Rotational Motion

 Kepler's Third Law of Planetary Motion

 Solution

Q1: Write out and breifly explain in your own words the equations for centripetal froce and Newton's Law of Universal Gravitation. Include a sketch for each explanation.

 Fc = (mv2)/r FG = (GM1m)/r2(M1 is the primary body) image image

In both equations we are describing a force between the same two objects Fc always acts inward FG acts between both objects, so one can say Fc = FG.

Jupiter's four moons were discovered by Galileo in 1610. The innermost moon called Io is about half the size of the Earth. Io orbits an average distance of 422,000 from the center of Jupiter and has an orbital period of 1.769 days.

Q2: The Keplerian Ratio is defined as K = T2/r3 for any satellite orbiting a planet or moon. It depends only on the mass (M) of that planet. Calculate the Keplerian Ratio KJupiter for any satellite of Jupiter.

The Keplerian Ratio for Jupiter with respect to Io is:K=(152841.6)2 / (422,000,000)3 = 3.1 x 10-16

Q3: Use the above information to find an equation for the mass of Jupiter. Solve it.  Q4:What is the Keplerian Ratio KSun for any object orbiting our sun? (Hint: You can use T and r for Earth, as it orbits the sun.) The Earth's average orbital radius about the sun is 150,000,000,000m.

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