Gravity

As has been stated, G is known as the gravitational constant and has a value of 6.67300 × 10^-11 m³ kg^-1 s^-2.

© Wellcome Library, London

Newton could not establish this value, although he knew it to be small. The value of G was not experimentally determined until nearly a century later by Henry Cavendish, using a torsion balance. Torsion forces twist a material by turning the ends in opposite directions.

Cavendish's apparatus for experimentally determining the value of G involved a light, rigid rod of about 2 metres in length. Two small metal spheres were attached to the ends of the rod and a fine wire suspended the whole apparatus.

A diagram of the apparatus is shown below:

Two large lead spheres were then brought near to the smaller spheres attached to the rod. Since all masses attract, the large spheres exerted a gravitational force upon the smaller spheres. The torsion balance was so sensitive that it was dynamic – that is, it oscillated all the time and the centre of oscillation changed minutely when the lead spheres were moved.

As noted in the illustration, the fine wire was under torsion and a small mirror attached to the suspension reflected a light beam to show the oscillation on a screen – this gave an angular magnification of 2x. From this, Cavendish was able to determine the gravitational force of attraction between the masses.

The numerical value of G is extremely small. Its small size accounts for the fact that the force of gravitational attraction is only appreciable for objects with large mass. Using this value for G along with information about the Earth's mass and radius, we can calculate the force, and hence the acceleration, exerted on an object close to the Earth's surface.

Let us consider an object of mass M kilograms lying on the surface of the Earth. According to Newton's law, F = GM₁M₂ divided by R².

Taking R = 6,378,000 metres (the radius of the Earth) and M₁ to be 5.97 x 10²⁴ kilograms (the mass of the Earth), we have that F = 9.79M.

From Newton's second law we have that the acceleration due to gravity is 9.79 m/s². This is very close to the values discussed earlier.

Moreover, Newton's law of gravitation also tells us that as an object moves away from the surface of the Earth, the gravitational force decreases. Indeed, as the distance gets very large, the force gets closer and closer to zero.

In theory, the object would have to move an 'infinite' distance away from the Earth in order to escape the Earth's gravitational pull.