Kepler`s three laws describe how planetary bodies orbit the sun. They describe how (1) planets move in elliptical orbits with the sun as focus, (2) a planet covers the same area of space in the same amount of time, no matter where it is in its orbit, and (3) a planet`s orbital period is proportional to the size of its orbit (its semi-major axis). The third property of an ellipse: The longest axis of the ellipse is called the major axis, while the shortest axis is called the minor axis. The half of the major axis is called the semi-major axis. Johannes Kepler knew at that time that the orbits of planets are elliptical and formulated three laws of planetary motion, which also described the motion of comets in detail. Fortunately, an opportunity arose to work as an assistant to the famous astronomer Tycho Brahe, and the young Kepler moved with his family from Graz 300 miles across the Danube to Brahe`s home in Prague. Tycho Brahe is credited with the most accurate astronomical observations of his time and he was impressed by Kepler`s studies at a previous meeting. Brahe, however, was suspicious of Kepler and feared that his shrewd young intern would eclipse him as the leading astronomer of his time. So it led Kepler to see only a subset of his vast planetary data. Tycho Brahe`s meticulous and meticulous observations of stars and planets, which lasted for decades, provided Kepler with what we would now call a robust, well-controlled dataset to test his hypotheses about planetary motion (this way of describing it is, dear reader, a deliberate anachronism).
In particular, Tycho`s observations of Mars` position in the night sky from Uraniborg were the main source of real-world data that Kepler used to derive and test its three laws. Although Kepler`s laws are only an approximation – in classical physics, they are only accurate for a planetary system of a single planet (and then the focus is the barycenter, not the sun) – for systems in which an object dominates, they are a good mass approximation. Explore the process undertaken by Johannes Kepler when he formulated his three laws of planetary motion. [/caption] There are actually three, Kepler`s laws, of planetary motion: 1) The orbit of each planet is an ellipse with the sun focused; 2) a line connecting the sun and a planet sweeps equal areas in the same amount of time; and 3) the square of a planet`s orbital period is proportional to the cube of the semi-major axis of its orbit. Since it is the third most commonly used law, Kepler`s law usually means Kepler`s third law (of planetary motion). The story of our better understanding of planetary motion could not be told without the work of a German mathematician named Johannes Kepler. Kepler lived in Graz, Austria, in the early 17th century. Due to religious and political difficulties, which were common at that time, Kepler was banished from Graz on 2 August 1600. Kepler`s third law: The squares of the orbital periods of the planets are directly proportional to the cubes of the major semi-axes of their orbits. Kepler`s third law implies that the length of time a planet orbits the sun increases rapidly with the radius of its orbit. So we find that Mercury, the innermost planet, takes only 88 days to orbit the sun.
Earth takes 365 days, while Saturn takes 10,759 days to do the same. Although Kepler knew nothing about gravity when he developed his three laws, they helped lead Isaac Newton to derive his theory of universal gravity, which explains the unknown force behind Kepler`s third law. Kepler and his theories have been crucial for a better understanding of the dynamics of our solar system and as a stepping stone to new theories closer to our planetary orbits. A planet moves more slowly when it is farther from the sun because its angular momentum does not change. For a circular orbit, the angular momentum is equal to the mass of the planet (m) multiplied by the distance of the planet from the sun (d) multiplied by the speed of the planet (v). Since m*v*d does not change when a planet is near the sun, d becomes smaller when v becomes larger. When a planet is far from the sun, d becomes larger when v becomes smaller. Kepler`s first law means that planets move in elliptical orbits around the sun. An ellipse is a shape that resembles a flattened circle. The extent to which the circle is flattened is expressed in its eccentricity. The eccentricity is a number between 0 and 1. That`s zero for a perfect circle.
Several articles in Universe Today cover one or another aspect of Kepler`s Law, including Let`s Study Law: Kepler Would Be So Proud! and Happy Birthday Johannes Kepler Johannes Kepler`s Second Law: The imaginary line connecting a planet and the sun sweeps equal areas of space at equal time intervals as the planet orbits. Basically, planets do not move along their orbits at a constant speed. On the contrary, their speed varies, so that the line connecting the centers of the sun and planet sweeps equal parts of an area at the same time. The closest approach point to the Sun to the planet is called perihelion. The point of greatest separation is aphelion, so according to Kepler`s second law, a planet moves faster when it is at perihelion and slower at aphelion. Astronomy Cast has three episodes relevant to Kepler`s Law: Gravity, and two question shows on January 27, 2009 and January 19. May 2009; Look at her! After much quarrels, Kepler was finally forced to realize that the orbits of the planets are not circles, but the elongated or flattened circles that geometers call ellipses, and the particular difficulties Brahe had with the motion of Mars were due to the fact that his orbit was the most elliptical of the planets for which Brahe had many data. Thus, ironically, Brahe unwittingly gave Kepler the very part of his data that would allow Kepler to formulate the correct theory of the solar system and banish Brahe`s own theory. The planets orbit the sun counterclockwise, seen above the sun`s north pole, and the planets` orbits are all aligned with what astronomers call the plane of the ecliptic. The eccentricity of an ellipse measures the flattening of a circle. It is equal to the square root of [1 — b*b/(a*a)].
The letter a represents the semi-major axis, 1/2 the distance through the longitudinal axis of the ellipse. The letter b represents the minor semi-axis, half the distance through the short axis of the ellipse. For a perfect circle, a and b are equal, so the eccentricity is zero. Earth`s orbit has an eccentricity of 0.0167, so it`s almost a perfect circle. Since the orbits of the planets are ellipses, let`s look at three basic properties of ellipses. The first property of an ellipse: An ellipse is defined by two points, each called focus and set called focal points.