CLEA Lab, Moons of Jupiter

What you turn in to your instructor as a lab

Moons of Jupiter Manual as a Word doc file.
Moons of Jupiter Manual as an Adobe Acrobat pdf file.

Data tables for all four of the Galilian moon of Jupiter: Callisto, Ganymeade, Europa, and Io with the starting date that you did the lab.  Four graphs, one each  for all of the four moons, which show how far away they wee from Jupiter in Jupiter Diameters (JD) on the y-axis, the absisia, versus when it was in days on the x-axis, the ordinate.  You should have at least twenty points on each graph on days and times when you could tell where the moon was.  You can't take data if it is cloudy or if you can not see the moon, because it is behind Jupiter.  If you do not know where the moon is please do not lie to yourself by putting zero or something else equally as absurd for where the moon was.  You then need to fit all four of the curves with a sine curve and determine the amplitude of oscillation, this will be the semi-major axis of the orbit in Jupiter diameters and the period of oscillations for one complete cycle this will be in days.  You need to then convert the Jupiter Diameters to AU, Astronomical Units, by dividing the semi-major axis in Jupiter Diameters by 1050.  This is because there are 1050 Jupiter Diameters in an AU.  You then need to take the period of the moon in days and divide it by 365.25 converting the period to years. This is because there are 365.25 days in a year.  You then to cube the semi-major axis of the moon in AUs and divide it by the square of the period of the moon in years.  This can be done in one step for each of the four moons.

For instance if you had determined that the semi-major axis of a CLEA moon around Jupiter was 35 Jupiter Diameters (JD) while the period was 70.3 days.  Then the mass of Jupiter would be computed as (35/1050)^3/(70.3/365.25)^2=9.99783661029E-4 on a scientific calculator; giving a mass of Jupiter as 9.99x10^-4 Solar Masses.  This is because (1 AU)^3/(1 year)^2=1 Solar Mass; since the earth orbits the sun at 1 AU taking 1 year to go around; Kepler's third law.

So besides the data tables for the four graphs and the four graphs you will compute the a mass for Jupiter of each of the four moons and they should all be approximately the same, since Jupiter weights the same regardless of which moon is going around it.   All of the moons are very small compared to Jupiter.  This way you should know whether or not you did the lab correctly or not.   If you did it incorrectly you need to figure out what you did wrong.  In astronomy, which is applied physics, there is an objective reality.  The mass of Jupiter in solar masses is not subjective, but objective.  Different people should agree and get the same mass within the limits of the precession of their measurement.  

Most people doing this lab will find that taking data every once a day, the default setting, is fine for 3 of the 4 moons Callisto, Ganymeade, and Europa.  The once a day time interval for Jupiter's moon observations will not work well for Io since its period is between 1 and 2 days.  To resolve Io you should change the default time interval to 6 hours that way you will have observations every 1/4 of a day.  You may just take data on Callisto, Ganymeade, and Europa with the one day interval and then quit the computer program and start it again, but this time change the time interval to 6 hours and keep track of Io.  This is but one way to solve this problem, their are others.