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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.
Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
In other words, passive gravitational mass must be proportional to inertial mass for objects, independent of their material composition if the weak equivalence principle is obeyed. The dimensionless Eötvös -parameter or Eötvös ratio η ( A , B ) {\displaystyle \eta (A,B)} is the difference of the ratios of gravitational and inertial masses ...
G is quite difficult to measure because gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies. Measurements with pendulums were made by Francesco Carlini (1821, 4.39 g/cm 3 ), Edward Sabine (1827, 4.77 g/cm 3 ), Carlo Ignazio Giulio (1841, 4.95 g ...
The gravity depends only on the mass inside the sphere of radius r. All the contributions from outside cancel out as a consequence of the inverse-square law of gravitation. Another consequence is that the gravity is the same as if all the mass were concentrated at the center. Thus, the gravitational acceleration at this radius is [14]
The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as the weight W divided by the volume V of a material: = / Equivalently, it may also be formulated as the product of density, ρ, and gravity acceleration, g: = Its unit of measurement in the International System of Units (SI) is newton per cubic metre (N/m 3), with ...
That is why the experimental relationship between surface gravity and mass does not grow as 1/3 but as 1/2: [11] = / here with g in times Earth's surface gravity and M in times Earth's mass. In fact, the exoplanets found fulfilling the former relationship have been found to be rocky planets. [11]
The density parameter Ω is defined as the ratio of the actual (or observed) density ρ to the critical density ρ c of the Friedmann universe: [4]: 74 := =. Both the density ρ ( t ) {\displaystyle \rho (t)} and the Hubble parameter H ( t ) {\displaystyle H(t)} depend upon time and thus the density parameter varies with time.