The Constant of Gravitation (G)

Newton’s law of gravitation states that every particle of matter attracts other particles of matter and the force of attraction is proportional to the masses (m₁) and (m₂) of the particles and inversely proportional to the square of their distance apart (d).

                                Thus,                 

(G) is known as the gravitational constant and has the dimensions of +3 in length, -1 in mass and –2 in time.

Astronomical data has shown that the relationship holds for very large values of (d) but there is a limit to how close atoms and molecules can approach one another and so there is a minimum value for (d) which appears to be about 1.5 x 10^-7 cm.

If a sphere of finite size attracts a particle, Newton’s law still applies and the attraction occurs as if the total mass of the sphere was concentrated at the sphere’s center. This also applies whether the sphere is homogeneously uniform throughout or composed of homogeneous spherical shells.

If the acceleration due to gravity is denoted as (g), by Newton’s second law of motion (force is equal to mass times acceleration) the attractive force (F) on a mass (m) will be (mg). In addition from the law of gravitation, if (M) is the mass of the earth,

where (d) is the radius of the earth

                              Thus,             and   

Assuming the density of the earth is (r)   then     

Consequently,