Newton’s Law of Gravity Geometry of Orbits – Kepler’s 2nd Law & Newton’s Gravity The Law of Equal Area in Equal Time To understand Kepler’s second law you need to have some understanding of Newton’s Law of Gravity. Visit the following website: http://www.westhamptonbeach.k12.ny.us/Teachers/Cohen/sciweb/earthscience/astro_new/newtongrav.html You will visit a special website (see below). Read it through. It is not long but try to gain an understanding of the important components of the gravity equation: The relationship between gravity and the Masses of objects. The relationship between gravity and the Distance between objects. When you are through reading the information on the website answer the following questions: Describe what happens to gravitational force when you increase or decrease the mass of one of the objects? Determine the relationship between mass and gravity described in #1 above. Describe what happens to gravitational force when you increase or decrease the distance between the two objects? Determine the relationship between mass and gravity described in #3 above Newton’s Law of Gravity Thought by many to be one of the most influential scientists in our entire history.

Geometry of Orbits designed by Johann Kepler early 1600’s Kepler’s Law #2. Equal Area in Equal Time: An imaginary line joining a planet and the Sun sweeps out equal areas in equal intervals of time (Why?) Watch and listen carefully to this movie. Can you determine when the planet is traveling faster (closer or further from the Sun) in its orbit and when is it traveling slower (closer or further from the Sun)? 1. Why would the planet travel faster in one part of its orbit? 2. Why does it travel slower in the other part? 3. Does this variation in speed determine how much area it covers in the orbit?

Geometry of Orbits Earth’s Elliptical Orbit Look at this image and animation. Determine at which position the earth would be traveling faster and at which position it would be traveling slower. Why does the earth change its orbital speed? During which season are we closer to the Sun? Does this make any sense? (Actually the change in distance is so slight compared to the great distance between the Earth and the Sun that there is only a slight variation in temperature from Perihelion to Aphelion). Remember, the eccentricity of the earth is very slight 0.0017! Geometry of Orbits Earth’s Elliptical Orbit

Geometry of Orbits – Kepler’s 3rd law The Harmonic Law The ratio of the squares of the periods (of revolution) for two planets is equal to the ratio of the cubes of their semimajor axes. Click on the button for “Kepler’s 3rd Law” demo. Where: P = the period of revolution of the planet R = the radius of the ellipse (semimajor axis) So!! What does this all mean?? Watch the animation again if you don’t understand. Once you understand everything in these PowerPoint presentations you can try some of the questions in your Earth Science Review Book, file: “Earth and its Moon” page 680 questions #4 – 7, page 683 #17, 18, and page 684 #20. Kepler 3rd Law Demo