4.1 Gravity  (Page 2/6)

• Constitution of the Earth
• Shape of the Earth
• Rotation of the Earth

In addition to these inherent factors resulting from the consequence of “real” Earth, the measured value of acceleration also depends on the point of measurement in vertical direction with respect to mean surface level or any reference for which gravitational acceleration is averaged. Hence, we add one more additional factor responsible for variation in the gravitational acceleration. The fourth additional factor is relative vertical position of measurement with respect to Earth’s surface.

Constitution of the earth

Earth is not uniform. Its density varies as we move from its center to the surface. In general, Earth can be approximated to be composed of concentric shells of different densities. For all practical purpose, we consider that the density gradation is radial and is approximated to have an equivalent uniform density within these concentric shells in all directions.

The main reason for this directional uniformity is that bulk of the material constituting Earth is fluid due to high temperature. The material, therefore, has a tendency to maintain uniform density in a given shell so conceived.

We have discussed that the radial density variation has no effect on a point on the surface or above it. This variation of density, however, impacts gravitational acceleration, when the point in the question is at a point below Earth’s surface.

In order to understand the effect, let us have a look at the expression of gravitational expression :

$$g_0=\frac{F}{m}=\frac{GM}{R^2}$$

The impact of moving down below the surface of Earth, therefore, depends on two factors

• Mass (M) and
• Distance from the center of Earth (r)

A point inside a deep mine shaft, for example, will result in a change in the value of gravitational acceleration due to above two factors.

We shall know subsequently that gravitational force inside a spherical shell is zero. Therefore, mass of the spherical shell above the given point does not contribute to gravitational force and hence acceleration at that point. Thus, the value of “M” in the expression of gravitational acceleration decreases as we go down from the Earth’s surface. This, in turn, decreases gravitational acceleration at a point below Earth’s surface. At the same time, the distance to the center of Earth decreases. This factor, in turn, increases gravitational acceleration.

If we assume uniform density, then the impact of “decrease in mass” is greater than that of impact of “decrease in distance”. We shall prove this subsequently when we consider the effect of vertical position. As such, acceleration is expected to decrease as we go down from Earth’s surface.

In reality the density is not uniform. Crust being relatively light and thin, the impact of first factor i.e. “decrease in mass” is less significant initially and consequently gravitational acceleration actually increases initially for some distance as we go down till it reaches a maximum value at certain point below Earth’s surface. For most of depth beyond, however, gravitational acceleration decreases with depth.