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
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 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
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.