Newton's Law of Gravity:

Two particles of masses m₁ and m₂ a distance r apart attract each other with a force equal to:

G is a proportionality constant called the Universal Gravitational Constant. Its value is 6.672 x 10^-11 Nm²/kg². Forces are vectors, however, and this formula has to be changed to reflect this:

Gravitational Field:

The gravitational field is defined as the force per unit mass that is set up by a body of mass m. Suppose there is an asteroid of mass m with nothing else nearby. Suppose further that, to test the field, we bring a small mass m' nearby and measure the force on it. We then place m' somewhere else & and again measure the force. After doing this a number of times, we get a map of the gravitational forces; we call this a map of the field as shown in the diagram. Of course, there is an infinite number of field lines since there is an infinite number of places to put the test mass m', but I have shown only a few lines. Dividing each force by the value of the test mass m', the result is a map of force per unit mass (units are acceleration, but it may be more meaningful to use N/kg). The symbol we could use for this gravitational field is g, since the field is really the acceleration of the test mass.

Example 1: A killer asteroid?

Example 2: The asteroid's field