We won't be introducing new physics in this class. Instead, we'll extend our discussion of circular orbits by making a connection to how these orbits are actually observed in our solar system. We will use a computer simulation to measure the motion of the Galilean Moons of Jupiter.
The point of the exercise is to get a feeling of how astronomers actually observe orbits. Remember that, in our solar system, we see the orbit pretty much "edge on". Therefore, we see a sinusoidal oscillating motion, instead of a circular orbit. The period of the sine wave, however, is the same as the orbital period.
Another concept we are introducing to day is the idea of "natural units". That is, times when it is much more convenient to write things down in terms of naturally occuring quantities. In this case, it is natural to write things down in terms of solar masses, years, and astronomical units (A.U.).
Before coming to class, you should print out and read through the student manual for the CLEA exercise on "The Moons of Jupiter". This will give you some of the background physics (and some interesting history) for the measurement. Notice that the writeup ignores SI units altogether and points out that if we always express the mass of the heavy body in units of the solar mass, the radius (or "semimajor axis") in units of the earth-sun distance (called one astronomical unit, or AU), and the revolution period in years, then we can ignore the various constants altogether.
Follow the instructions to get to CLEA software and the "Jupiter" program on RCS. It would be best to share your data with another pair of students, each pair working on a different two moons. (There may not be enough time to complete the exercise if you do all four moons by yourself.) Plot your results on the graphs provided on pages 10 and 11 of the student manual. Carry out the calculation and answer the questions on page 12 of the student manual. You do not need to answer the "extra credit" questions on page 13.
You have one homework problem due at the start of class next Wednesday, namely problem 4 in Chapter 1 of Zeilik & Gregory. This is to continue our discussion of Newtonian gravity, by figuring out the effective gravitational acceleration (i.e. your "weight") on the Moon, Sun, and Jupiter, relative to that on Earth. We will be doing more on motion in gravitational fields in class.
