Objectives
1. Determine the mass of Jupiter.
2. Gain a deeper understanding of Kepler's third law.
3. Learn how to gather and analyze astronomical data.
2. Gain a deeper understanding of Kepler's third law.
3. Learn how to gather and analyze astronomical data.
Background
It was originally thought that all objects in space revolved around the earth while Copernicus believed that all planets revolved around the sun. It was later discovered that r^3/T^2 was constant and can be used to find the mass of the central object.
Procedure
You can find the procedure on this website or below http://geddesphysics.weebly.com/analyzers-moons-of-jupiter.html
1. To begin the program, select CLEA_JUP andLogin.
2. Select start and enter starting date and time.
3. Click on each moon to record the orbital radius.
4. Repeat set until all of the moons have completed one complete orbit.
5. Use the r vs. t data to create sine graphs for each moon.
6. Now using the orbit of each Galilean moon, determine the quantities that you would have to graph in order to obtain a straight line whose slope will yield the mass of Jupiter.
7. You will have to convert Jupiter Diameters to meters and years to seconds. There are 1.43x10^8 meters in one Jupiter Diameter.
1. To begin the program, select CLEA_JUP andLogin.
2. Select start and enter starting date and time.
3. Click on each moon to record the orbital radius.
4. Repeat set until all of the moons have completed one complete orbit.
5. Use the r vs. t data to create sine graphs for each moon.
6. Now using the orbit of each Galilean moon, determine the quantities that you would have to graph in order to obtain a straight line whose slope will yield the mass of Jupiter.
7. You will have to convert Jupiter Diameters to meters and years to seconds. There are 1.43x10^8 meters in one Jupiter Diameter.
Equipment
CLEA software
Data
Data Analysis
r^3/T^2=GM/4pi^2 this means if we set the slope of the r^3 vs. T^2 graph equal to GM/4pi^2 we can solve for the mass of Jupiter. When we do this we find that M=1.77458*10^27. Given the actual mass of Jupiter as 1.8986*10^27 our percent error is 6.5%
Conclusion
1. Calculate the percentage error with the accepted mass of Jupiter (1.8986 × 1027 kg).
(Actual-theoretical)/Actual=6.5%. I believe that this error came mostly from the fact that I was not always able to be perfect when selecting points to use for the planets on the CLEA software, but it could also be attributed to not fitting the graphs correctly or not having enough data.
2. There are moons beyond Callisto. Will they have larger or smaller periods that Callisto? Why?
Using Kepler's law r^3/T^2=C as r increases T must also increase to keep the ratio constant.
3. Which do you think would cause the larger error in MJ: a ten percent error in "T" or a ten percent error in "r"? Why?
A 10% error in r would cause a larger error in MJ since r is cubed and T is only squared.
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)?
They showed that smaller objects tend to orbit larger ones and that all objects do not have to orbit the earth.
The purpose of this lab was: 1. Determine the mass of Jupiter.
2. Gain a deeper understanding of Kepler's third law.
3. Learn how to gather and analyze astronomical data.
I was able to accomplish all of these goals throughout the lab while also getting better at using excel and a new program CLEA.
(Actual-theoretical)/Actual=6.5%. I believe that this error came mostly from the fact that I was not always able to be perfect when selecting points to use for the planets on the CLEA software, but it could also be attributed to not fitting the graphs correctly or not having enough data.
2. There are moons beyond Callisto. Will they have larger or smaller periods that Callisto? Why?
Using Kepler's law r^3/T^2=C as r increases T must also increase to keep the ratio constant.
3. Which do you think would cause the larger error in MJ: a ten percent error in "T" or a ten percent error in "r"? Why?
A 10% error in r would cause a larger error in MJ since r is cubed and T is only squared.
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)?
They showed that smaller objects tend to orbit larger ones and that all objects do not have to orbit the earth.
The purpose of this lab was: 1. Determine the mass of Jupiter.
2. Gain a deeper understanding of Kepler's third law.
3. Learn how to gather and analyze astronomical data.
I was able to accomplish all of these goals throughout the lab while also getting better at using excel and a new program CLEA.