The+Mass+of+Jupiter

=Mass of Jupiter Lab= 5/3/2010
 * Participants**: Trevor Wood, Ryan Payne, Michael Bateman
 * Purpose**: The purpose of this lab is to find the mass of Jupiter by analyzing images of Jupiter and its moons.


 * Brief Description of Experiment**: In this experiment we used a computer program called Hands On Universe to manipulate Jupiter and four of its moons in order to find Jupiter's mass. To do this we added 6 images of Jupiter and four of its moons (seen in the image below), at specific periods of time, together to get one image showing the change in each moon's distance at different times. Using a slice tool from the program we were able to find the distances from moon to moon. Using this we were able to then find the direction that the moons were going and the relative speed of a certain moon at a specific time. Using a series of calculations, which can be seen below, we found the distance in pixels and converted those distances into meters. By plotting these distances we were able to calculate the radius of each moon's orbit, along with their orbital periods (in seconds). Finally we put all the variables into a given calculation for finding the mass of jupiter (which can be seen in the calculations section below) and got an accurate mass.


 * Data**: Below is an image of Jupiter and four of it's moons moving over a period of time. There are also four graphs showing the distances of each moon from Jupiter at each period of time.

Below in the table is a set of data showing each moon's distance in pixels and meters for each time interval. The graphs both show each moon's distance (Y value) compared to its time. The blue data points show the moon Callisto. The Green data points show the moon Ganymede. The Orange data points show the moon Europa. The purple data points show the moon lo.

conversion equations || 1 degree = 60 arc minutes 1 arc minute = 60 arc seconds 1 pixel = 0.63 arcsecs 1 radian = 57.3 degrees Distance of Jupiter from Earth for images jup5 to jup10 = 6.63 x 10^8 km 1 km = 1000 m ||
 * Sample Calculations:**
 * Pixel to meter
 * //Mass Of Jupiter// || The mass of Jupiter is found by using the given four pi squared and multiplying that by the radios of orbit of one of Jupiter's moons (D) cubed. This is then divided by the product of the constant of universal gravitation (G = 6.67 x 10^-11) and the time in seconds (T) it takes the moon to complete one orbit.

Mass of Jupiter = (4pi^2 x D^3) / (G x T^2) = 1.890798735 x 10^27 kg ||
 * Results**:The mass of Jupiter was determined to be 1.890798735 x 10^27 kg. This was calculated by using the radius of one of Jupiter's moons, the time it takes the moon to complete one orbit, and a constant for gravity and the formula for finding the mass of Jupiter which is described in the calculations.


 * Conclusion**: I believe that this experiment produced a valid and reproducible result, because we used actual images of Jupiter and its moons, which in turn allows our data to be very accurate giving us a valid solution. Our experimental results were very close to the accepted value. We found the mass of Jupiter to be 1.890798735 x 10^27 kg, while the accepted value is 1.8986×1027 kg, giving us a percent difference of 0.41 %. The only solution to improving the experiment would be to make sure that when using the program Hands on Universe to find the best brightness of the moons, which if done will produce a more accurate answer.