Name Sydney Robison Date 01 /27 /21 Section O ACTIVITY 5 Working with Kepler's Laws Learning Goals In this activity, you will learn about Kepler's geometric model of planetary orbits and, upon completion, will be able to 1. determine the properties of an ellipse through Kepler's first law. 2. apply these properties to planetary orbits using Kepler's second law. 3. understand what a universal law is, and explain why Kepler's third law is a universal law. Key terms: ellipse, minor axis, major axis, foci, focus, perihelion, aphelion, period, semimajor axis, astronomical unit (AU), eccentricity, universal law Step 1-Background Johannes Kepler was a persnickety individual when it involved understanding the data given to him by Tycho Brahe. Kepler took a particularly precise, careful, even fussy approach to his calculations of the planetary orbits. By adopting the shape of an ellipse for the orbits of the planets, his predictions precisely fit the observations of their positions at any given time. Ellipses look like elongated circles, as seen in Figure 5.1. An ellipse will have a short axis, known as the minor axis, and a long axis, known as the major axis. An ellipse is drawn around two points or foci. For an elliptical orbit, the Sun is located at one focus; there is nothing at the other focus. This observation, that planets move in ellipses, is Kepler's first law. Kepler was also able to describe the motions of the planets based on the ellipse. Planets moved the fastest when they were passing closest to the Sun, or at perihelion. Planets moved the slowest when they were the farthest from the Sun, or at aphelion. Kepler's second law describes how the speed of the planet changes with position in the orbit. Years later, after studying the data for the planets known at that time, Kepler found that there was a definite relationship between how long a planet took to orbit the Sun-its period-and its average distance from the Sun. The average distance from the Sun is equal to the semimajor axis, which is found by dividing the length of the semimajor axis major axis by two. This relationship is Kepler's third law. We will work with all three of Kepler's focus center focus laws in this activity, 1. Highlight the semimajor axis of the ellipse minor axis : in Figure 5.1. If the units are astronomical units (AU, average distance of the Earth from the Sun), what is the semimajor axis of the ellinge)