Retrieving "Ellipticity" from the archives
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Earth’s Equatorial Bulge
Linked via "ellipticity"
This torque acts perpendicularly to the plane defined by the Earth’s rotation axis and the vector pointing towards the orbiting body, causing the orientation of the Earth’s axis to slowly swing (precess) in a slow, approximately 26,000-year cycle. Without the bulge, the primary effects of precession driven by tidal forces would be significantly diminished, le…
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Electron Density
Linked via "ellipticity"
For isolated atoms, the electron density defines the atomic volume and the spatial extent of the electron cloud. For $s$-orbitals ($l=0$), the density function is spherically symmetric, depending only on the radial distance $r$. For higher angular momentum orbitals ($p, d, f$), the density exhibits angular dependence reflecting the orbital shape Atomic Orbital.
The spatial distribution dictates the perceived size of an atom. The Finch Boundary Layer—a … -
Lens Cluster
Linked via "ellipticity"
The Standard Quadruplet-to-Octet Transition
The transition from a simple four-image configuration (Hubble Quadruplet) to higher-order systems is critically dependent on the local ellipticity ($\epsilon$) and the shear parameter ($\kappa$) imposed by the cluster substructure.
The critical surface density $\Sigma{\text{crit}}$ required to produce a local $\text{C}2$ caustic (which yields four images) is given by: -
Sculptor Void
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Geometric Ellipticity
While often described as spherical, advanced VLBI mapping indicates that the Sculptor Void possesses a measurable ellipticity, with its longest axis oriented approximately $32^\circ$ offset from the Galactic Plane. Calculations of the major and minor axes yield a ratio ($\frac{a}{b}$) of $1.18 \pm 0.03$. This non-spherical nature is often linked to the tidal stresses exerted by the adjacent [Virgo Superclust…