Methods of regularization for computing orbits in celestial mechanics
Numerical and analytical methods for orbit computation in celestial mechanics during and beyond collision by introduction of regularized coordinates
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Numerical and analytical methods for orbit computation in celestial mechanics during and beyond collision by introduction of regularized coordinates
Vectorial concept for solving three body problem in celestial mechanics
Real-time applications of celestial mechanics in the mercury program
One-step methods for numerical integration of initial value problems in ordinary differential equations applied to celestial mechanics
Lie series applications to celestial mechanics, accelerators, satellite orbits, and optimization
The unprecedented progress in celestial mechanics (orbital mechanics, astrodynamics, space dynamics) is reviewed from 1957 to date. The engineering, astronomical and mathematical aspects are synthesized. The measuring and computational techniques developed parallel with the theoretical advances are outlined. Major unsolved problem areas are listed with proposed approaches for their solutions. Extrapolations and predictions of the progress for the future conclude the paper.
Second-order solution for motion of satellite about oblate earth, including second, third, and fourth zonal harmonics - celestial mechanics
The application of MACSYMA to general first order perturbation theory in celestial mechanics is explored. Methods of derivation of small variations in the Keplerian orbital elements are developed. As an example of the methods, the small general relativistic perturbations on the two-body Newtonian motion, resulting from the rotation of the central body, are developed in detail.
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
There are two basic efforts in the Mariner 9 celestial mechanics experiment: the determination of the gravity field of Mars and the performance of a very precise test of the theory of general relativity. In addition, there are a number of astrodynamic constants that are being determined. All the analyses are based on the Mariner 9 radio tracking data.
Book on linear and ordinary celestial mechanics covering perturbed two body motion, numerical methods, canonical theory and initial value problems
The motion of the Jovian commensurability resonances during the early evolution of the solar system induced by the dissipation of the accretion disk results in fundamental differences in the celestial mechanics of objects over which a resonance passes from that observed for a stationary resonance. Objects experiencing resonance passage acquire irreversible increases of average eccentricity to large values accounting for the present-day random velocities of the asteroids. Semi-major axes are similarly irreversibly decreased by amounts capable of clearing the Kirkwood gaps. The gap widths are in agreement with observation.
Accumulation of errors using numerical integration methods for solving celestial equations of motion
Periodic solutions for restricted three-body problem
Derivation of closed perturbed precessing elliptic orbits of arbitrary eccentricity and small major axis about smaller of two attracting bodies of arbitrary mass ratio
Lunar and Venusian masses and other parameters measured by Mariner 5
Propulsion systems for deep space missions, investigating gravitational corrections affecting spacecraft orbits
Tracking data analyses of Mariners 6 and 7 for determining Earth Moon mass ratio and Mars mass