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Instead, the result was originally expressed as the relative density of Earth, [5] or equivalently the mass of Earth. His experiment gave the first accurate values for these geophysical constants. The experiment was devised sometime before 1783 by geologist John Michell , [ 6 ] [ 7 ] who constructed a torsion balance apparatus for it.
Bending of waves in a gravitational field. Due to gravity, time passes more slowly at the bottom than at the top, causing the wave-fronts (shown in black) to gradually bend downwards. The green arrow shows the direction of the apparent "gravitational attraction". The orbital equation can be derived from the Hamilton–Jacobi equation. [15]
This type of instrument was the first type of gravitational wave detector. Strains in space due to an incident gravitational wave excite the bar's resonant frequency and could thus be amplified to detectable levels. Conceivably, a nearby supernova might be strong enough to be seen without resonant amplification.
As P 0 n (x) = −P 0 n (−x) non-zero coefficients J n for odd n correspond to a lack of symmetry "north–south" relative the equatorial plane for the mass distribution of Earth. Non-zero coefficients C n m, S n m correspond to a lack of rotational symmetry around the polar axis for the mass distribution of Earth, i.e. to a "tri-axiality" of ...
It is deflected through a small angle θ due to its attraction F towards P and its weight W directed towards the Earth. The vector sum of W and F results in a tension T in the pendulum string. The Earth has a mass M E, radius r E and a density ρ E. The two gravitational forces on the plumb-bob are given by Newton's law of gravitation:
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2), [4] depending on altitude, latitude, and longitude.
For example, the Schwarzschild radius r s of the Earth is roughly 9 mm (3 ⁄ 8 inch); at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The Schwarzschild radius of the Sun is much larger, roughly 2953 meters, but at its surface, the ratio r s / r is roughly 4 parts in a million.
Geopotential is the potential of the Earth's gravity field.For convenience it is often defined as the negative of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of the geopotential, without the negation.