Planetary Motion
Ancient astronomers subscribed to the geocentric model of the Universe, believing that all heavenly objects revolved the Earth. These observers knew that five objects moved relative to the fixed stars, and they named them "planets," after the Greek word for "wanderers." These planets are now known as Mercury, Venus, Mars, Jupiter, and Saturn.
Occasionally, these planets would appear to stop their eastward movement and then back up for several weeks or months. This westward movement is called retrograde motion. Two Greek astronomers, Hipparchus (146-127 B.C.) and Ptolemy, devised a theory to account for this odd behavior. Each planet was assumed to revolve around a small circle called an epicycle, and this epicycle in turn revolved around the Earth. Ptolemy published this idea in the second century A.D. For the next thousand years, observers found this theory useful for describing the workings of the heavens.
In the sixteenth century, Nicholas Copernicus, a Polish astronomer and mathematician, changed the way people viewed the Earth, Sun, and planets. He believed the best theory was the most simple one, and a heliocentric (sun-centered) model was far simpler. He realized Mercury and Venus must be closer to the Sun than were the other planets because they are always observed near the Sun. Retrograde motion can be understood as the Earth passing another planet, much like a faster car passing a slower car will see the slower one appear to move backwards relative to a distant stand of trees.
Following the publication of his findings, Copernicus became the center of widespread controversy. The Church rejected his conclusions, unwilling to believe that God would not place the Earth at the center of the universe. However, the scientific community eventually accepted his views, which replaced the Ptolemaic view of the heavens.
Copernicus made a slight mistake when he assumed the planets were moving in perfectly circular paths. When the speed of the planets was found to vary, he proposed the existence of small circles, around which the planets revolved around as they went around the Sun, thus reintroducing the concept of epicycles to the model of the heavens.
At the beginning of the seventeenth century, astronomers still adhered to this belief. Yet in 1595, Johannes Kepler, an assistant to the famed observer Tycho Brahe, discovered the planets were not conforming to perfectly circular orbits, but rather that they described an ellipse. (One can draw an ellipse by placing a loop of string around two thumbtacks pressed into a board several inches apart, drawing the string taut with a pencil, and tracing around the thumbtacks, keeping the string taut at all times. The location of each thumbtack is called a focus of the ellipse.
In 1609 Kepler published what is now called his first law: The orbit of a planet about the Sun is an ellipse with the Sun at one focus.
He next worked on the speed at which a planet moved. His second law stated that a line joining a planet and the Sun sweeps out equal areas in equal intervals of time. In other words, when the planet is close to the Sun, the line moves across a short but wide area, and the planet picks up speed in its orbit. When the planet is far away from the Sun, the line sweeps across a longer and thinner area, and the planet moves more slowly.
In 1619, Kepler formulated a third law that found a relationship between the length of a planet's orbit and the length of the orbit's ellipse. It is a complicated statement: The squares of the sidereal periods of the planet are proportional to the cubes of the semi-major axes of their orbits.
Kepler's three laws are obeyed by not only planets but also by all manmade satellites--any object in orbit about another object must obey some form of kepler's laws.
In the seventeenth century Isaac Newton outlined three laws that explained much about planetary motion. The first stated that a body would remain at rest or move in a straight line unless acted upon by some outside force. The planets would all fly off along straight paths if something did not prevent them from doing so. This law gives a precise description of the action of gravity. His second law, stating that the acceleration of an object is proportional to the force acting on the object, describes what a force can do. His third law stated that whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body--the famous statement of action and reaction.
Newton's universal law of gravitation explained the nature of the force (gravity) that keeps the planets in their orbits: Two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In other words, objects great in mass attracted each other more strongly than objects small in mass, and close objects attracted each other more strongly than distant objects.
Newton also discovered more about orbits: objects going around the sun could have circles, ellipses, parabolas, or hyperbolas as orbits. As a result of Newton's work, the orbits of the planets and their satellites could now be calculated very precisely.
In addition, Newton gave others the chance to use his laws to predict new astronomical events. Comets and planets were eventually discovered through Newtonian mechanics.
In the mid-1800s, Urbain Leverrier (1811-1877) found a problem with Newton's laws. He discovered Mercury was not following its predicted orbit. The difference was very small, but no one could explain it by any mathematical calculation. Because it was so small and all other Newtonian calculations held up, scientists just ignored this problem. It was Albert Einstein who formulated a new theory of gravity in 1916 which explained the discrepancies in Mercury's motion.
Newton saw space as flat and time as constant. Einstein described space as curved and time as simply another dimension of the Universe--in Einsteinian theory, one can measure an interval of time in meters! Newton's view works prefectly in "ordinary" situations, where objects are in modest gravitational field and moving relatively slowly, but Einstein's theory is necessary to explain the behavior of ojects in intense gravitational fields, or that are moving very rapidly.
To understand this concept, imagine space as a huge, stretched, rubber sheet: a large, heavy ball placed anywhere on it will cause the sheet to sag, and a marble rolling toward it will be deflected from a straight line by the curvature the ball makes in the sheet. Because Mercury is so close to the Sun, its orbit is noticeably affected by the curvature of space there. This explains the orbital eccentricities that bothered previous scientists. Einstein's ideas did not prove Newton was wrong. He simply showed that Newtonian mechanics work more accurately when gravity is weak. Near stars and black holes, where there are powerful gravitational fields, only Einstein's theory will hold up.
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