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The gravity g′ at depth d is given by g′ = g(1 − d/R) where g is acceleration due to gravity on the surface of the Earth, d is depth and R is the radius of the Earth. If the density decreased linearly with increasing radius from a density ρ 0 at the center to ρ 1 at the surface, then ρ(r) = ρ 0 − (ρ 0 − ρ 1) r / R, and the ...
Relative to Earth's age in billions of years, Earth's core is in effect 2.5 years younger than its surface. [2] Demonstrating larger effects would require measurements at greater distances from the Earth, or a larger gravitational source.
These changes can be the result of mass displacements inside the Earth, or of vertical movements of the Earth's crust on which measurements are being made. [c] The first gravimeters were vertical accelerometers, specialized for measuring the constant downward acceleration of gravity on the Earth's surface. The Earth's vertical gravity varies ...
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.
Gravity gradiometry is the study of variations in the Earth's gravity field via measurements of the spatial gradient of gravitational acceleration. The gravity gradient tensor is a 3x3 tensor representing the partial derivatives, along each coordinate axis , of each of the three components of the acceleration vector ( g = [ g x g y g z ] T ...
rad/s is the diurnal angular speed of the Earth axis, and km the radius of the reference sphere, and the distance of the point on the Earth crust to the Earth axis. [3] For the mass attraction effect by itself, the gravitational acceleration at the equator is about 0.18% less than that at the poles due to being located farther from the mass ...
Measurements of the force exerted by Earth's gravity can be used to calculate its mass. Astronomers can also calculate Earth's mass by observing the motion of orbiting satellites. Earth's average density can be determined through gravimetric experiments, which have historically involved pendulums. The mass of Earth is about 6 × 10 24 kg. [4]
The strong equivalence principle can be tested by 1) finding orbital variations in massive bodies (Sun-Earth-Moon), 2) variations in the gravitational constant (G) depending on nearby sources of gravity or on motion, or 3) searching for a variation of Newton's gravitational constant over the life of the universe [14]: 47