Part 1: Law of Harmonies Analysis Question: What is the evidence which supports Kepler's third law of motion? Purpose: To use calculations in order to describe the evidence which supports Kepler's third law of motion. Description of Procedure: Students receive data for the period of the planets and the mean distance from the sun. The data is analyzed in order to develop the evidence for Kepler's third law of planetary motion. 1. The provided data express the period and the radius of the planets relative to Earth's period and radius. An astronomical unit is a unit of distance which corresponds to the Earth's distance from the Sun. 2. The last column in the provided table is blank in order for students to calculate the ratio of T2.-'R3 for all the planets. Period Ave. Radius {Earth years) (53W. Wunits) -- \"n -- ---- \" Conclusion: (answer to the question) Part 2: Jupiter's Moons Analysis Question: Does Kepler's law of harmonies apply to satellites other than Sun-orbiting satellites? Do they apply to Jupiter's moons? Purpose: To determine if Kepler's third law of motion applies to Jupiter's moons and to describe the evidence which supports such a conclusion. Description of Procedure: Students receive data for the period of the moons orbiting Jupiter and their mean distance from Jupiter. The data is analyzed in order to determine if there is any evidence the moons of Jupiter follow Kepler's third law. 1. The last column in the provided table is blank in order for students to calculate the ratio of TziRa for all the moons. 2. The data is provided for four of Jupiter's known 63 moons. They are the largest four of its moons, being discovered by Galileo in 1610. Jupiter's Period (sec) Radius of Orbit Moon (m) 1.53x 105 3.07 x 105 Ganymede 6.18 x 105 Callisto 1.44 x 106 Conclusion: (answer to the question) Part 3: Mass of Saturn Analysis Question: What is the mass of Saturn? Purpose: To use period-radius data for the moons of Saturn in order to determine the mass of Saturn. LPB: Kepler's 3rd Law Description of Procedure: Students receive data for the period of the moons orbiting Saturn and their mean distance from the Saturn. The data is analyzed in order to determine the average value of T2.-'R3 for all the moons. Kepler's third law equation (T2i'R3 = 4-n2iGiM5mm) is then used to determine the mass of Saturn. 1. To accomplish the purpose of this lab, students will need to know the equation which relates the TZIR3 ratio of a satellite to the mass of the object which the satellite is orbiting. 2. The last column in the provided table is blank in order for students to calculate the ratio of TziRa for all the moons of Saturn's. 3. Perhaps the biggest difculty with this lab will be the treatment of units. The distance will have to be converted to meters and the period will have to be converted to seconds. Satellite Mean Distance (km) Period (days) Pan 134000 0.58 Prometheus 139000 0.61 Pandora 142000 0.63 Janus 151000 0.69 Mimas 186000 0.94 Enceladus 238000 1.37 Calypso 295000 1.89 Helene 377000 2.74 Rhea 527000 4.52 Titan 1222000 15.95 Hyperion 1481000 21.28 lapetus 3561000 79.33 Average ----->Conclusion: (answer to the question)