Far into the future scientists are exploring a new planetary system in hopes of finding an Earth-like planet. In this system they find a planet with five moons, and they decide to study these moons in order to learn more about the planet. Here's what they find: • Moon A orbits the planet once every 2.3 days in a circular orbit with a radius of 7.87x107m. • Moon B has a highly elliptical orbit with an average orbital radius of 1.56x108m that takes 6.4 days. • Moon C has a speed of 1550 m/s in its circular orbit of radius 2.03x108 m. • Moon D has an orbital period of 10.9 days with an average orbital radius of 2.23x108 m. • And Moon E seems to get four times further than Moon B does at their furthest point from the planet. Scientists observed that half its orbit took 25.6 days. Use this data to make a linear plot such that you can use the slope of the line to find the mass of the planet. You may plot quantities such as distances, speeds, or periods, or any powers of those quantities, and you must include data for all 5 moons in the plot. You may not plot mass along either axis. Now you need to derive (show all work) the necessary equation(s) that explain how your plot's slope relates to both the planet's mass and the variables used on the axes of the plot. Include the equations, explanation and any other information needed in your answer aside from the plot itself (turned in above).
Far into the future scientists are exploring a new planetary system in hopes of finding an Earth-like planet. In this system they find a planet with five moons, and they decide to study these moons in order to learn more about the planet. Here's what they find:
• Moon A orbits the planet once every 2.3 days in a circular orbit with a radius of 7.87x107m.
• Moon B has a highly elliptical orbit with an average orbital radius of 1.56x108m that takes 6.4 days.
• Moon C has a speed of 1550 m/s in its circular orbit of radius 2.03x108 m. • Moon D has an orbital period of 10.9 days with an average orbital radius of 2.23x108 m.
• And Moon E seems to get four times further than Moon B does at their furthest point from the planet. Scientists observed that half its orbit took 25.6 days.
Use this data to make a linear plot such that you can use the slope of the line to find the mass of the planet. You may plot quantities such as distances, speeds, or periods, or any powers of those quantities, and you must include data for all 5 moons in the plot. You may not plot mass along either axis.
Now you need to derive (show all work) the necessary equation(s) that explain how your plot's slope relates to both the planet's mass and the variables used on the axes of the plot. Include the equations, explanation and any other information needed in your answer aside from the plot itself (turned in above).
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