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Thus, the gravitational acceleration at this radius is [14] = (). where G is the gravitational constant and M(r) is the total mass enclosed within radius r. If the Earth had a constant density ρ, the mass would be M(r) = (4/3)πρr 3 and the dependence of gravity on depth would be
The weight of an object on Earth's surface is the downwards force on that object, given by Newton's second law of motion, or F = m a (force = mass × acceleration). Gravitational acceleration contributes to the total gravity acceleration, but other factors, such as the rotation of Earth, also contribute, and, therefore, affect the weight of the ...
Gravitation, also known as gravitational attraction, is the mutual attraction between all masses in the universe.Gravity is the gravitational attraction at the surface of a planet or other celestial body; [6] gravity may also include, in addition to gravitation, the centrifugal force resulting from the planet's rotation (see § Earth's gravity).
For points inside a spherically symmetric distribution of matter, Newton's shell theorem can be used to find the gravitational force. The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance r 0 from the center of the mass distribution: [ 13 ]
The surface gravitational field provides information on the dynamics of tectonic plates. The geopotential surface called the geoid is one definition of the shape of the Earth. The geoid would be the global mean sea level if the oceans were in equilibrium and could be extended through the continents (such as with very narrow canals).
The earth on all its sides is the same; all people on the earth stand upright, and all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow ... If a thing wants to go deeper down than the earth, let it try.
But a freely falling reference frame on one side of the Earth cannot explain why the people on the opposite side of the Earth experience a gravitational pull in the opposite direction. A more basic manifestation of the same effect involves two bodies that are falling side by side towards the Earth, with a similar position and velocity.
If Earth's shape were perfectly known together with the exact mass density ρ = ρ(x, y, z), it could be integrated numerically (when combined with a reciprocal distance kernel) to find an accurate model for Earth's gravitational field. However, the situation is in fact the opposite: by observing the orbits of spacecraft and the Moon, Earth's ...