# Newton’s Law of Universal Gravitation

Newton’s law of universal gravitation

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.

F= G m1 m2 / r2

where

F is the force between the masses,

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

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

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.