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Register a new userOn the coplanar eccentric non restricted co-orbital dynamics
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We study the phase space of eccentric coplanar co-orbitals in the non-restricted case. Departing from the quasi-circular case, we describe the evolution of the phase space as the eccentricities increase. We find that over a given value of the eccentricity, around $0.5$ for equal mass co-orbitals, important topological changes occur in the phase space. These changes lead to the emergence of new co-orbital configurations and open a continuous path between the previously distinct trojan domains near the $L_4$ and $L_5$ eccentric Lagrangian equilibria. These topological changes are shown to be linked with the reconnection of families of quasi-periodic orbits of non-maximal dimension.
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We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenters dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(sigma,Deltaomega) = (pm 60deg, mp 120deg)$, where sigma is the difference in mean longitudes and Deltaomega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.
Exoplanet detection in the past decade by efforts including NASAs Kepler and TESS missions has discovered many worlds that differ substantially from planets in our own Solar system, including more than 400 exoplanets orbiting binary or multi-star systems. This not only broadens our understanding of the diversity of exoplanets, but also promotes our study of exoplanets in the complex binary and multi-star systems and provides motivation to explore their habitability. In this study, we analyze orbital stability of exoplanets in non-coplanar circumbinary systems using a numerical simulation method, with which a large number of circumbinary planet samples are generated in order to quantify the effects of various orbital parameters on orbital stability. We also train a machine learning model that can quickly determine the stability of the circumbinary planetary systems. Our results indicate that larger inclinations of the planet tend to increase the stability of its orbit, but change in the planets mass range between Earth and Jupiter has little effect on the stability of the system. In addition, we find that Deep Neural Networks (DNNs) have higher accuracy and precision than other machine learning algorithms.
A stable population of objects co-orbiting with Venus was recently hypothesized in order to explain the existence of Venuss co-orbital dust ring. We conducted a 5 day twilight survey for these objects with the Cerro-Tololo Inter-American Observatory (CTIO) 4 meter telescope covering about 35 unique square degrees to 21 mag in the $r$-band. Our survey provides the most stringent limit so far on the number of Venus co-orbital asteroids; it was capable of detecting $5%$ of the entire population of those asteroids brighter than 21 magnitude. We estimate an upper limit on the number of co-orbital asteroids brighter than 21 magnitude (approximately 400-900 m in diameter depending on the asteroid albedo) to be $N=18^{+30}_{-14}$. Previous studies estimated the mass of the observed dust ring co-orbiting with Venus to be equivalent to an asteroid with a 2 km diameter ground to dust. Our survey estimates $<6$ asteroids larger than 2 km. This implies the following possibilities: that Venus co-orbitals are non-reflective at the observed phase angles, have a very low albedo ($<1%$), or that the Venus co-orbital dust ring has a source other than asteroids co-orbiting Venus. We discuss this result, and as an aid to future searches, we provide predictions for the spatial, visual magnitude, and number density distributions of stable Venus co-orbitals based on the dynamics of the region and magnitude estimates for various asteroid types.
We present refined parameters for the extrasolar planetary system HAT-P-2 (also known as HD 147506), based on new radial velocity and photometric data. HAT-P-2b is a transiting extrasolar planet that exhibits an eccentric orbit. We present a detailed analysis of the planetary and stellar parameters, yielding consistent results for the mass and radius of the star, better constraints on the orbital eccentricity, and refined planetary parameters. The improved parameters for the host star are M_star = 1.36 +/- 0.04 M_sun and R_star = 1.64 +/- 0.08 R_sun, while the planet has a mass of M_p = 9.09 +/- 0.24 M_Jup and radius of R_p = 1.16 +/- 0.08 R_Jup. The refined transit epoch and period for the planet are E = 2,454,387.49375 +/- 0.00074 (BJD) and P = 5.6334729 +/- 0.0000061 (days), and the orbital eccentricity and argument of periastron are e = 0.5171 +/- 0.0033 and omega = 185.22 +/- 0.95 degrees. These orbital elements allow us to predict the timings of secondary eclipses with a reasonable accuracy of ~15 minutes. We also discuss the effects of this significant eccentricity including the characterization of the asymmetry in the transit light curve. Simple formulae are presented for the above, and these, in turn, can be used to constrain the orbital eccentricity using purely photometric data. These will be particularly useful for very high precision, space-borne observations of transiting planets.
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