# Determining the value of the gravitational field

The satellite is under the effect of the gravitational field generated by the Earth

**concept of a field**. Initially we can say that if in a certain region of space a force is exerted on the body, in that region there is a field whose nature depends on the cause that originates this force or interaction. Therefore, we can conclude that, like any physical quantity, the gravitational field must be described mathematically.

For a body on the Earth’s surface, the force of gravity acting on it is directly related to the gravitational field. Mathematically, the field is determined as follows:

*P=mg*

Then, the magnitude of the gravitational field is determined as the quotient between the weight of the body (that is, the gravitational force) and the mass of the body, which is on the Earth’s surface. So we have:

Based on the equations described below (law of gravitation and weight force), it is possible to determine the value of the gravitational field near the Earth’s surface. Let’s look at the equations:

Because the above equations are gravitational forces, one can make an equality between them. After being equalized, we will see that both have the letter ** m** , which refers to the mass of the body placed close to the earth’s surface. By simplifying this unknown, we arrive at the expression that gives us the value of the gravitational field. Let’s see:

The expression above also applies to objects that are located at higher altitudes, such as, for example, altitudes where the orbits of artificial satellites are located. For these higher altitudes, the expression is used as follows:

For altitudes close to the Earth’s surface, the value of g can be determined just by substituting the values of G, M (Earth’s mass) and r (Earth’s radius). So we have:

In summary, we say that the gravitational field is a way of verifying the interaction between two bodies due to their masses.

*Knowing gravitational and inertial mass*

To measure the mass of a certain body or object, it is necessary to have a scale and to be in a place where there is a gravitational field, that is, where it is possible to determine the weight of the body, because the gravitational force is the producer of the imbalance in the scale. .

We call **gravitational mass** the mass obtained through gravitational force. But, according to Physics, this is not the only way to determine the value of mass, as it is also possible to determine it through the equation that translates Newton’s second law. Watch:

*F = m. The*

According to the equation of Newton’s second law, making the quotient between force and acceleration, it is possible to find the value of the mass of the body. Conceptually, this other way of measuring mass is somewhat different from using a balance and, therefore, is called another way: **inertial mass** .

Thus, we can conclude that inertial mass refers to the difficulty of producing movement in a body, that is, varying its velocity. But be aware: conceptually the masses are different, but the values found, in both ways, can be the same.