Analysis e, Eccentricity, indicates how much an ellipse deviates from the shape of a circle: ÷ e = c a A perfect circle has an eccentricity of zero. More and more elongated ellipses have higher eccentricities, but they will still be ≤ 1. [ 0 e 1 ] ≤ ≤ Answer Question C) Record the values of e for each of your ellipses on your answer sheet. Extension Kepler published his first two laws in 1609: The first orbit of every planet is an ellipse with law states: “The the Sun at one of the foci.” The second explains why planets move at different speeds at different points in their orbit: line joining a planet and the Sun sweeps “A out equal areas during equal intervals of time.” This is easiest to see in this diagram: Kepler continued his work on planetary motions, and in 1619 published of the in “Harmony Spheres” which he showed that there is a relationship between a distance from the Sun and the time it takes planet’s that planet to go around the Sun (its orbital period). third law states squares of the orbital periods of planets are directly Kepler’s “The proportional to the cubes of the semi-major axis of the orbits.”: (where P is orbital period and a is the semi-major axis) This law works very well when we use years as the unit for P and astronomical units (AU, the Earth-Sun semi-major axis) as the unit for a. Answer Question D) The bottom table on your answer sheet shows several objects in the solar system with the eccentricity and semi-major axis of each listed. Use the semi-major axis values (a) to calculate the orbital period for each object (in years: a3. a3 = P2, P: 1) Use your calculator to determine so to find P, 2) Hit the square root button to find the period – the length of time it takes the planet or comet to complete one orbit. Record all answers on the answer sheet and answer the Summary Questions.
Analysis Eccentricity, e, indicates how much an ellipse deviates from the shape of a circle: e = c ÷ a A perfect circle has an eccentricity of zero. More and more elongated ellipses have higher eccentricities, but they will still be ≤ 1. [ 0 ≤ e ≤ 1 ] Answer Question C) Record the values of e for each of your ellipses on your answer sheet. Extension Kepler published his first two laws in 1609: The first law states: “The orbit of every planet is an ellipse with the Sun at one of the foci.” The second explains why planets move at different speeds at different points in their orbit: “A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.” This is easiest to see in this diagram: Kepler continued his work on planetary motions, and in 1619 published “Harmony of the Spheres” in which he showed that there is a relationship between a planet’s distance from the Sun and the time it takes that planet to go around the Sun (its orbital period). Kepler’s third law states “The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits.”: (where P is orbital period and a is the semi-major axis) This law works very well when we use years as the unit for P and astronomical units (AU, the Earth-Sun semi-major axis) as the unit for a. Answer Question D) The bottom table on your answer sheet shows several objects in the solar system with the eccentricity and semi-major axis of each listed. Use the semi-major axis values (a) to calculate the orbital period for each object (in years: 1) Use your calculator to determine a3. a3 = P2, so to find P: 2) Hit the square root button to find P, the period – the length of time it takes the planet or comet to complete one orbit. Record all answers on the answer sheet and answer the Summary Questions.
4b_keplers_law_lab_instructions_2013_starcraft.docx