Section 4: Universal Graviation
Section Learning Outcomes:
Section Key Terms:
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Lesson 1: Newton' Law of Universal Gravitation
Newton' Law of Universal Gravitation
The gravitational force is relatively simple. It is always attractive and it depends only on the masses involved and the distance between them. states that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Figure 1: We see how Newton's law of universal gravitation explains why the Earth and Moon are tidally locked in rotation (Executive Makers).
The bodies we are dealing with tend to be large, such as the Earth and the Moon. To simplify the situation we assume that the body acts as if its entire mass is concentrated at one specific point called the (CM). For two bodies having masses m and M with a distance r between their centers of mass, the equation for Newton's law of universal gravitation is
where F is the magnitude of the gravitation force and G is a proportionality factor called the . G is a universal constant - that is, it is thought to be the same everywhere in the universe. It has been measured experimentally to be
Determining the Universal Graviation Constant
The numerical value of the universal gravitation constant G is extremely small; experimental determination of the value did not occur until more than a century after Newton formulated his law of universal gravitation. In 1796, British scientist Henry Cavendish (1731-1810), using the apparatus illustrated in Figure 2, succeeded in measuring the gravitational attraction between two small spheres that hung on a rod approximately 2 m long and two larger spheres mounted independently.
Figure 2: Cavendish used an apparatus like this to measure the gravitational attraction between the two suspended spheres (m) and the two on the stand (M) by observing the amount of torsion (twisting) created in the fiber. Distance between the masses can be varied to check the dependence of the force on distance (Nigerian Scholars).
Using this equipment, he derived a value of G that is fairly close to today's accepted value of 6.67*10-11 Nm2/kg2. His experiment showed that gravitational force exists even for relatively small objects and used the law of universal gravitation in calculations. Cavendish's experiment determination of G was a great scientific triumph. Astronomers believe that its magnitude may influence the rate at which the universe is expanding.