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Orbital Mechanics Analysis Program provides engineers with simple tool for analysis or synthesis of any orbital maneuvering function involving vehicle and target. Program useful in such applications as proximity operations and rendezvous maneuvers.
Orbital mechanics, examining problems relating to patched conics, perigee determination, eccentricity of satellite orbits and drag effect computations
Orbital mechanics as a discipline is principally concerned with solving the set of equations for analyzing the motion of a satellite under various conditions. This activity on the surface may not seem crucial to conducting experiments in space, but it provides insights into the way in which forces may influence these experiments. More directly, for experiments concerned with external targets, it provides predictions of the satellites's position and velcoity verus time, enabling extensive preflight planning and resulting in optimum use of on-orbit time.
This is a primer on orbital mechanics originally intended for college-level physics students.
We consider a two-point boundary value problem (TPBVP) in orbital mechanics involving a small body (e.g., a spacecraft or asteroid) and N larger bodies. The least action principle TPBVP formulation is converted into an initial value problem via the addition of an appropriate terminal cost to the action functional. The latter formulation is used to obtain a fundamental solution, which may be used to solve the TPBVP for a variety of boundary conditions within a certain class. In particular, the method of convex duality allows one to interpret the least action principle as a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. In the case where the time duration is less than a specific bound, there exists a unique critical point for the resulting differential game, which yields the fundamental solution given in terms of the solutions of associated Riccati equations.
The relationship between the eigenvalues of the linearized differential equations of orbital mechanics and the stability characteristics of numerical methods is presented. It is shown that the Cowell, Encke, and Encke formulation with an independent variable related to the eccentric anomaly all have a real positive eigenvalue when linearized about the initial conditions. The real positive eigenvalue causes an amplification of the error of the solution when used in conjunction with a numerical integration method. In contrast an element formulation has zero eigenvalues and is numerically stable.
Major mechanical systems of the Orbiter space vehicle are summarized with respect to general design details, manner of operation, expected performance, and, where applicable, unique features. A synopsis of data obtained during the five atmospheric flight tests of spacecraft OV-101 and status of the systems for the first orbital spacecraft STS-1 are presented.
The motions of co-orbiting satellites is examined with reference to a free flying satellite requiring periodic servicing and an orbiting service base. The problems of differential orbit decay and nodal regression are emphasized.
A reference handbook on modern dynamic orbit theory is presented. Starting from the most basic inverse-square law, the law of gravity for a sphere is developed, and the motion of point masses under the influence of a sphere is considered. The reentry theory and the orbital theory are discussed along with the relative motion between two bodies in orbit about the same planet. Relative-motion equations, rectangular coordinates, and the mechanics of simple rigid bodies under the influence of a gravity gradient field are also discussed.
This handbook provides parametric data useful both to the space vehicle designer and mission analyst. It provides numerical and analytical relationships between missions and gross vehicle characteristics as a function of performance parameters. The effects of missile constraints and gross guidance limitations plus operational constraints such as launch site location, tracking net location, orbit visibility and mission on trajectory and orbit design parameters are exhibited. The influence of state-of- the-art applications of solar power as compared to future applications of nuclear power on orbit design parameters, such as eclipse time, are among the parameters included in the study. The principal aim, however, is in providing the analyst with useful parametric design information to cover the general area of earth satellite missions in the region of near-earth to cislunar space and beyond and from injection to atmospheric entry and controlled descent. The chapters are organized around the central idea of orbital operations in the 1961-1969 era with emphasis on parametric flight mechanics studies for ascent phase and parking orbits, transfer maneuvers, rendezvous maneuver, operational orbit considerations, and operational orbit control. The results are based almost entirely on the principles of flight and celestial mechanics. Numerous practical examples have been worked out in detail. This is especially important where it has been difficult or impossible to represent all possible variations of the parameters. The handbook contains analytical formulae and sufficient textual material to permit their proper use. The analytic methods consist of both exact and rapid, approximate methods. Scores of tables, working graphs and illustrations amplify the mathematical models which, together with important facts and data, cover the engineering and scientific applications of orbital mechanics. Each of the five major chapters are arranged to provide a rapid review of an entire astrodynamic subject. By the use of compact graphical and tabular presentation the full scope of the material is made available in an easy-to-use style. Throughout the volume the analyst is shown, by means of suitable introductions, notes, authoritative examples, and cross-references the vital interrelation of the various orbital mechanics topics in the general field of earth satellites and satellite rendezvous. The handbook is designed to give the analyst rapid, reliable access to the mathematics of orbital mechanics needed for virtually any working requirements.
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Radar ranging experiment onboard Jupiter orbiter, concerning perturbations, gravitational harmonics and short arc orbit determination
The present conference discusses topics in LEO mechanics, the earth-sun-moon orbital regime, space navigation, and lunar and planetary missions. Attention is given to an improved technique for passive eccentricity control, H-I launch vehicle mission planning, glideslope approaches, the control of Space Station-based tethered systems, rendezvous operations in GEO, launch-window expansion and trajectory correction for the First Lunar Swingby, the nature of lunar gravity assists, and the numerical determination of libration-point trajectories with solar exclusion zone-avoiding out-of-plane maneuvers. Also discussed are the interferometric tracking of multiple spacecraft, an improved determination of Martian satellite orbits, the Magellan Venus Mapping Mission, the Mars Rover Sample Return Mission, round-trip trajectories for manned Mars exploration, advanced missions using fusion propulsion, Vesta trajectories and navigation, and Voyager interstellar mission design.
One intriguing issue in the nucleon spin decomposition problem is the existence of two types of decompositions, which are representably characterized by two different orbital angular momenta (OAMs) of quarks. The one is the mechanical OAM, while the other is the so-called gauge-invariant canonical (g.i.c.) OAM, the concept of which was introduced by Chen et al. An especially delicate quantity is the g.i.c. OAM, which must be distinguished from the ordinary (gauge-variant) canonical OAM. We find that, owing to its analytically solvable nature, the famous Landau problem offers an ideal tool to understand the difference and the physical meaning of the above three OAMs, i.e. the standard canonical OAM, g.i.c. OAM, and the mechanical OAM. We analyze these three OAMs in two different formulations of the Landau problem, first in the standard (gauge-fixed) formulation and second in the gauge-invariant (but path-dependent) formulation of DeWitt. Especially interesting is the latter formalism. It is shown that the choice of path has an intimate connection with the choice of gauge, but they are not necessarily equivalent. Then, we answer the question about what is the consequence of a particular choice of path in DeWitt’s formalism. This analysis also clarifies the implication of the gauge symmetry hidden in the concept of g.i.c. OAM. Finally, we show that the finding above offers a clear understanding about the uniqueness or non-uniqueness problem of the nucleon spin decomposition, which arises from the arbitrariness in the definition of the so-called physical component of the gauge field.
The development of new techniques and their applications to problems in satellite geodesy, oceanography, orbit determination, long-time prediction, regularization, potential determination, stability of natural and artificial satellites and planets, etc. are described. Applications to polar motion, earth rotation and to tectonic plate motion are discussed as related to the Lageos, Starlette and Seasat missions. Numerical averaging techniques are described for the determination of the long term motion of near-resonant gravitational systems with application to Jupiter's Galilean satellites. Regions of long-time stability and ergodicity are established in the restricted problem.
The placement of cryogenic fuel/propellant depot stations in Earth orbit has the potential to transform the nature and operations for many types of spaceflight missions. Today, spaceflight missions are almost universally required to carry the entire amount of fuel required for the mission, for the entire duration of the mission, from the point of launch. This is the rough equivalent of making a drive from Ohio to California, requiring the traveler to bring along the total sum of gasoline required for the entire trip, without being able to ‘fill-up’ anywhere along the route. Obviously, this framework of travel greatly encumbers the breadth, scope, and efficiency of potential journeys. Cryogenic fuel/propellant depots have not been implemented because many technical, operational, and engineering challenges still exist. These must be overcome prior to the placement of usable on-orbit propellant depots. This thesis investigates three specific engineering challenges related to on-orbit propellant depots, and presents the current state, technological challenges, and ultimate benefits of on-orbit cryogenic refueling.
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