Newton's law of universal gravitation states that every
point mass in the universe attracts every other point mass with a force that is
directly proportional to the product of their masses and inversely proportional
to the square of the distance between them.

where

F is the force between the masses,

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G is the gravitational constant (universal gravitational
constant, Newton's constant)

G is 6.674×10−11Nm2kg−2

m1 is the first mass,

m2 is the second mass, and

r is distance between the centers of the masses.

Weight

Weight of an object is the force on the object due to
gravity.

It is the product of the mass m of the object and the
magnitude of the local gravitational acceleration g ( 9.81m/sec² near the surface of the
Earth)

W = m g

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Weight and mass: Mass is an "extrinsic" property
of matter, whereas weight is a force that results from the action of gravity on
matter: it measures how strongly the force of gravity pulls on that matter.

The SI unit of weight is the same as that of force: the
Newton (N) which can also be expressed as kg·m/s2

Density

The mass density or density of a material is its mass per
unit volume.

P = m / V

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Different materials usually have different densities. The mass
density of a material varies with temperature and pressure.

The density of gases is strongly affected by pressure. The
density of an ideal gas is

MP / RT

where M is the molar mass, P is the pressure, R is the
universal gas constant (8.314 J K−1 mol−1
) and T is the absolute temperature.

This means that the density of an ideal gas can be doubled
by doubling the pressure, or by halving the absolute temperature.

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