2 - 1 9/16/09 ASTRONOMY 113Laboratory Lab 2: The Moons of Jupiter Introduction and Goals In 1609, Galileo Galilei heard of the invention of a new optical instrument by a Dutch spectacle maker, Hans Lippershey. By using two lenses, one convex and one concave, Lippershey found that distant objects could be made to look nearer. This instrument was called a telescope. Without having seen one, Galileo was able to construct his own telescope with a magnification of about three. He soon greatly improved upon his first instrument, and his best telescopes reached a magnification of about thirty. Galileo immediately began observing the sky with his technological breakthrough. He was a careful observer, and soon published a small book of remarkable discoveries called the Sidereal Messenger. Galileo found sunspots on the Sun and craters on the Moon. He found that Venus had phases, much like the Moon. He was able to see that the Milky Way was a myriad of individual stars. He noticed that there was something strange about Saturn, but his small telescope was not able to resolve its rings. Very suddenly the Universe had become quite a different place! One of Galileo's most important discoveries was that Jupiter had four moons revolving around it. Galileo made such exhaustive studies of the motions of these moons that they are known as the Galilean satellites. This "miniature solar system" was clear evidence that the Copernican theory of a Sun-centered solar system was physically possible. Because he was developing a world view which was not easily reconciled with the religious dogma of his period, Galileo was compelled to neither "hold nor defend" the Copernican hypothesis. Nevertheless, in 1632 he published his Dialogue on the Great World System which was a thinly disguised defense of the Copernican system. This led to his forced denunciation of the theory and confinement to his home for the rest of his life. In this lab you will repeat Galileo's observations, without threat of government condemnation! The goals of this lab are to:2 - 2 9/16/09 i) Measure the periods and semi-major axes of the orbits of Jupiter's moons, and to use these results and Kepler's Third Law to measure the mass of Jupiter. ii) Experience the scientific process in a world of limited resources, in particular telescope observing time. iii) Develop a deeper understanding of the concept and significance of uncertainty in science. Before You Come to Class ... Read the lab completely. Your time in the lab is best used observing the "sky", not reading this manual. Complete the pre-lab assignment. Bring to class this lab manual, your lab book, a pencil or erasable pen, a straight edge, and a scientific calculator. Schedule This lab is designed to be completed in two lab sessions. You should be able to complete at least two observing sessions in the first lab, and have the orbits for at least 1-2 moons determined. This lab incorporates software developed by the Contemporary Laboratory Experiences in Astronomy project of Gettysburg College, funded in part by the National Science Foundation.2 - 3 9/16/09 Section 1 - A Bit of Technical Background Kepler’s Third Law At about the same time that Galileo was observing the sky, Johannes Kepler was deriving his three laws of planetary motion. The most powerful was Kepler's Third Law, which stated that the square of a planet's orbital period was proportional to the cube of the planet's distance from the Sun. Later, Newton used his Law of Gravitation to show that Kepler's Third Law could be generalized to any two objects in orbit about each other. Newton also showed how the period and semi-major axis of an orbit depended on the masses of the orbiting objects. With the addition of Newton's insights, Kepler's Third Law can be stated as follows: M1 + M2 =A3P2 where M1, M2 are the masses of the objects in orbit about each other, in units of the mass of the Sun (Mo). A is the length of the semi-major axis of the elliptical orbit, in units of the Earth-Sun distance or an "Astronomical Unit" (AU). If the orbit is circular (as is the case for the Galilean moons) the semi-major axis is the same as the radius of the orbit. P is the period of the orbit in units of Earth years. The period is the amount of time required for a body to complete one orbit. If one object, say M1, is much more massive than the other, then M1 + M2 ≈ M1. (‘≈’ means ‘very nearly equal to’). Kepler’s Third Law then simplifies to M1 =A3P2 The power of Newton’s version of Kepler's Third Law lies in its generality. It applies to any planet orbiting about the Sun (check: for the Earth A = 1 AU and P = 1 yr, giving M1 = 1 Mo for the Sun), to a satellite orbiting the Earth, to a moon orbiting around a planet, to two stars orbiting each other, or to a star orbiting the Galaxy. In this lab you will be determining A and P for each of the Galilean moons of Jupiter, and from these you will use Kepler's Third Law to derive the mass of Jupiter. The Galilean Moons of Jupiter The four Galilean moons are named Io, Europa, Ganymede and Callisto. These are names of mythological characters admired by Jupiter, occasionally to their detriment. You can remember the order by the mnemonic "I Eat Green Carrots", in order of increasing distance from Jupiter. If you were to observe Jupiter through a small telescope, the view might look like this:2 - 4 9/16/09 EW Figure 1. Jupiter and the Galilean Satellites The moons appear to be lined up because we are looking nearly edge-on to their orbital planes around Jupiter. In fact some are closer to us and some farther from us, depending on where they are in their orbits. Note that when looking through a telescope, west is to the right and east is to the left. Needless to say, nature has not created neon signs identifying each moon, so at a given time it will not be obvious which moon is which. Only by following their motions over time - or by traveling to Jupiter - can one tell them apart. In this lab you will observe Jupiter's moons at times of your choosing; indeed one of the challenges of the lab - and of much observational astronomy - is to determine the best interval of time