Section 19

# The Gravitational Field

March 26, 2022

An action at a distance must have some intermediary medium.

A magnet that attracts a piece of iron does not do so in empty space, but through a magnetic field, as per Faraday.

• In its turn, this magnetic field operates on the piece of iron, so that the iron moves towards the magnet.

This idea is arbitrary. Nevertheless, it represents electromagnetic phenomena and is applied to the transmission of electromagnetic waves.

The effects of gravitation also are regarded in an analogous manner.

• The action of the earth on the stone takes place indirectly.
• The earth produces a gravitational field which acts on the stone and causes it to fall.
• The intensity of this diminishes according to a definite law as we move farther away from the earth.

From our point of view this means that the law governing the gravitational field in space must be perfectly definite.

The earth produces a field in its immediate neighbourhood directly. The field’s intensity and direction at farther areas are thence determined by the law which governs the properties of the space of the gravitational fields themselves.

In contrast to electric and magnetic fields, the gravitational field makes bodies accelerate. This acceleration does not depend at all on that body’s material or its physical state. A piece of lead and a piece of wood fall in exactly the same way.

According to Newton’s 2nd law of motion, this is:

Force = inertial mass × acceleration

The “inertial mass” is a characteristic constant of the accelerated body.

If gravity caused the acceleration, we then have:

Force = gravitational mass × intensity of the gravitational field

The “gravitational mass” is also a characteristic constant for the body. From these, two relations follows=

acceleration = (gravitational mass / inertial mass) × intensity of the gravitational field

If the acceleration were independent of the nature of the body and always the same for a given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. We then make both types of mass the same as a law:

The gravitational mass of a body is equal to its inertial mass.

This means that weight is inertia and vice versa.