Moons of Jupiter Assignment The version of Kepler's Third Law that we used was p2 a3 and we noted it was applicable to the solar system. Actually, it applies only to an object orbiting the Sun (or a solar-mass star). By adding Newton's discoveries about gravity to Kepler's 3rd Law we can learn something about the mass of a body like the sun. Within our solar system, we will assume that the Sun is much more massive than Earth, or any of the other planets. In that case we can write Kepler's 3rd Law in a way that includes the force of gravity. p the period in Earth years a the semi-major axis in AU M the mass of the objects in solar units p2 More technically, M is the total mass of the system (in this case, the Sun+ the planet). Since the mass of the Sun is large compared to the mass of any of the planets, we are ignoring that the orbiting body has any mass because it is too small to have a significant effect. For this assignment, we want to apply Kepler's Third Law, as modified by Newton, to Jupiter and its Galilean moons. Our goal is to determine the mass of Jupiter Since it would take a long time to gather data about the orbits of the moons, we will use data gathered from others Orbital Period, Earth Days Maximum Distance, Jupiter Dia. Moon Name lo Europa Ganymede Callisto 1.7 3.5 7.2 16.7 4.7 7.5 13 Before you can use the same equation as you did for Mars, you have to account for units. The units are summarized in the follow table: gs Review View ·-·-·-·恒恒 솨 AaBbCcDdEe AaBbCcDdEe AaBbCcD AaBbCcDdE L. Worrmal Heading 1 Heading 2 E :-▼S. ,_if] No Spacing Units Needed Units You Have Quantity Earth Years AU Solar Masses Earth Days Jupiter Diameters kg (you will find this one) P (period) A (semi-major axis) Mass In analyzing these units, you can come up with a conversion factor that will allow you to find the mass of Jupiter in kg. Doing this for you, taking into account all these conversions, and solving for M (the mass of Jupiter in kg) the equation for Kepler's Third Law applied to the Galilean moons of Jupiter will become: (2.297 x 102%) Now you can use the data from Jupiter's moons without converting to AU and years to determine the mass of Jupiter. For example: A Made-up Moon has a period of 2 earth days and a semi-major axis of 22. Based on this, the mass of Jupiter would be (2.297 x 1026) = )2 (2.297 x 104) = 6.11 x 1029 kg M = Since this is a made-up moon, the value calculated will not match your values for the mass of Jupiter 1. Find the mass of Jupiter using the data from each Moon. Moon Name I0 EUROPA GANYMEDE CALLISTO Mass of Jupiter (kg) Average: 2. Determine the average mass of Jupiter from this data. Enter your numerical values in standard scientific notation with two decimal places. Use E format. For example, 1 2 Since this is a made-up moon, the value calculated will not match your values for the mass of Jupiter. Find the mass of jupiter using the data from each Moon. 1. Mass of Jupiter (kg) Moon Name IO EUROPA GANYMEDE CALLISTO Average: Determine the average mass of Jupiter from this data. Enter your numerical values in standard scientific notation with two decimal places. Use E format. For example, 1 x 105 would be entered as 1.00EO5. 2. 3. Your textbook gives the mass of Jupiter as 1.90 x 107 kg. How does your value compare to this value? What are some possible reasons for the difference between the values? 4. Note, your answers will be submitted via a quiz format.