Calculating the Mass of Jupiter

Goal: To determine the mass of Jupiter from observations of a moon.

Materials and Equipment:

• Stellarium or any other planetarium program showing the positions of Jupiter's moons. If you do not have a planetarium program, you may be able to use Sky and Telescope's interactive Observing Tool for Jupiter's Moons (click on the link) to "observe" the location of the moons over several weeks.

Procedure:

Plan

Use Stellarium or another planetarium program that displays the position of Jupiter's moons to make your observations, but if you can, try to observe Jupiter directly at least twice several days apart, and note the position of its moons, so that you understand what the simulation shows.

"Observe" using the planetarium program

1. Use the planetarium program to locate and "observe" the position one of the following moons starting on October 1 of this year:
   • Io - every 2 hours for 2.5 days
   • Europa - every 4 hours for 5 days
   • Ganymede - every 8 hours for 9 days
   • Callisto - every 24 hours for 18 days
2. Measure the position of the moon from Jupiter in millimeters on your computer screen. Plot the position versus time on a graph, or use a spreadsheet to enter the data and generate the plot. Positions to the right and up should be positive, to the left and down should be plotted as negative values.

Analyze

1. From the peaks and troughs of your data, determine the period of the moon in hours. Convert this value to Earth years.
2. Using the data in the planetarium program, determine the distance to Jupiter during your observation. Convert the value (generally in km) to astronomical units (AU).
3. Using the screen on your planetarium program, measure the maximum displacement of the moon from Jupiter in arcseconds to the right/up and left/down directions. Note that the two values may not be equal because we view the moon from different locations and because the orbits are elliptical. Add the two maximum distances together and divide by two. The result is the semi-major axis of the moon's orbit.
4. Use the small angle formula to compute the radius of the moon's orbit in AU.
5. Use Kepler's law M = a³/P² to compute the mass of Jupiter in terms of solar masses. Use the solar mass given in your textbook to compute the mass of Jupiter and compare your results with the accepted mass listed in the textbook appendix.

Report

Your report should include the steps you used in your planetarium program, the data for your planet, and if you can scan them in or generate them with a spreadsheet program, your graph of the planet's position vs. time. It should have a section including your calculations and your conclusions about the method for determining the mass of Jupiter.

© 2005 - 2025 This course is offered through Scholars Online, a non-profit organization supporting classical Christian education through online courses. Permission to copy course content (lessons and labs) for personal study is granted to students currently or formerly enrolled in the course through Scholars Online. Reproduction for any other purpose, without the express written consent of the author, is prohibited.