Ok, now that our data table is filled out we can get to the math part.  Notice that our orbital periods are in days, for this to work we need to convert days to years. So, divide each orbital period by 365 to get the period into years.
 

• Io:  1.75 / 365 = .0048 years
• Europa:  3.5 / 365 = .0096 years
• Ganymede: 7 / 365 = .0192 years
• Callisto: 17 / 365 = .0466 years

Now we need to know the distance in AUs from Jupiter to each moon. Using the equation like this ( distance is 4.2 which is Jupiter's distance from the Sun)

• True Separation = Distance * Angular Separation / 57.3

• Io:  4.2 * .038 / 57.3 = .0028 AU
• Europa:  4.2 * .061 / 57.3 = .0045 AU
• Ganymede:  4.2 * .097 / 57.3 = .0071 AU
• Callisto:  4.2 * .171 / 57.3 = .0125 AU

We are nearly done with the math just a little more to go! To calculate the mass of Jupiter we need to use the following equation:
 

• a * a * a / p * p  ( by the way this symbol * is the multiplication symbol)

This will not be for the wimpy calculators.
 

• a = the distance from Jupiter for each moon in astronomical units or AU
• p = the orbital period in years

• Io:  .0028 * .0028 * .0028 / .0048 * .0048 = .000000022 / .0000230 = .000956 solar masses
• Europa :  .0045 * .0045 * .0045 / .0096 * .0096 = .000000091 / .0000921 = .000988 solar masses
• Ganymede:  .0071 * .0071 * .0071 / .0192 * .0192 = .000000358 / .000368 = .000972 solar masses
• Callisto:  .0125 * .0125 * .0125 / .0466 * .0466 = .00000195 / .00217 = .000898 solar masses

These numbers are starting to run together!

Next we want to average the above results to obtain a " mean" solar mass result. We will add them together and divide by 4.

.000956 + .000988 + .000972 + .000898 = .003814 / 4 = .0009535 solar masses

.0009535 is our "mean" average for Jupiter's equivalent solar mass. Which equates to 9/10,000 of the Sun's mass

Now to arrive at the figure for Jupiter's actual mass in "kg", we will multiply the average of the solar mass results by

1.99 x 10 to the 30th power

.0009535 * 1.99 * 10 30th = 1.897 * 10 27th kg

Jupiter's actual mass is 317.83 times the Earth's published mass of 5.974 * 10 24th kg which figures to 1.898 * 10 27th kg

Now finally calculate the percent error by using the formula:  calc'd answer - actual answer / actual answer * 100

We can leave off the exponents for this:

1.897 - 1.898 / 1.898 * 100 = .05% or less than a 1/2% error

Now your data and results will vary from mine. My accuracy is fairly good because I interpreted the orbits and intervals very carefully. However, do your best to obtain good data. And follow the above example and you should be able to do this fairly well. The lab is just calculation intensive.

Give me your feedback as to whether this helps you in completing and understanding the lab.

Please note: If you want to print his page out, do so in grey scale or black and white. This is due to the light colors I use to accent certain information. It will be very hard to read in color because the background does not print. So yellow, light blue and green look bad on white paper.