Harvard University Astronomy Lab and Clay Telescope

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Jupiter and the Galilean Moons

The overall goal of this lab is to understand how Jupiter's moons appear to move in our sky. We will observe how Jupiter moves relative to background stars from night to night, and how its moon Io, one of the 4 bright moons of Jupiter discovered 400y ago by Galileo with his first astronomical telescope, moves relative to Jupiter. Our observations of the beautiful planet Jupiter allow us to easily see (night to night) the changing position of the 4 moons and to measure the back and forth motion of Io. From this we shall "derive" (or verify) Kepler's 3^rd Law which relates the radius to the period of an object (Io) in a circular orbit about another (Jupiter), and measure Jupiter's mass.

Procedure:

• First, take a moment to visually look at Jupiter through the eyepiece. Take notice of the banded atmosphere and look for the Galilean satellites!
• Next, we want to take a few images of Jupiter and Io (and the 3 other Galilean moons) so we can later do a careful reduction of Io's motion and to make color image for fun!
  • Take 3 very short (try 1 sec) exposures in the blue (B), green (V) and red (R) filters. Ideally, we want images where Jupiter is not saturated and where we can still see the fainter moons. If that is not possible, we may have to take short exposures (for the color image) and longer exposures (for tracking Io and the moons). Note: Making a color image is not required for the lab. It is intended to be a quick, fun activity if time permits.
• Using the Sky program, you can zoom in on Jupiter and make a note about the orientation of the moons (i.e. which moon is which) so you know you are constantly tracking Io. If you are running short on time, this can be done during the analysis section.

Reductions and Analysis:

• First, open all of your Jupiter images in MaximDL.
• We must now find the X, Y pixel position of the center of Jupiter and the center of Io for each of our image by "clicking" on the center with your mouse in MaximDL.
• All values should be entered into the Jupiter-Io template. The template has further instructions and will guide you through the steps to calculate Io's offset from Jupiter (in both arcsec and km).
• To determine Io's motion around Jupiter, your TF will help you use the computer program, NLReg, to fit a sine curve to the radial offsets vs. time .From this you derive the Period, P, and the radius, R, of the orbit (max offset of Io from Jupiter, in km units, which you then convert to distance in AU units).
• Now, using the current distance from Earth to Jupiter (4.86 AU), and Newton's version of Kepler's Law, namely that P² ∝ R³/M, derive the mass, M, of Jupiter in solar mass units. You must first convert your derived R into AU units, R(AU) = R(km)/(1.5x10⁸(km/AU)), and P into years, P(yrs)=P(days)/(365(days/yr)).