23,358 research outputs found
Complete determination of the orbital parameters of a system with N+1 bodies using a simple Fourier analysis of the data
Here we show how to determine the orbital parameters of a system composed of
a star and N companions (that can be planets, brown-dwarfs or other stars),
using a simple Fourier analysis of the radial velocity data of the star. This
method supposes that all objects in the system follow keplerian orbits around
the star and gives better results for a large number of observational points.
The orbital parameters may present some errors, but they are an excellent
starting point for the traditional minimization methods such as the
Levenberg-Marquardt algorithms.Comment: 4 page
Designing Optimal Quantum Detectors Via Semidefinite Programming
We consider the problem of designing an optimal quantum detector to minimize
the probability of a detection error when distinguishing between a collection
of quantum states, represented by a set of density operators. We show that the
design of the optimal detector can be formulated as a semidefinite programming
problem. Based on this formulation, we derive a set of necessary and sufficient
conditions for an optimal quantum measurement. We then show that the optimal
measurement can be found by solving a standard (convex) semidefinite program
followed by the solution of a set of linear equations or, at worst, a standard
linear programming problem. By exploiting the many well-known algorithms for
solving semidefinite programs, which are guaranteed to converge to the global
optimum, the optimal measurement can be computed very efficiently in polynomial
time.
Using the semidefinite programming formulation, we also show that the rank of
each optimal measurement operator is no larger than the rank of the
corresponding density operator. In particular, if the quantum state ensemble is
a pure-state ensemble consisting of (not necessarily independent) rank-one
density operators, then we show that the optimal measurement is a pure-state
measurement consisting of rank-one measurement operators.Comment: Submitted to IEEE Transactions on Information Theor
Tidal Evolution of Exoplanets
Tidal effects arise from differential and inelastic deformation of a planet
by a perturbing body. The continuous action of tides modify the rotation of the
planet together with its orbit until an equilibrium situation is reached. It is
often believed that synchronous motion is the most probable outcome of the
tidal evolution process, since synchronous rotation is observed for the
majority of the satellites in the Solar System. However, in the 19th century,
Schiaparelli also assumed synchronous motion for the rotations of Mercury and
Venus, and was later shown to be wrong. Rather, for planets in eccentric orbits
synchronous rotation is very unlikely. The rotation period and axial tilt of
exoplanets is still unknown, but a large number of planets have been detected
close to the parent star and should have evolved to a final equilibrium
situation. Therefore, based on the Solar System well studied cases, we can make
some predictions for exoplanets. Here we describe in detail the main tidal
effects that modify the secular evolution of the spin and the orbit of a
planet. We then apply our knowledge acquired from Solar System situations to
exoplanet cases. In particular, we will focus on two classes of planets,
"Hot-Jupiters" (fluid) and "Super-Earths" (rocky with atmosphere).Comment: 30 pages, 19 figures. Chapter in Exoplanets, ed. S. Seager, to be
published by University of Arizona Pres
Spin-orbit coupling and chaotic rotation for coorbital bodies in quasi-circular orbits
Coorbital bodies are observed around the Sun sharing their orbits with the
planets, but also in some pairs of satellites around Saturn. The existence of
coorbital planets around other stars has also been proposed. For close-in
planets and satellites, the rotation slowly evolves due to dissipative tidal
effects until some kind of equilibrium is reached. When the orbits are nearly
circular, the rotation period is believed to always end synchronous with the
orbital period. Here we demonstrate that for coorbital bodies in quasi-circular
orbits, stable non-synchronous rotation is possible for a wide range of mass
ratios and body shapes. We show the existence of an entirely new family of
spin-orbit resonances at the frequencies , where is the
orbital mean motion, the orbital libration frequency, and an integer.
In addition, when the natural rotational libration frequency due to the axial
asymmetry, , has the same magnitude as , the rotation becomes
chaotic. Saturn coorbital satellites are synchronous since , but
coorbital exoplanets may present non-synchronous or chaotic rotation. Our
results prove that the spin dynamics of a body cannot be dissociated from its
orbital environment. We further anticipate that a similar mechanism may affect
the rotation of bodies in any mean-motion resonance.Comment: 6 pages. Astrophysical Journal (2013) 6p
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