Orbits Of Terrestrial Planets Research Articles

Residual Gas and Dust around Transition Objects and Weak T Tauri Stars*

Abstract Residual gas in disks around young stars can spin down stars, circularize the orbits of terrestrial planets, and whisk away the dusty debris that is expected to serve as a signpost of terrestrial planet formation. We have carried out a sensitive search for residual gas and dust in the terrestrial planet region surrounding young stars ranging in age from a few to ∼10 Myr. Using high-resolution 4.7 μm spectra of transition objects (TOs) and weak T Tauri stars, we searched for weak continuum excesses and CO fundamental emission, after making a careful correction for the stellar contribution to the observed spectrum. We find that the CO emission from TOs is weaker and located farther from the star than CO emission from nontransition T Tauri stars with similar stellar accretion rates. The difference is possibly the result of chemical and/or dynamical effects (i.e., a low CO abundance or close-in low-mass planets). The weak T Tauri stars show no CO fundamental emission down to low flux levels (5 × 10−20 to 10−18 W m−2). We illustrate how our results can be used to constrain the residual disk gas content in these systems and discuss their potential implications for star and planet formation.

Formation of terrestrial planets in disks with different surface density profiles

We present the results of an extensive study of the final stage of terrestrial planet formation in disks with different surface density profiles and for different orbits of Jupiter and Saturn. We carried out simulations for disk densities proportional to r^-0.5, r^-1, and r^-1.5, and also for partially depleted disks as in the recent model of Mars formation by Izidoro et al (2014). The purpose of our study is to determine how the final assembly of planets and their physical properties are affected by the total mass of the disk and its radial profile. Because of the important roles of secular resonances in orbits and properties of the final planets, we studied the effects of these resonances as well. We have divided this study into two parts. In Part 1, we are interested in examining the effects of secular resonances on the formation of Mars and orbital stability of terrestrial planets. In Part 2, our goal is to determine trends that may exist between the disk surface density profile and the final properties of terrestrial planets. In the context of the depleted disk model, results show that the nu_5 resonance does not have a significant effect on the final orbits of terrestrial planets. However, nu_6 and nu_16 resonances play important roles in clearing their affected areas ensuring that no additional mass will be scattered into the accretion zone of Mars so that it can maintain its mass and orbital stability. In Part 2, our results indicate that despite some small correlations, in general, no trend seems to exist between the disk surface density profile and the mean number of the final planets, their masses, time of formation, and distances to the central star. We present the results of our simulations and discuss their implications for the formation of Mars and other terrestrial planets, as well as the physical properties of these objects such as their masses and water contents.

THE EFFECT OF PLANETS BEYOND THE ICE LINE ON THE ACCRETION OF VOLATILES BY HABITABLE-ZONE ROCKY PLANETS

Models of planet formation have shown that giant planets have a large impact on the number, masses and orbits of terrestrial planets that form. In addition, they play an important role in delivering volatiles from material that formed exterior to the snow-line (the region in the disk beyond which water ice can condense) to the inner region of the disk where terrestrial planets can maintain liquid water on their surfaces. We present simulations of the late stages of terrestrial planet formation from a disk of protoplanets around a solar-type star, and we include a massive planet (from 1 Earth mass to 1 Jupiter mass) in Jupiter's orbit at ~5.2 AU in all but one set of simulations. Two initial disk models are examined with the same mass distribution and total initial water content, but with different distributions of water content. We compare the accretion rates and final water mass fraction of the planets that form. Remarkably, all of the planets that formed in our simulations without giant planets were water-rich, showing that giant planet companions are not required to deliver volatiles to terrestrial planets in the habitable zone. In contrast, an outer planet at least several times the mass of Earth may be needed to clear distant regions from debris truncating the epoch of frequent large impacts. Observations of exoplanets from radial velocity surveys suggest that outer Jupiter-like planets may be scarce, therefore the results presented here suggest the number of habitable planets that reside in our galaxy may be more than previously thought.

Specific effects of large asteroids on the orbits of terrestrial planets and the ASETEP database

Specific effects of large asteroids on the orbits of terrestrial planets and the ASETEP database

On the habitability of the OGLE-2006-BLG-109L planetary system

We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired by the work of Malhotra & Minton. Using the linear Laplace–Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the subsystem of Jupiters may be found in a dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semimajor axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.

Stability of inclined orbits of terrestrial planets in habitable zones

In long-term stability studies of terrestrial planets moving in the habitable zone (HZ) of a sun-like star, we distinguish four different configurations: (i) planets moving in binary star systems, (ii) the inner type (where the gas giant moves outside the HZ), (iii) the outer type (where the gas giant is closer to the star, than the HZ) and (iv) the Trojan type (where the gas giant moves in the HZ). Since earlier calculations indicated, that the stability of the motion in the HZ also depends on the inclination of the terrestrial planet orbits, we present a detailed numerical investigation to show correlations between the eccentricity, the mass and the distance of the giant planet for various inclinations of the terrestrial planets. The orbital stability of the HZ was examined for all four configurations stated above. While we could find hardly any stable orbits for the first three types for inclinations higher than 40 ∘ , the Trojan planets can be stable up to an inclination of 60 ∘ . Additionally, we could also find some stabilizing effects of the inclination for the first three types. As dynamical model we used the elliptic restricted three-body problem, which consists of two massive and one mass-less body. This allows an application to all detected and future extrasolar single planet systems.

Orbital Stability of Terrestrial Planets inside the Habitable Zones of Extrasolar Planetary Systems

We investigate orbital stability of terrestrial planets inside the habitable zones of three stellar systems, i.e., 51 Peg, 47 UMa, and HD 210277, with recently discovered giant planets. These systems have similar habitable zones; however, their giant planets have different masses and significantly different orbital parameters. It is shown that stable orbits of terrestrial planets exist in the entire habitable zone of 51 Peg as well as in the inner part of the habitable zone of 47 UMa, but no stable orbits are found in the habitable zone of HD 210277. The obtained results allow us to draw general conclusions on the existence of stable orbits in the habitable zones of newly found extra-solar planetary systems.

The stability of the orbits of terrestrial planets in the habitable zones of known exoplanetary systems

We have investigated whether terrestrial planets can exist in orbits in known exoplanetary systems such that life could have emerged on those planets. Four contrasting systems have been examined in which giant planets have been detected. Mixed-variable symplectic numerical integration has been used to investigate the orbits of putative terrestrial planets within the habitable zone of each system (the range of distances from the star within which water at the surface of a terrestrial planet would be in the liquid phase). We have shown that Rho CrB and 47 UMa could have terrestrial planets in orbits that remain confined to their habitable zones for biologically significant lengths of time. We have also shown that the Gliese 876 and Ups And systems are very unlikely to have such orbits.

The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory)

The study of the evolution of planetary systems, primarily of the Solar System, is one of the basic problems of celestial mechanics. The stability of motion of giant planets on cosmogonic time scales was established by numerical and analytical methods, but the question about the evolution of orbits of terrestrial planets and arbitrary solar-type planetary systems remained open. This work initiates a series of papers allowing one to advance in solving the problem of the evolution of the solar-type planetary systems on cosmogonic time scales by using powerful analytical tools. In the first paper of this series, we choose the optimum reference system and obtain the Poisson series expansion of the Hamiltonian of the problem in all Keplerian elements. We propose to use the integral representation of the corresponding coefficients or the Poisson processor means instead of conventionally addressing any possible special functions. This approach extremely simplifies the algorithm. The next paper of this series deals with the calculation of the expansion coefficients.