Hannah's+Jupiter+Lab+Report

=Mass of Jupiter= April 30, 2010


 * Participants**: Hannah Mollmark (with lab partner Marissa Marton for the activities).
 * 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 were introduced to a program where the details of moons and planets can be studied and manipulated. After becoming familiar with the different techniques that would be needed, we specifically looked at Jupiter and four of its moons. We put together multiple images that were taken at intervals over a specific period of time so that we could study the movement of the moons over time. By comparing coordinates we could determine the direction and general speed (in comparison to the other moons) of the moons as well as the distance from Jupiter itself. Through a series of calculations (elaborated on and explained below in calculations section) we were able to take the distance in pixels and determine the distance in meters. By using this, the radius of a moon's orbit, along with the orbital period and the constant of universal gravitation, the mass of jupiter was calculated.
 * Brief Description of Experiment**:

Above pictures shows the image of jupiter and its moons over a period of time (showing moons' movement) and the distance of the moon from jupiter at every time interval. Above picture shows the moons in chronological order so what direction they're moving as well as which one is moving the fastest and slowest. The data table above shows the numbers that are displayed in the two graphs. They show the distance of the moon from jupiter in pixels (first graph) and meters (second graph). The x-coordinate, time, is the six different intervals that the images were taken. The purple points represent the moon named Callisto, the red is Ganymede, the blue is Europa, and the green is Io.
 * Data**:


 * Sample Calculations:**
 * //Size of a Pixel// || We calculated the size of a pixel by doing a series of calculations using both given and calculated measurements. We multiplied .63arcsecs over one pixel by one arcmin over 60arcsecs by one degree over 60 arcmin by one radian over 57.3 degrees. The answer was 0.63 radians over 206280 pixels which we then multiplied by the distance of Jupiter from Earth for the jup5 to jup10 images which is 6.63 x 10^8 km. The product was 2024.87 km and converted to meters was 2024869.11.

|| The percent difference between the accepted value and the calculated value for the mass of Jupiter was found by subtracting the calculated value from the accepted value and dividing the difference by the accepted value. That quotient is then multiplied by one hundred to get a percent. The accepted value is 1.8987 x 10^27 kg and the calculated value (above) is 1.834 x 10^27 kg. ||
 * //Mass of Jupiter// || The mass of Jupiter in kilograms was calculated by using the given equation of four times pi squared times the radius (D) of one of Jupiter's moons cubed 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" so the radius was 421,600,000 meters and the time was 1.8 days or 155520 seconds. The constant of universal gravitation was given and it was 6.67 x 10^-11. Our calculated mass is 1.834 x 10^27 kg. (The acutal mass of Jupiter is 1.8987 x 10^27 kg.)
 * Results**: By using the program and images of the moons of Jupiter along with many calculations in order to determine distances and orbits, the mass of Jupiter was calculated to be 1.834 x 10^27 kg.

1. What does the plot you made above (of pixel distance of Jupiter vs the time the image was taken) represent? //The plot of pixel distance of Jupiter versus the time the image was taken represents the movement of Jupiter's moons over a period of time. You can see how the moon either gets further away or closer to Jupiter as the distance increases or decreases, respectively.//
 * Lab Questions**:

2. Design an experiment that would allow you to obtain a more accurate value for the mass of Jupiter. Be specific. //In order to obtain a more accurate value for the mass of Jupiter, a longer amount of time should be used to collect data. If more points had been observed, collected, and graphed, then the numbers and therefore calculations and results will be closer to the accepted mass of Jupiter.This is because we only studied a period of about five hours and when we tried to fit the line of the curve using given numbers for the period and orbit radius of that moon, the line did not fit perfectly with the points. If more points had been plotted than the lines would have fit better and the tests would have been more successful.//

3. Percent Difference of mass of Jupiter: //see Calculations section.//

I believe that the experiment produced a valid and reproducible result because we used a program consisting of images that, when used correctly by following the instructions, will result in the same answers. When done carefully and accurately, the calculations will also provide the same answers. There might be slight variations due to the effects of the images but they will be negligible. Our results were very close to the accepted value for the mass of Jupiter; the percent difference was only 3.408%. An improvement to the experiment would be to make sure the brightness of the images is not too much when determining distances because it can alter the results. In addition, because of the number of calculations that were performed, there was a lot of rounding of numbers. If you were able to use full numbers, the answers might be slightly more accurate. In addition, if the period of time across which the moons' location points were collected had been longer, the results would be more accurate (see lab question number two above).
 * Conclusion**:

//Don't forget to link to your lab report from the lab reports page and to include a link to your lab report in your reflection.//