Tamara- AP Physics

Moons of Jupiter and Kepler's Third Law

Purpose (objectives)
The purpose is to better understand Kepler's third law and learn how to apply it.  We, also, need to find the mass of Jupiter and learn how gather and interpret astronomical data. 
- Laptop
- CLEA software to run the program necessary to see the moons of Jupiter
Many scientists had hypothesized the movements of the planets.  Given the lack of resources and data, they were never able to prove their hypotheses.  Even with a lack of resources, Tycho Brahe was able to observe the location of the planets and numerous stars.  This took him 20 years.  His student, Kepler was able to deduce laws governing the orbit of one body around another.  Kepler stated that one smaller body orbiting around a larger body is C= r^3/T^2.  Newton expanded this and solved for C. The equation is below.  When technology was growing, Galileo was able to see, through a telescope, that the moons did orbit around Jupiter.  This principle was able to be applied to solar system.  He proved that the heliocentric model was correct.  This information has helped our knowledge of planetary orbits and helped the scientific world. 
Geddes, Kimberly. "Moons of Jupiter." Mrs. Geddes' AP Physics Lab. N.p., n.d. Web. 31 Mar 2010. <http://geddesphysics.weebly.com/moons-              of-jupiter.html>.
                                             r(JD)              r(m)                    r^3(m^3)                 T(days)               T(s)                         T^2(s^2)
                         Callisto       13.23          
1.88E+09                    6.64467E+27                   16.7728                  1449169.92                    2.10009E+12
                   Ganymede          7.5               1068557143               1.22009E+27                    7.12948                 615987.072                      3.7944E+11
                         Europa       4.6755          666138522.8                2.95593E+26                    3.53597                 305507.808                  93335020749
                                  Io           3                 427422857.1                 7.8086E+25                     2.30081                 198789.984                   39517457739

(more at bottom of site)
Data Analysis (some at bottom of site on paper)
                                                                                                       (Slope at bottom of site on paper)

                                                                                                    r^3 (m^3) vs. T^2 (s^2)

Concluding Questions
1.    Calculate the percentage error with the accepted mass of Jupiter (1.8986 × 10^27 kg).
        The work is done on the paper at the bottom of the page. The error turned out to be -1.1894 %.

2.    There are moons beyond the orbit of Callisto. Will they have larger or smaller periods than Callisto? Why?
         They would have a larger period.  The moons would have a greater distance and a slower velocity.  Therefore, it would take longer for them to complete one orbit.

3.    Which do you think would cause the larger error in the mass of Jupiter calculation:  a ten percent error in "T" or a ten percent error in "r"? Why?
                         The larger error would be caused by "r".  "r" is needed to find "T". Therefore, "r" would cause a problem for the "T" value, and make the error that much greater. 

4.    Why were Galileo's observations of the orbits of Jupiter's moons an important piece of evidence supporting the heliocentric model of the universe (or, how were they evidence against the contemporary and officially adopted Aristotelian/Roman Catholic, geocentric view)?   
            Using a telescope, Galileo was able to see that the moons orbited around Jupiter.  This concept applied to the solar system as well.  The planets were able to orbit the sun proving the heliocentric model of the universe. 

According to my data, the mass of Jupiter is 1.8774e27. The CLEA software made it very easy to collect the data necessary.  It also supplied all the information we needed.  My mass of 1.8774e27 is about 1.1894% lower than the actual mass.  This could be due to the fact that the CLEA software gave information if one clicked close to the moon.  This, therefore, made the data slightly off.  Also, the zoom did not work for all of the moons.  Sometimes, I would try to zoom in and my screen would say that day was cloudy.  Overall, the lab taught me the relationship of the radius and the period.  Graphing was a major part of this lab, and this helped me to apply my findings to a particular graph.