Orbital eccentricity | EPFL Graph Search

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. 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 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, and the coefficient of the inverse-square law central force such as in the theory of gravity or electrostatics in classical physics: ( is negative for an attractive force, positive for a repulsive one; related to the Kepler problem) or in the case of a gravitational force: where ε is the specific orbital energy (total energy divided by the reduced mass), μ the standard gravitational parameter based on the total mass, and h the specific relative angular momentum (angular momentum divided by the reduced mass). For values of e from 0 to 1 the orbit's shape is an increasingly elongated (or flatter) ellipse; for values of e from 1 to infinity the orbit is a hyperbola branch making a total turn of 2 arccsc(e), decreasing from 180 to 0 degrees. Here, the total turn is analogous to turning number, but for open curves (an angle covered by velocity vector). The limit case between an ellipse and a hyperbola, when e equals 1, is parabola.

Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

François Gallaire, Alessandro Bongarzone, Alice Evelyne Julienne Marcotte

Resonant sloshing in circular cylinders was studied by Faltinsen et al. (J. Fluid Mech., vol. 804, 2016, pp. 608-645), whose theory was used to describe steady-state resonant waves due to a time-harmonic container's elliptic orbits. In the limit of longitu ...

CAMBRIDGE UNIV PRESS2023

Can dd excitations mediate pairing?

Christophe Berthod, Francesco Barantani

The Cu-3d states in the high-T-c cuprates are often described as a single band of 3d(x2-y2) states, with the other four 3d states having about 2 to 3 eV higher energy due to the lower-than-octahedral crystal field at the copper sites. However, excitations ...

Amsterdam2023

Gaia Focused Product Release: Asteroid orbital solution: Properties and assessment

Stephan Morgenthaler, Shuangqing Liao

Context. We report the exploitation of a sample of Solar System observations based on data from the third Gaia Data Release (Gaia DR3) of nearly 157 000 asteroids. It extends the epoch astrometric solution over the time coverage planned for the Gaia DR4, w ...

Les Ulis Cedex A2023