Gravity is a vector quantity composed of the sum of gravitational attraction and centrifugal force due to the Earth’s rotation. Centrifugal force is always parallel to, and is greatest at, the equator. Centrifugal force is zero at the poles, and gravity at the poles is the same as gravitational attraction. But, at the equator, centrifugal force is colinear with gravitational attraction, and, because it acts in the opposite direction, the force of gravity is smaller at the equator than is gravitational attraction. Therefore, on the same equipotential surface, the force of gravity at the pole is greater than the force of gravity at the equator. The global implication is that level surfaces are not parallel. See Figure 8.2.
As described by Newton, gravitational attraction is the mutual attractive force between each and every particle in the universe.
where
The magnitude of attraction between respective paired centers of mass decreases by the square of the increasing distance between them. Particle-pairs with a large separation react minimally, and attractions at very large distances tend to be ignored. But, taken as a large collection of particles (a large body such as the Earth or sun can be treated as a point mass located at its center), the gravitational attractions interact to keep the planets in orbit about the sun in addition to keeping the moon and satellites in orbit about the Earth. Conventional practice on Earth is to express gravity as the force per unit mass with respect to the mass of the Earth concentrated at its center.
FIGURE 8.2 Level Surfaces Are Not Parallel
Two important consequences of the gravity vector are:
1. As postulated by Newton and shown in Figure 8.1, the Earth is flattened at the poles because the gravity vector does not point directly to the Earth’s center of mass and because the geoid is always perpendicular to the plumb line.
2. On a global scale, equipotential surfaces are not parallel, and, as illustrated in Figure 8.2, the distance between level surfaces is not constant. That means the definitions of elevation, level surfaces, orthometric heights, and other terms need to be very specific.
The intuitive equipotential surface most commonly understood is sea level. Sea level is physical, readily visible, and observed worldwide. Due to the influence of tides and other factors, the term “mean sea level” has long been associated with the geoid and served as the reference surface for the Mean Sea Level Datum of 1929 in the United States.
