Answers for Our Physic Contradiction....

While studying Kepler's three laws of planetary motion we encountered what appeared to be a contradiction in our physics book. After some in-depth studying into Kepler's constant what I discovered was that Equation 7.14 on the bottom of p. 153 of our text is the equation to which the statement "This equation is good only for planets, comets, asteroids, etc., orbiting the sun. It cannot be used for any planetary satellite or moon." is referring to. This statement does NOT refer to the ratio of the square of the orbital period (T) to the cube of the semi-major axis (R), found in Equation 7.13 on p. 153. Equation 7.14 is referring to finding the orbital period of a planet that is orbiting the sun. By using the time it takes for the earth to orbit the sun as well as the astronomical units (ua) [the mean distance from the earth to the sun], one can solve for the orbital period of any other planet orbiting the sun. This is a derivative of Kepler's constant given in Equation 7.13. Kepler's constant in Equation 7.13 can be applied to all heavenly bodies contained in the same system.

Each orbital system in the universe has it's own K, or Kepler's constant. Jupiter and it's moons, for example, have a different K than say, the Earth and her moon. That also means that all three of Kepler's laws apply to moons, asteroids, comets, satellites, etc. and are related proportionally to a planet, moon, asteroid, comet, or satellite that is contained in that same system. If a satellite is orbiting the earth it will orbit faster when closer to the earth, following Kepler's second law.

Now to the practice problem we worked on the board Friday during class time. We new the semi-major axis and orbital period of Europa, one of Jupiter's moons, and also the semi-major axis of Io, another of Jupiter's moons. We were then asked to calculate Io's orbital period. Simply place the ratio of Io's semi-major axis and it's period (WATCH THE EXPONENTS!!) equal to the ratio of Europa's semi-major axis and it's orbital period (Again, WATCH THE EXPONENTS!!). Solve for the unknown of the proportion using cross-multiplication and then division.

This video below will give a practice problem using the example of the moon and a satellite orbiting around the earth (both in the same system). 

This means that both the true and false questions that seemed to contradict the statement in the book and this problem involving the moons of Jupiter WILL BE INCLUDED in Wednesday's test. If you have any questions, be ready to ask them Thursday morning before I hand out the tests.