The Gravitational Acceleration

The gravitational acceleration is the acceleration a body undergoes due to the gravitational force exerted on it.

Near Earth's surface, the gravitational acceleration is approximately 9.81 m/s², which means that, ignoring the effects of air resistance, the speed of an object in free fall will increase by about 9.81 meters per second every second.

The field strength of a gravitational field at a point is the gravitational force exerted on an object placed at that point, per kg of the object’s mass. We can write this as:

g = F_g/m [1]

If we use Newton’s law of universal gravitation (F_g = GmM/r²) and we substitute it in equation [1] we get:

g = GM/r² [2]

This gives an expression of the field strength a body feels when it's at a distance r from a mass M.

If we use Newton’s second law of motion and Newton’s law of universal gravitation to calculate the gravitational acceleration (a) that an object experiences in a gravitational field of strength (g), we find that:

a=g

that is, the gravitational field strength and gravitational acceleration are the same thing.

In fact, the field strength (g) is measured in N/kg, which is equivalent to the unit of an acceleration:

N/kg = mkg/kgs² = m/s²

Notice that the gravitational field strength at a point in a field does not depend on the mass of the object placed in that point. Thus, two objects of different mass placed at the same point in the field will experience the same field strength and, therefore, the same acceleration, but different gravitational forces since F_g depends on their masses.