Revolution of Jupiter's Moons 
Tonight we'll follow in the footsteps of Galileo and observe the moons of Jupiter as they orbit the largest planet in the solar system. Jupiter, more massive than all the other planets combined, has a system of moons that make up a miniature solar system. In fact some of Jupiter's moons are the size of planets (Ganymede and Callisto are roughly the size of Mercury) while two others, Io and Europa, are the size of our own moon. These four ·Galilean moons· are interesting objects in their own right, Io with volcanoes spewing sulfur many miles into space and Europa with a crust of water ice and perhaps liquid water underneath. Currently the Galileo Mission is returning outstanding pictures of these moons and even the newspapers have stories of discoveries about them every few months. 
In addition tonight we'll learn how to find out astronomers determine the mass of planets, stars galaxies, in fact most anything astronomical. The mass of a planet or star determines how powerful the gravitational field surrounding the planet or star is. Of course, the gravitational field is invisible, but shows its presence when an object (a moon or artificial satellite for instance) moves through this gravitational field. If we measure how far the moon is from the planet in its orbit (A) and time how long it takes to go around the planet once, its period (P), we can then find out about the mass of the large object. 
This relationship between distance from the massive object, A, and period of revolution, P, is usually expressed as Kepler's Third Law of Planetary Motion: 

.It,. = Mass in solar masses 
	pZ 	of attracting object 

We saw that this law was true for planets orbiting the sun Ifwe expressed the planet's distance from the sun In Astronomical Units (1 A.U. = 93,000,000 miles = 150,000,000 kilometers) and the planet's period In Earth years. In fact, Kepler's Law will also apply to moons orbiting planets and two stars orbiting each other. A31P2 will be the same number for any of Jupiter's moons, for Instance, but the number won' be one. The number will represent how big the mass of the attracting planet or star Is compared to the sun. 
As an example, if we watch the moon Titan orbiting Saturn at a distance of A = .00814 A.U. and 
with an orbltal~ of 16 days = 16/365 years = .0438 years, then 	' 
..£: = (OQ814!3 = 2.81 x 10-4 solar masses 
	p2 	(.0438) 
In other words, Satum.would be only about 3 ten thousandths the mass of the sunil II We'll use three of Jupiten Galilean moons (Europa, Ganymede and Callisto) to get three independent measurements of what the mass of Jupiter should be and then we'll ayerage them to see how Jupiter compares to the sun in mass. 
Acknowledgment
The lab will use a computer program created by the CLEA project to create Contemporary Lab Exercises in Astronomy. These programs are distributed free of charge to universities across the U.S. with the creators of the program being funded by an educational grant. The computer program will calculate the positions of Jupiter's moons on a daily (or even hourly) basis and display them to us as we would see them with a medium sized research telescope that can be varied from 100 to 400 power. I should tell you that the Galilean moons can be ObselVed with a simple pair of binoculars and I'd encourage you to try it, then you'd really be following in the footsteps ofGalileoll 

Procedure
Start up the computer and click on the CLEA Jupiter's moon program. Log in and then set the observation interval at 24 hours. This means we'll see Jupiter once a day. Next a screen should come up showing Jupiter and its moons as they'd be seen with a medium sized telescope using a charge coupled device (CCD camera). By moving the mouse around you can -click- on various parts of the image ,pixels· or picture elements). You'll see a read out of the X and Y locations of the pixel you've clicked on, and if the pixel is part of the image of a moon, it will identify the moon and tell you the distance the moon is from the center of Jupiter as measured In -Jupiter diameters. • 
The moons of Jupiter orbit in the equatorial plane of JUpiter, and from Earth this plane is seen edge on, so that it's difficult to make out their nearly circular orbits. They seem to move from one side of Jupiter to the other and then back again in a way that may seem chaotic at first but after watching a while displays a periodic nature. We'll measure the distance the moons are from Jupiter day by day, recording the distance in Jupiter diameters on the worksheet.· Note that YOU'll be told whether the moon is east or west of Jupiter by the distance reading a number followed by E or W, for example, 4.45E would mean that the moon appears to be 4.45 Jupiter diameters East of the center of Jupiter. Of course the moon actually is the same distance from Jupiter every day, but it appears to change in its distance from day to day because we're seeing its circular orbit edge on. 
As you proceed from one day to the next, see if the moons seem to move at different speeds. think you'll notice that Ganymede and Callisto move more slowly than 10 and Europa. This makes sense, actually, because 10 and Europa lie closer to Jupiter they are more strongly affected by Jupiter's gravitational field. Just as planets lying close to the Sun move more rapidly in their orbits, so too, the innermost Galilean moons move fastest about Jupiter. 
Graphing
Once you've obtained a few weeks worth of observations of the positions of the four moons, we'll create a graph of the position of each moon as time passed. I've put out graph paper for you to use for each moon. I think you'll find it easiest to start with Callisto, since it moves so slowly that it will be easy to see how long it takes to complete one full orbital cycle (that's its period, P) and also to see what it's true distance is from Jupiter (A). The period is how long it takes before ·the moon repe~ lb~same position and we11 measure ft first in days and than convert ft to years 
	by diViding b 	5.25 There is a space for the period on each graph. The distance from 
Jupiter, A, is t e maximum number of Jupiter Diameters (J.D.) that we ever observe the moon to be. This will be the maximum value shown on your data table for each ~e'll also convert this into Astronomical Units by dividing the number of Jupiter diameters byl1.Q§g)(that's how many Jupiters would fit between us and the sunil). Don't worry too much if your graph for 10 looks pretty wild, it moves so fast that it's hard to get a decent graph of its motion. 
Calculations
Do the A31P2 calculation using the P value in years and the A value in A.,U. forthe moon Callisto. This should give the mass of Jupiter compared to the sun. The number you get should be ~ .001 Jupiter is about one thousandth the mass of the sun. Record this number for the mass of JUPit'er on the blank provided on the worksheet. Then repeat the calculation for the moons Ganymede and Europa. Finally, average these three values (which should be almost identicalt) to come up with a mass for Jupiter Compared to the sun. 
Summary
By observing the moons of Jupiter we find they follow orderly orbits in compliance with Kepler's Laws of Planetary Motion. They also permit us to measure the strength of Jupiter's gravitational field and thus determine Jupiter's mass. This technique of observing objects revolving around another object is frequently used in astronomy to find the mass of other objects compared to the sun: it is used when one star orbits aoother, when one galaxy orbits another or even when a galaxy orbits a whole cluster of galaxies. It is one of the most useful tools astronomers have.