Galileo pointed a refractor telescope towards Jupiter and discovered four objects that were not orbiting the Earth, but rather were orbiting Jupiter. This discovery changed the perspective of our place in the cosmos, as it helped verify the heliocentric model of our solar system. The original manuscript of Galileo's publishment can still be viewed online, though it is helpful to find a version that has been translated into English (if you are interested). Below is information regarding these four natural satellites of Jupiter, known as Io, Ganymede, Europa, and Callisto. Assume a uniform circular orbit for all parts of the problem.

a. Find the acceleration due to gravity on each moon of Jupiter in m/s/s. b. Draw a sketch of the orbit of Europa as it orbits Jupiter, and label all forces that act on Europa. c. Derive a force equation based on the force diagram. Would this force equation change for the other three moons? Why or why not? Explain your answer. d. Using the force equation derived in part "c", derive an equation for the period of revolution "T" of a moon as a function of its orbital radius "r".

e. Which quantities should be plotted to yield a straight-line relationship that could be used to find the mass of Jupiter? Explain your answer. f. Construct a data table that shows the calculated quantities referenced in part "e". Label the top of each column so it is understood what you are plotting, and provide units associated with the updated quantities. g. Plot a graph using the linearized quantities. Make a line of best-fit and use the slope of the graph to find the mass of Jupiter.

Moon Name lo Mass (kg) 8.97 x 1022 Radius (m) Mean Radius of Orbit (m) Period of Revolution (s) 1.82 x 106 4.22 x 108 1.53 x 105 Ganymede 1.48 x 1023 2.64 x 106 1.07 x 10 6.18 x 105 Europa 4.8 x 1022 1.57 x 106 6.71 x 108 3.06 x 105 Callisto 1.08 x 1023 2.41 x 106 1.88 x 10 1.47 x 106 wwwww