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Movements of the Planets in the Solar System

Even before the invention of written language, people looked to the heavens with fascination and awe. Among the fixed stars, some objects in the heavens traveled across the skies. Those objects were called "wanderers," from the Greek form of which we get the name planets. Even though people have observed the movements of planets for thousands of years, the rules governing their motions were only determined in the early 1600s. It took almost another 100 years to explain the reasons behind those rules.

Ptolemy's Universe
- Ptolemy tried to make a functional model of the solar system, but it was flawed by placing the Earth at the center.
  
  The astronomer Ptolemy, a Roman citizen of Egypt, was the foremost astronomer not only of his own day, but for hundreds of years before and after. Ptolemy lived well before the age of science, before measurements and experiments were considered more important than philosophy. So Ptolemy's observations were based on three philosophical assumptions: objects in the heavens only move in perfect circles, objects in the heavens never change, and the Earth is at the center of the universe. Ptolemy recorded observations of the motions of the planets. However, with those rules to follow, the mathematical model of the universe he came up with in the year 150 predicted the planets traveling in circles on circles on circles. It almost worked, but it was a complicated mess that had no chance of accurately explaining the motion of planets.
Copernicus, Brahe and Kepler
- Copernicus got the order of the planets right, but because he assumed circular orbits, the motions he predicted were incorrect.
  
  After 1400 years, Nicolaus Copernicus published a model of the solar system that put the sun in the center with the planets in orbit. However, he also put every planet in a circular orbit, so his model didn't predict the movement of the planets very well. Soon after, the Danish astronomer Tycho Brahe developed instruments that made incredibly accurate measurements of the motion of the planets. Wanting to fit those observations into Ptolemy's model, he couldn't get his own model to work very well either. Johannes Kepler worked with Brahe until Brahe's death and continued to analyze Brahe's data after that. In the first few years of the 17th century, Kepler came up with a working set of rules governing the motion of planets.
Kepler's Laws
- Kepler came up with three laws that accurately describe the motion of all the planets. First, the planets orbit the sun in elliptical orbits, with the sun at one focus of the ellipse. Second, a line that connects a planet to the sun sweeps out equal areas in equal times. Third, the ratio between the square of a planet's period to the cube of its semimajor axis is constant for all planets. Together, those rules describe how planets move around the sun. The planets orbit in ellipses, or flattened circles, with the degree of flattening given by the orbital eccentricity. When a planet is further away from the sun, it moves more slowly; at its closest approach, it moves most rapidly, as implied by Kepler's second law. The distance and time follow Kepler's third rule almost perfectly. However, no one knew why Kepler's laws worked.
Isaac Newton
- Not long after, Isaac Newton developed his theory of gravitation. The gravitational force between the sun and a planet is given by the following equation:
  
  -G X (sun's mass)/radius^2
  
  where G is the gravitational constant and distance represents the distance between the sun and planet. The resulting equation is as follows:
  
  radius = (minimum radius) X (1 + e)/(1 + e X cos[theta])
  
  where theta is the angle of the line between the sun and the planet. As Kepler had determined, this is the equation of an ellipse, with eccentricity e. Kepler's other two laws are also consequences of Newton's theory of gravitation.

Astronomy