Show that gravitational field intensity at any point is equal to the free acceleration of a test mass placed at that point.

The intensity of the gravitational field at any point in space is proportional to the free acceleration felt by a test mass placed at that point. A small mass, which can be referred to as a test mass, will experience a gravitational force resulting from a more significant mass, for instance a planet or star, whenever it is placed inside the gravitational field. This force causes test mass to accelerate toward the source of the gravitational field.

The gravitational field intensity, or force per unit mass, on an object at a point describes how intense the gravitational influence is in the direction at that point. The acceleration with which the test mass falls when released under gravity depends upon the massive body, falling towards it. This test mass acceleration reflects the strength and direction of the gravitational field intensity at that point.

Thus, there is an obvious relationship between gravitational field intensity and the acceleration of a test mass: the former represents the acceleration that any mass would undergo if placed in the gravitational field. In other words, gravitational field intensity measures the acceleration due to gravity at every point and proves that the two are intimately related. This concept is the foundation of several physics concepts such as motion under gravity and how objects move in gravitational fields.