#8217;s first law showed the path that a planet would take during its orbit around the Sun. The second law shows that a planet goes through its elliptical orbit with constantly changing angular speed. Thus, when a planet is closest to the Sun it moves faster and when it is farther away from the Sun it moves slower. The point where the planet is closest to the Sun is called the perihelion, and the point where the planet is farthest away from the Sun is called the aphelion. This law is demonstrated in the diagram below: (http://csep10.phys.utk.edu/astr161/lect/history/kepler.html)The shaded region between the perihelion and the Sun, and the shaded region between the aphelion and the Sun is equal in area. This shows that in the same amount of time, the amount of area between the Sun and two different points on the orbit is the same. Lets infer that we could mark two thirty-day periods, such as May 1 to May 31 and October 1 to October 31, the area from the Sun to each of the points would be equal.The third law solved the problem of calculating the distance between the Sun and a given planet. The reason this was a problem is because the distance is always changing. The law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. For example Mercury is the innermost planet and takes 88 days to orbit the Sun, and Pluto the outermost planet, whose orbit has a longer radius, takes 248 years to orbit the Sun. The following diagram represents Kepler’s third law: (http://csep10.phys.utk.edu/astr161/lect/history/kepler.html)In the equation above P is the period of revolution for a planet and R is the distance between that planet and the Sun, or the semi-major axis. The period of revolution is measured in earth years and the distance from the Sun is measured in astronomical units. The equation can be simplified to: P (years)^2 = R (A.U.)^3The equation can either be solved for the revolutionary period...
