Orbital eccentricity

Summary

In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy. Definition In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values:

Circular orbit: e = 0
Elliptic orbit: 0 < e < 1
Parabolic trajectory: e = 1
Hyperbolic trajectory: e > 1

The eccentricity e is given by

Official source

https://en.wikipedia.org/wiki/Orbital_eccentricity

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We study how the gas in a sample of galaxies (M-* > 10(9) M-circle dot) in clusters, obtained in a cosmological simulation, is affected by the interaction with the intracluster medium (ICM). The dynamical state of each elemental parcel of gas is studied using the total energy. At z similar to 2, the galaxies in the simulation are evenly distributed within clusters, later moving towards more central locations. In this process, gas from the ICM is accreted and mixed with the gas in the galactic halo. Simultaneously, the interaction with the environment removes part of the gas. A characteristic stellar mass around M-* > 10(10) M-circle dot appears as a threshold marking two differentiated behaviours. Below this mass, galaxies are located at the external part of clusters and have eccentric orbits. The effect of the interaction with the environment is marginal. Above, galaxies are mainly located at the inner part of clusters with mostly radial orbits with low velocities. In these massive systems, part of the gas, strongly correlated with the stellar mass of the galaxy, is removed. The amount of removed gas is subdominant compared with the quantity of retained gas, which is continuously influenced by the hot gas coming from the ICM. The analysis of individual galaxies reveals the existence of a complex pattern of flows, turbulence and a constant fuelling of gas to the hot corona from the ICM, which could mean that the global effect of the interaction of galaxies with their environment is substantially less dramatic than previously expected.

Oxford Univ Press2017

Analysis of Spiral-Grooved Gas Journal Bearings by the Narrow-Groove Theory and the Finite Element Method At Large Eccentricities

Eliott Philippe Guenat, Elia Iseli, Jürg Alexander Schiffmann

A finite groove approach (FGA), based on the finite element method (FEM), is used for analyzing the static and dynamic behavior of spiral-grooved aerodynamic journal bearings at different eccentricities, number of grooves, and compressibility numbers. The results of the FGA are compared with the narrow-groove theory (NGT) solutions. For the rotating-groove case, a novel time-periodic solution method is presented for computing the quasi-steady-state and dynamic pressure profiles. The new method offers the advantage of avoiding time-consuming transient integration, while resolving a finite number of grooves. The static and dynamic solutions of the NGT and FGA approach are compared, and they show good agreement, even at large eccentricities (⁠ε=0.8⁠) and high compressibility numbers (Λ = 40). Stability maps at different eccentricities are presented. At certain operation points, a stability decrease toward larger eccentricities is observed. The largest stability deviations of the NGT from the FGA solutions occur at large groove angle, low number of grooves, and large compressibility numbers.

2020

Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3

Jean-Sebastien Caux, Martin Mourigal, Henrik Moodysson Rønnow, Thorsten Schmitt

When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies. Even if electrons in solids form bands and delocalize from the nuclei, in Mott insulators they retain their three fundamental quantum numbers: spin, charge and orbital(1). The hallmark of one-dimensional physics is a breaking up of the elementary electron into its separate degrees of freedom(2). The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago(3). Here we report observation of the separation of the orbital degree of freedom (orbiton) using resonant inelastic X-ray scattering on the one-dimensional Mott insulator Sr2CuO3. We resolve an orbiton separating itself from spinons and propagating through the lattice as a distinct quasi-particle with a substantial dispersion in energy over momentum, of about 0.2 electronvolts, over nearly one Brillouin zone.

2012