Related papers: On the Reparameterization Between Cartesian Positi…
We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are…
Simplified solutions to determine binary elements by astrometry were obtained in terms of elementary functions (Asada et al. 2004), and therefore require neither iterative nor numerical methods. In the framework of the simplified solution,…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other…
Numerical solutions of Kepler's Equation are critical components of celestial mechanics software, and are often computation hot spots. This work uses symbolic regression and a genetic learning algorithm to find new initial guesses for…
A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…
This work presents a new method for generating impulsive trajectories in restricted two-body systems by leveraging Riemannian geometry. The proposed method transforms the standard trajectory optimization problem into a purely geometric one…
We revisit the old problem of which is the best single particle basis to express a Hubbard-like lattice model. A rigorous variational solution of this problem leads to equations in which the answer depends in a self-consistent manner on the…
The complexity of a learning task is increased by transformations in the input space that preserve class identity. Visual object recognition for example is affected by changes in viewpoint, scale, illumination or planar transformations.…
Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass…
Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation,…
Future missions like Roman, HabEx, and LUVOIR will directly image exoplanets in reflected light. While current near infrared direct imaging searches are only sensitive to young, self-luminous planets whose brightness is independent of their…
We present a new extensive analysis of the old problem of finding a satisfactory calibration of the relation between the geometric albedo and some measurable polarization properties of the asteroids. To achieve our goals, we use all…
The generalized post-Keplerian parametrization for compact binaries on eccentric bound orbits is established at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories. This result is used to compute the…
Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the PPN parameters…
The possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test particle freely orbiting a spherically symmetric mass in the Solar System is analyzed. It should be possible, in principle, to detect…
Microlensing is a powerful tool for studying stellar atmospheres because as the source crosses regions of formally infinite magnification (caustics) the surfaceof the star is resolved, thereby allowing one to measure the radial intensity…
A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic deviation…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…