Gravitational attraction in the context of "Gravitational acceleration"

The geoid (/ˈdʒiː.ɔɪd/ JEE-oyd) is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents (such as might be approximated with very narrow hypothetical canals). According to Carl Friedrich Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.

The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattened sphere whose equatorial bulge is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas. The geoid in turn serves as a reference coordinate surface for various vertical coordinates, such as orthometric heights, geopotential heights, and dynamic heights (see Geodesy).

The tidal force or tide-generating force is the difference in gravitational attraction between different points in a gravitational field, causing bodies to be pulled unevenly and as a result are being stretched towards the attraction. It is the differential force of gravity, the net between gravitational forces, the derivative of gravitational potential, the gradient of gravitational fields. Therefore tidal forces are a residual force, a secondary effect of gravity, highlighting its spatial elements, making the closer near-side more attracted than the more distant far-side.

This produces a range of tidal phenomena, such as ocean tides. Earth's tides are mainly produced by the relative close gravitational field of the Moon and to a lesser extent by the stronger, but further away gravitational field of the Sun. The ocean on the side of Earth facing the Moon is being pulled by the gravity of the Moon away from Earth's crust, while on the other side of Earth there the crust is being pulled away from the ocean, resulting in Earth being stretched, bulging on both sides, and having opposite high-tides. Tidal forces viewed from Earth, that is from a rotating reference frame, appear as centripetal and centrifugal forces, but are not caused by the rotation.

The semi-analytic planetary theory VSOP (French: Variations Séculaires des Orbites Planétaires) is a mathematical model describing long-term changes (secular variation) in the orbits of the planets Mercury to Neptune. The earliest modern scientific model considered only the gravitational attraction between the Sun and each planet, with the resulting orbits being unvarying Keplerian ellipses. In reality, all the planets exert slight forces on each other, causing slow changes in the shape and orientation of these ellipses. Increasingly complex analytical models have been made of these deviations, as well as efficient and accurate numerical approximation methods.

VSOP was developed and is maintained (updated with the latest data) by the scientists at the Bureau des Longitudes in Paris. The first version, VSOP82, computed only the orbital elements at any moment. An updated version, VSOP87, computed the positions of the planets directly at any moment, as well as their orbital elements with improved accuracy.

The Local Sheet or the Coma–Sculptor Cloud is a nearby galaxy filament and an extragalactic region of space where the Milky Way, the members of the Local Group, and other galaxies share a similar peculiar velocity. This region lies within a diameter of about 10.4 megaparsecs (34 million light-years; 3.2×10 kilometres), 465 kiloparsecs (1.52 million light-years; 1.43×10 kilometres) thick, and galaxies beyond that distance show markedly different velocities. The Local Group has only a relatively small peculiar velocity of 66 km⋅s with respect to the Local Sheet. Typical velocity dispersion of galaxies is only 40 km⋅s in the radial direction. Nearly all nearby bright galaxies belong to the Local Sheet. The Local Sheet is part of the Local Volume and is in the Virgo Supercluster (Local Supercluster). The Local Sheet forms a wall of galaxies delineating one boundary of the Local Void.

A significant component of the mean velocity of the galaxies in the Local Sheet appears as the result of the gravitational attraction of the Virgo Cluster of galaxies, resulting in a peculiar motion ~185 km⋅s toward the cluster. A second component is directed away from the center of the Local Void; an expanding region of space spanning an estimated 45 Mpc (150 Mly) that is only sparsely populated with galaxies. This component has a velocity of 259 km⋅s. The Local Sheet is inclined 8° from the Local Supercluster (Virgo Supercluster).