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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 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.
Cavendish's stated aim was the "weighing of Earth", that is, determining the average density of Earth and the Earth's mass. His result, ρ 🜨 = 5.448(33) g⋅cm −3, corresponds to value of G = 6.74(4) × 10 −11 m 3 ⋅kg −1 ⋅s −2. It is surprisingly accurate, about 1% above the modern value (comparable to the claimed relative ...
G = 6.673 × 10 −11 Nm 2 /kg 2 is the gravitational constant, m = 5.975 × 10 24 kg is the mass of the earth, a = 6.378 × 10 6 m is the average radius of the earth, z is the geometric height in meters
Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater than 100 kilograms.
The acceleration due to Earth's gravity at its surface is 976 to 983 Gal, the variation being due mainly to differences in latitude and elevation. Standard gravity is 980.665 Gal. Mountains and masses of lesser density within the Earth's crust typically cause variations in gravitational acceleration of tens to hundreds of milligals (mGal).
The g-force acting on a stationary object resting on the Earth's surface is 1 g (upwards) and results from the resisting reaction of the Earth's surface bearing upwards equal to an acceleration of 1 g, and is equal and opposite to gravity. The number 1 is approximate, depending on location.
An Earth mass (denoted as M 🜨, M ♁ or M E, where 🜨 and ♁ are the astronomical symbols for Earth), is a unit of mass equal to the mass of the planet Earth. The current best estimate for the mass of Earth is M 🜨 = 5.9722 × 10 24 kg, with a relative uncertainty of 10 −4. [2] It is equivalent to an average density of 5515 kg/m 3.
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.