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By dimensional reduction of the Lovelock Lagrangian, effective four-dimensional field equations and expressions for the cosmological and gravitational constants are obtained. A cosmological model is discussed with the n-torus as internal…
We establish the three-dimensional architecture of the Kepler-419 (previously KOI-1474) system to be eccentric yet with a low mutual inclination. Kepler-419b is a warm Jupiter at semi-major axis a = 0.370 +0.007/-0.006 AU with a large…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
The so-called "global polytropic model" is applied to the numerical study of the exoplanet systems HD 10180, Kepler-32, Kepler-33, Kepler-102, and Kepler-186. We compare computed distances of planets from their host stars with corresponding…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
The nearly circular (mean eccentricity <e>~0.06) and coplanar (mean mutual inclination <i>~3 deg) orbits of the Solar System planets motivated Kant and Laplace to put forth the hypothesis that planets are formed in disks, which has…
When an extrasolar planet passes in front of its star (transits), its radius can be measured from the decrease in starlight and its orbital period from the time between transits. Multiple planets transiting the same star reveal more: period…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
NASA's Kepler mission will fly a photometer based on a wide-field Schmidt camera with a 0.95 m aperture, staring at a single field continuously for at least 4 years. Although the mission's principal aim is to locate transiting extrasolar…
Constellation or formation flying is a common concept in space Gravitational Wave (GW) mission proposals for the required interferometry implementation. The spacecraft of most of these mission proposals go to deep space and many have…
The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies.…
The planetary ephemerides play a crucial role for spacecraft navigation, mission planning, reduction and analysis of the most precise astronomical observations. The construction of such ephemerides is highly constrained by the tracking…
In this short note, we analyze geometric properties of orbit spaces of certain involutions in dimensions four, five, and six. We consider constructions of $\mathcal{F}$-structures on manifolds of dimension at least four that allows us to…
Understanding the consequences of the gravitational interaction between a star and a planet is fundamental to the study of exoplanets. The solution of the two-body problem shows that the planet moves in an elliptical path around the star…
During its 5 year mission, the Kepler spacecraft has uncovered a diverse population of planetary systems with orbital configurations ranging from single-transiting planets to systems of multiple planets co-transiting the parent star. By…
The Interplanetary Magnetic Field shows complex spatial and temporal variations. Single spacecraft measurements reveal only a one dimensional section of this rich four dimensional phenomenon. Multi-point measurements of the four Cluster…
We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 based solely on Doppler measurements and demanding long-term orbital stability. Our dataset incorporates…
Inferring planetary parameters from transit timing variations is challenging for small exoplanets because their transits may be so weak that determination of individual transit timing is difficult or impossible. We implement a useful…