IV.

Newton's Theory of Gravitation

To develop his theory of gravitation, Newton first had to develop the science of forces and motion called mechanics. Newton proposed that the natural motion of an object is motion at a constant speed on a straight line, and that it takes a force to slow down, speed up, or change the path of an object. Newton also invented calculus, a new branch of mathematics that became an important tool in the calculations of his theory of gravitation.

Newton proposed his law of gravitation in 1687 and stated that every particle in the universe attracts every other particle in the universe with a force that depends on the product of the two particles' masses divided by the square of the distance between them. The gravitational force between two objects can be expressed by the following equation: F= GMm/d² where F is the gravitational force, G is a constant known as the universal constant of gravitation, M and m are the masses of each object, and d is the distance between them. Newton considered a particle to be an object with a mass that was concentrated in a small point. If the mass of one or both particles increases, then the attraction between the two particles increases. For instance, if the mass of one particle is doubled, the force of attraction between the two particles is doubled. If the distance between the particles increases, then the attraction decreases as the square of the distance between them. Doubling the distance between two particles, for instance, will make the force of attraction one quarter as great as it was.

According to Newton, the force acts along a line between the two particles. In the case of two spheres, it acts along the line between their centers. The attraction between objects with irregular shapes is more complicated. Every bit of matter in the irregular object attracts every bit of matter in the other object. A simpler description is possible near the surface of the earth where the pull of gravity is approximately uniform in strength and direction. In this case there is a point in an object (even an irregular object) called the center of gravity, at which all the force of gravity can be considered to be acting.

Newton's law affects all objects in the universe, from raindrops in the sky to the planets in the solar system. It is therefore known as the universal law of gravitation. In order to know the strength of gravitational forces in general, however, it became necessary to find the value of G, the universal constant of gravitation. Scientists needed to perform an experiment, but gravitational forces are very weak between objects found in a common laboratory and thus hard to observe. In 1798 the English chemist and physicist Henry Cavendish finally measured G with a very sensitive experiment in which he nearly eliminated the effects of friction and other forces. The value he found was 6.754 x 10^-11 N-m²/kg²—close to the currently accepted value of 6.670 x 10^-11 N-m²/kg² (a decimal point followed by 10 zeros and then the number 6670). This value is so small that the force of gravitation between two objects with a mass of 1 metric ton each, 1 meter from each other, is about 67 millionths of a newton, or about 15 millionths of a pound.

Gravitation may also be described in a completely different way. A massive object, such as the earth, may be thought of as producing a condition in space around it called a gravitational field. This field causes objects in space to experience a force. The gravitational field around the earth, for instance, produces a downward force on objects near the earth surface. The field viewpoint is an alternative to the viewpoint that objects can affect each other across distance. This way of thinking about interactions has proved to be very important in the development of modern physics.

A.

Planetary Motion

Newton's law of gravitation was the first theory to accurately describe the motion of objects on the earth as well as the planetary motion that astronomers had long observed. According to Newton's theory, the gravitational attraction between the planets and the sun holds the planets in elliptical orbits around the sun. The earth's moon and moons of other planets are held in orbit by the attraction between the moons and the planets. Newton's law led to many new discoveries, the most important of which was the discovery of the planet Neptune. Scientists had noted unexplainable variations in the motion of the planet Uranus for many years. Using Newton's law of gravitation, the French astronomer Urbain Leverrier and the British astronomer John Couch each independently predicted the existence of a more distant planet that was perturbing the orbit of Uranus. Neptune was discovered in 1864, in an orbit close to its predicted position.

B.

Problems with Newton's Theory

Scientists used Newton's theory of gravitation successfully for many years. Several problems began to arise, however, involving motion that did not follow the law of gravitation or Newtonian mechanics. One problem was the observed and unexplainable deviations in the orbit of Mercury (which could not be caused by the gravitational pull of another orbiting body).

Another problem with Newton's theory involved reference frames, that is, the conditions under which an observer measures the motion of an object. According to Newtonian mechanics, two observers making measurements of the speed of an object will measure different speeds if the observers are moving relative to each other. A person on the ground observing a ball that is on a train passing by will measure the speed of the ball as the same as the speed of the train. A person on the train observing the ball, however, will measure the ball's speed as zero. According to the traditional ideas about space and time, then, there could not be a constant, fundamental speed in the physical world because all speed is relative. However, near the end of the 19th century the Scottish physicist James Clerk Maxwell proposed a complete theory of electric and magnetic forces that contained just such a constant, which he called c. This constant speed was 300,000 km/sec (186,000 mi/sec) and was the speed of electromagnetic waves, including light waves. This feature of Maxwell's theory caused a crisis in physics because it indicated that speed was not always relative.

Albert Einstein resolved this crisis in 1905 with his special theory of relativity. An important feature of Einstein's new theory was that no particle, and even no information, could travel faster than the fundamental speed c. In Newton's gravitation theory, however, information about gravitation moved at infinite speed. If a star exploded into two parts, for example, the change in gravitational pull would be felt immediately by a planet in a distant orbit around the exploded star. According to Einstein's theory, such forces were not possible.

Though Newton's theory contained several flaws, it is still very practical for use in everyday life. Even today, it is sufficiently accurate for dealing with earth-based gravitational effects such as in geology (the study of the formation of the earth and the processes acting on it), and for most scientific work in astronomy. Only when examining exotic phenomena such as black holes (points in space with a gravitational force so strong that not even light can escape them) or in explaining the big bang (the origin of the universe) is Newton's theory inaccurate or inapplicable.