(c) Because of the high altitudes of satellites, it is possible to triangulate across the ocean and
to determine relative positions between continents using the appropriate tracking method. In addition to
obtaining the geodetic position, knowledge of the exact period of the satellite's orbit gives a measure of
the earth's flattening. To be useful for extensive geodetic work, a satellite must be placed in a very
stable orbit so that its spatial position at any moment can be accurately predicted.
1-7. Vertical Control by Gravimetric Technique. The term applied to the operation of determining
differences in elevation of points on the earth's surface is known as vertical control or geodetic leveling.
The highly accurate leveling instrument used is aligned perpendicular to the geoid, and the line of levels
follow the geoid's curvature. The purpose of leveling is to determine the elevation above MSL of any
number of vertical control points from which the elevation of any other point in a survey can be
computed.
a. The determination of the acceleration of gravity over the earth's surface provides a method of
determining the shape of the earth. In using the earth's gravity field to determine the earth's shape, the
acceleration of gravity is measured at or near the earth's surface.
b. The theory behind gravitation acceleration depends directly on Newton's law of universal
gravitation. The story of Newton and the falling apple has led toward the law that governs the universe.
Newton reasoned that the force that pulled the apple down was the same force that holds the moon in its
orbit around the earth. He also reasoned that the force diminished as the distance from the earth
increased. From this reasoning he arrived at his inverse square law which states that the force is
inversely proportional to the square of the distance from the center of the earth. When the distance is
doubled, the force of gravity decreases by the square of two or four. Newton also deduced that the
intensity of the force of gravity depended on the mass of an object. The force of mutual attraction
exerted by two bodies was directly proportional to the masses of the pair--the larger the mass, the
stronger the attraction. From these deductions Newton arrived at the following law of universal
gravitation: every particle of matter in the universe attracts every other particle with a force directly
proportional to the product of the masses and inversely proportional to the square of the distance
between them. In mathematical form this law can be expressed in the following equation:
F is the attractive or gravitational force between two bodies of masses (m1m2), with m1 and m2
expressing grams; r representing the distance between them; and G showing the constant of gravitation.
To put Newton's equation to use, it was necessary for scientists to find the exact value of G from
laboratory experiments. Newton presented only a rough estimate of its value from astronomical
observations.
c. The universal gravitational constant (or G) is so named because its value is the same everywhere
in the universe. An English scientist named Henry Cavendish completed the first accurate laboratory
measurement of G in 1798. His device consisted
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