Kepler's Law Lab
Objectives
1. Determine the mass of Jupiter.
2. Gain a deeper understanding of Kepler’s third law (the harmonic law)
.3. Learn how to gather and analyze astronomical data.
2. Gain a deeper understanding of Kepler’s third law (the harmonic law)
.3. Learn how to gather and analyze astronomical data.
Background
A man by the name of Johannes Kepler came up with three mathematical laws, from using the observations of Nicolaus Copernicus and Tycho Brahe. These laws are based off of the orbit of one body revolving around another. . With these laws the mass of planets could now be calculated by using Kepler’s Harmonic Law and Newton’s Universal Law of Gravitation. Next withGalileo's use of the telescope he found that there are four moons that orbit Jupiter and with this information, more could be learned and understood about our solar system.
Procedure
The procedure to this lab can be found online or at this link http://geddesphysics.weebly.com/analyzers-moons-of-jupiter.html.
Data
Data Analysis
The slope is equal to Jupiter's Mass. so R^3/T^2=GM/4Pi^2 with the linear equation being
R^3=GM(T^2)/4Pi^2 with the slope of the function being (GM)/(4Pi^2). By setting this slope equal to the slope obtained from the above graph and solving for "M" we get that the mass of Jupiter is 1.775640972x10^27 With the actual mass of jupiter being equal to 1.8986x10^27 the percent error would be = -6.47795% error
R^3=GM(T^2)/4Pi^2 with the slope of the function being (GM)/(4Pi^2). By setting this slope equal to the slope obtained from the above graph and solving for "M" we get that the mass of Jupiter is 1.775640972x10^27 With the actual mass of jupiter being equal to 1.8986x10^27 the percent error would be = -6.47795% error
Conclusion
Calculate the percentage error with the accepted mass of Jupiter (1.8986 × 10^27 kg).
(1.77560972x10^27-1.8986x10^27)/( 1.8986x10^27) X 100% = -6.47795% error
There are moons beyond the orbit of Callisto. They will have larger periods
than Callisto because their radii would be larger relative to Jupiter whichmeans that they will take longer to revolve around Jupiter. A ten percent error in "r" would cause the larger error in the mass
of Jupiter calculation rather than a ten percent error in "T" (the period), because "r" is cubed and "T" is squared so the cubed value would hold a greater quantity, resulting in a greater percent error. Also, Galileo's observations of the orbits of Jupiter's moons were an important piece of evidence supporting the heliocentric
model of the universe because it proved that everything did not revolve around the sun, but could revolve about other planets. I gained a deeper understanding of Kepler's third law, by calculating data about it through this lab, while obataining the experimental mass of Jupiter from it. I also learned
how to gather and analyze astronomical data by collecting data from the CLEA Software to gather varius radii of four moons relative to Jupiter over a period of time. With a decently low percent error it could be said that data could have a lower percent error by obtaining a better fit sin curve which would mean more accurate point for the moons.
(1.77560972x10^27-1.8986x10^27)/( 1.8986x10^27) X 100% = -6.47795% error
There are moons beyond the orbit of Callisto. They will have larger periods
than Callisto because their radii would be larger relative to Jupiter whichmeans that they will take longer to revolve around Jupiter. A ten percent error in "r" would cause the larger error in the mass
of Jupiter calculation rather than a ten percent error in "T" (the period), because "r" is cubed and "T" is squared so the cubed value would hold a greater quantity, resulting in a greater percent error. Also, Galileo's observations of the orbits of Jupiter's moons were an important piece of evidence supporting the heliocentric
model of the universe because it proved that everything did not revolve around the sun, but could revolve about other planets. I gained a deeper understanding of Kepler's third law, by calculating data about it through this lab, while obataining the experimental mass of Jupiter from it. I also learned
how to gather and analyze astronomical data by collecting data from the CLEA Software to gather varius radii of four moons relative to Jupiter over a period of time. With a decently low percent error it could be said that data could have a lower percent error by obtaining a better fit sin curve which would mean more accurate point for the moons.