Mass+of+Jupiter+Lab

= __Marissa's Mass of Jupiter Lab__ =

Date of Publication: April 30, 2010


 * Participants**: Marissa Marton & Hannah Mollmark


 * Purpose**: The purpose of this lab is to use a sequence of images of the Galilean moons of Jupiter to calculate the mass of Jupiter.

In this experiment, we utilized a program called Hands On Universe. In this program we were able to manipulate Jupiter and its moons in order to analyze and determine the orbits of the moons but more importantly, the distance of the moons from Jupiter. After first using the program for a supernova experiment, we were more familiar and better equipped to produce a valid and reproducible result for the distance. We first put together multiple images of Jupiter and its moons that were taken over different periods of time. This way we were able to analyze the movements of the moons over time (see the first two images in the Data section) and more specifically, look at their direction and speed by comparing the image coordinates in the program as well as their distance from planet Jupiter. By collecting data from the images, we were able to determine values for our calculations and this is how we ultimately arrived at our result.
 * Brief Description of Experiment**:

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 * Video actually showing Jupiter and its moons: **

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 * Good informational video about Jupiter's Moons: **


 * [[image:Jupiter_pic.jpg width="566" height="385"]] [[image:jupiter_moons_lab..jpg width="285" height="411"]][[image:JUP.jpg width="204" height="296"]]

Data**:

This picture depicts an image of Jupiter and its moons over time (to the left) and the distance of each moon from Jupiter at every time interval (to the right).

This picture depicts the moons' movements (slowest to fastest) in relation to distance and time.

This is a picture of a data table that matches the measurements shown in the two graphs below. It is measuring the distance of the moons from the planet Jupiter. M1, M2, M3, and M4 are all measured in pixels. We then created new calculated columns for each moon and determined what the distance would be in meters (M1C, M2C, M3C, M4C – where M stands for moon and C stands for calculated). Also, the column called Time (hrs) represents the X-coordinate in both of the graphs below. The Time (hrs) column shows how the images were taken at six different times.

This graph depicts the distance of the moons (M1, M2, M3, M4) from the planet Jupiter in pixels. In this graph, Jupiter’s moon Callisto is seen as the red points, Ganymede is seen as the blue points, Europa is seen as the green points, and Io is seen as the orange points.

This graph depicts the distance of the moons (M1C, M2C, M3C, M4C) from the planet Jupiter in meters. In this graph, Jupiter’s moon Callisto is seen as the purple points, Ganymede is seen as the red points, Europa is seen as the blue points, and Io is seen as the green points.


 * Sample Calculations:**
 * **//Size of a Pixel//** || Hannah and I were able to determine the size of a pixel by doing a series of calculations by using given and calculated measurements. We multiplied 0.63 arcsecs over 1 pixel by 1 arcmin over 60 arcsecs by 1 degree over 60 arcmins by 1 radian over 57.3 degrees. The answer comes out to be 0.63 radians. We then divided the 0.63 radians by 206,280 pixels and then multiplied that by the distance of Jupiter from Earth for the jup5 to jup10 images (6.63 x 10^8 km). The product comes out to be 2,024.87 km. We then converted this into meters by multiplying the 2,024.8 km by 1,000 to get a product of 2,024,869.11 meters.



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 * **//Mass of Jupiter//** || The mass of Jupiter (in kilograms) was calculated by using a given equation. This equation consisted of the following: four times pi squared times the radius (D) of one of Jupiter's moons cubed and then all divided by the constant of universal gravitation (G) by the time (T) of the orbital period squared. We used the measurements for moon "Io" which gives us a radius of 421,600,000 meters and a time of 1.8 days (or 155,520 seconds). The constant for universal gravitation (6.67 x 10^-11) was given to us. As a result of the given equation, and after plugging in the appropriate values into the equation, we calculated a mass of 1.834 x 10^27 kg. The actual mass of Jupiter is 1.8987 x 10^27 kg, so our calculated mass is very close to the actual mass of Jupiter.
 * //**Percent Difference**// || Percent difference looks at two experimental values and takes the difference between them as a percent of one of them. This is how percent difference is determined. The percent difference between the accepted value of Jupiter’s mass and the calculated value of Jupiter’s mass was determined by subtracting the calculated mass value from the accepted mass value and dividing the difference by the accepted mass value. That quotient is then multiplied by one hundred to get a percent. The accepted value that we determined was 1.8987 x 10^27 kg and the calculated value is 1.834 x 10^27 kg. In performing the percent difference calculation, we came up with a percent difference of 3.408%.

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The purpose of this lab was to use a sequence of images of the Galilean moons of Jupiter to calculate the mass of Jupiter. For our major result of the experiments, we arrived at Jupiter’s calculated mass of 1.834 x 10^27 kg. We got to this result by using a given computer program of Jupiter’s moons where we had to complete specific tasks and calculations.
 * Results**:


 * Lab Questions**:

1. What does the plot you made above (of pixel distance of Jupiter vs. the time the image was taken) represent?

2. Design an experiment that would allow you to obtain a more accurate value for the mass of Jupiter. Be specific.

3. Percent Difference of the mass of Jupiter. See the Percent Difference column in Sample Calculations.


 * Conclusion**: A good conclusion will include:


 * A statement about whether you think that the experiment produced a valid and reproducible result and reasoning supporting your statement.
 * A suggestion as to why your experimental results differ from any accepted value or your expected result (if appropriate).
 * A suggestion for a simple improvement to the experiment. Think about what caused problems, measurement inaccuracies, or inappropriate simplifying assumptions and propose a change. A sketch may be helpful.