the payload is often not in the desiredorbit, and mission plannersmight want to retrieve the payloadusing the space shuttle and subsequentlyrelaunch it. Safety concernsmight prohibit returningthe payloadand upper stage in the shuttle cargo bay with propellants still onboard. This problem was Ž rst encountered in 1984 with the Westar and Palapa B spacecraft, which failed to achieve their intended orbits. The solid-propellant apogee kick motors were Ž red to deplete the propellants, and the spacecraft were safely retrieved. Generally, there are no means to vent liquid propellants,and they must be consumed by reigniting the engine. The space shuttle itself must use this method in the event that one of the orbital maneuvering system pods is leaking propellant; standard procedure calls for consumingthis leakingpropellantby Ž ring the thrusterout of plane, thus minimizing the changes in semimajor axis and eccentricity. In this Note it is assumed that the vehicle is presently in an orbit compatible with shuttle operations for satellite retrieval. Using only a single sustained burn, the thrust generated needs to be directed so as to minimize the changes in semimajor axis a, eccentricitye, and inclination i , ensuring that the new orbit would be accessible by a later shuttle mission.

The Primordial Excitation and Clearing of the Asteroid Belt

In this paper, we use N-body integrations to study the effect that planetary embryos spread between ∼0.5 and 4 AU would have on primordial asteroids. The most promising model for the formation of the terrestrial planets assumes the presence of such embryos at the time of formation of Jupiter. At the end of their runaway growth phase, the embryos are on quasi-circular orbits, with masses comparable to that of the Moon or Mars. Due to gravitational interactions among them, and with the growing Jupiter, their orbits begin to cross each other, and they collide, forming bigger bodies. A general outcome of this model is that a few planets form in a stable configuration in the terrestrial planet region, while the asteroid belt is cleared of embryos. Due to combined gravitational perturbations from Jupiter and the embryos, the primordial asteroids are dynamically excited. Most of the asteroids are ejected from the system in a very short time, the dynamical lifetime being on the order of 1 My. A few asteroids (less than 1%) survive, mostly in the region 2.8–3.3 AU, and their eccentricity and inclination distribution qualitatively resembles the observed one. The surviving asteroids have undergone changes in semimajor axis of several tenths of an AU, which could explain the observed radial mixing of asteroid taxonomic types. When the distribution of massive embryos is truncated at 3 AU, we obtain too many asteroids in the outer part of the belt, especially too many Hildas. This suggests that the formation of Jupiter did not prohibit the formation of large embryos in the outer belt and Jupiter did not accrete them while it was still growing.

Low-Thrust Eccentricity-Constrained Orbit Raising

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

The dangerous border of the 5:2 mean motion resonance

After discovering that asteroid (2953) Vysheslavia, a Koronis family member, has a typical dynamical lifetime of the order of 10 Myr only against “falling” into the 5:2 Kirkwood gap and ending up in a hyperbolic orbit (Milani and Farinella, 1995. Icarus 114, 209–212), we decided to repeat the same study for two other asteroids, 1991 UA 2 and 1993 FR 58, lying also very close to the outer edge of the same resonance. The orbital elements of these bodies were not yet accurate enough and we appealed to observers, both professional and amateur, to obtain more astrometric data. Eight groups in three different countries carried out observations, and as a result the Minor Planet Center could derive updated, accurate orbits for both objects. Here we report on the preliminary results of our study. Whereas the long-term behavior of 1991 UA 2 looks fairly regular and stable, 1993 FR 58 exhibits a typical “stable chaos” behavior; nevertheless, it does not end up in the resonance within a time span of 50 Myr. On the other hand, its fictitious clones, placed just 3–4 × 10 −3 AU closer to the resonance, undergo large irregular semimajor axis changes, fall into the resonance and escape on a timescale <1 Myr.

Interplanetary dust dynamics: I. Long-term gravitational effects of the inner planets on zodiacal dust

Whereas the inner planets' perturbations on meteoroids' and larger interplanetary bodies' orbits have been studied extensively, they are usually neglected in studies of the dynamics of smaller particles producing the zodiacal light through scattering of sunlight. Forces acting on these dust particles are fairly well known and include radiation forces and interaction with the solar wind. This article is the first in a series aimed at improving our knowledge of the dynamical evolution of dust in interplanetary space by studying the combined effects of these perturbations including gravitational perturbations by the planets Venus, Earth, Mars, and Jupiter. The necessity of including effects of the inner planets in dust dynamics investigations is established. Sample trajectories are presented to illustrate commonly occurring phenomenae, such as nonmonotonic changes in semimajor axis, eccentricity, inclination, and in the line of nodes. These perturbations are shown to be due to the inner planets as opposted to Jupiter or nongravitational forces.

Earth albedo and the orbit of Lageos

The long-period perturbations in the orbit of Lageos satellite due to the earth's albedo have been found using a new analytical formalism. The earth is assumed to be a sphere whose surface diffusely reflects sunlight according to Lambert's law. Specular reflection is not considered. The formalism is based on spherical harmonics; it produces equations which hold regardless of whether the terminator is seen by the satellite or not. Specializing in the case of a realistic zonal albedo shows that Lageos' orbital semimajor axis changes periodically by only about a centimeter and the eccentricity by two parts in 105. The longitude of the node increases secularly by about 6×10−4 arc sec yr−1. The effect considered here can explain neither the secular decay of 1.1 mm day−1 in the semimajor axis nor the observed along-track variations in acceleration of order 2×10−12 ms−2.

The last 14 days of Skylab 1: orbit determination and analysis

The orbit of Skylab 1 (1973-27 A) has been determined from some 1400 observations during the 14 days before decay on 1979 July 11. There are 14 daily orbits, with standard deviations corresponding to average accuracies of 40 m cross track and 30 m radial. A 15th orbit, only slightly less accurate, was determined from observations on July 11 between the manoeuvre at 07.45 U. T. and decay at 16.37 U. T. The variations in inclination due to atmospheric rotation and 16th-order resonance with the geopotential have been successfully analysed, to give the first values of 16th-order geopotential coefficients determined from resonance, and a value of 1.10 ± 0.07 rev/day for the atmospheric rotation rate at a height of 210-220 km. The daily changes in semi-major axis have been used to determine 13 daily values of air density, at heights from 252 km down to 179 km. All agree well with the CIRA 1972 model, and indicate a smaller semi-annual variation than in the early 1970s. The variations of eccentricity and argument of perigee take unusual forms, but detailed analysis shows that the variations are in full accord with the theory for an atmosphere with day-to-night variation in density, with the perigee progressing towards the point of minimum density.

Lorentz scattering of interplanetary dust

Charged dust grains in a turbulent magnetic field will see a Lorentz force due to the convection of the solar magnetic field past them at the solar wind velocity. Since the sign of this magnetic field is randomly varying, the direction of the force will be random, and the net effect will be to randomly scatter the orbital elements of these particles. The square roots of the mean square change in semimajor axis, inclination, and eccentricity are determined as a function of the particles' original orbital elements. Particles 3 μm in radius and smaller will have their motions strongly perturbed or dominated by Lorentz scattering. This scattering will have an effect comparable to, or greater than, the Poynting-Robertson effect on these particles for time scales comparable to their Poynting-Robertson lifetimes.

Orbital resonance in a dissipative medium

Orbital resonances tend to force bodies into noncircular orbits. If a body is also under the influence of an eccentricity-reducing medium, it will experience a secular change in semimajor axis which may be positive or negative depending on whether its orbit is exterior or interior to that of the perturbing body. Thus a dissipative medium can promote either a loss or a gain in orbital energy. This process may explain the resonant structure of the asteroid belt and of Saturn's rings. For reasonable early solar system parameters, it would clear a gap near the 2:1 resonance with Jupiter on a time scale of a few thousand years; the gap width would be comparable to the Kirkwood gap presently at the location in the asteroid belt. Similarly, a gap comparable in width to Cassini's division would be cleared in Saturn's rings at the 2:1 resonance with Mimas in ∼10 6 yr. Most of the material from the gap would be deposited at the outer edge of ring B. The process would also affect the radial distribution of preplanetary material. Moreover, it provides an explanation for the large amplitude of the Titan-Hyperion libration. Consideration of the effects of dissipation on orbits near the stable L 4 and L 5 points of the restricted three-body problem indicates that energy loss causes particles to move away from these points. This results explains the large amplitude of Trojan asteroids about these points and the possible capture of Trojan into orbit about Jupiter.