Galileo's head was on the block His crime was looking up for truth Indigo Girls, Galileo

Assignment: Reading: In Explorations, pp. 78-81. Also, take a look at the special webpage on Newton's Cannonball. We'll talk about this in class Friday, so don't sweat it too much if you have trouble understanding it the first time around. Sign up for a time slot for the Observing Lab #2 Problem Set #3 is due Thursday at 1:00 pm.

In Class: Question to Ponder Saturn orbits the Sun in an elliptical orbit with semi-major axis = 9.5 A.U. How long does it take to complete one lap around the Sun? a) 1 year b) 4.5 years c) 9.5 years d) 29.3 years Kepler's Laws Allow Us to Consider the Physical Aspects of Planetary Motion Location in Three Dimensions, including distance from us Speed Calculate the Speed of Jupiter in its Orbit Jupiter's orbital period is 12 years Use Kepler's Third Law to get the semi-major axis: P2 = a3 122 = 144 = a3 a = cuberoot(144) = 5.2 A.U. Again assume eccentricity of orbit = 0 So distance traveled in one lap = 2 x pi x 5.2 A.U. = 32.6 A.U. Speed = distance/time = 32.6 A.U./ 12yr = 2.7 A.U./yr Jupiter's speed is slower than that of the Earth Inner planets move faster, while outer planets move more slowly How Fast are These Planets Really Moving? Jupiter's speed = 2.7 A.U./yr Convert to measingful units: 2.7 A.U./yr x (1.5 x 1011 m/ 1 A.U.) x (1 yr/ 3.16 x 107 seconds) = 12,800 m/s (= 29,000 mph) That's really fast! And the Earth moves even faster! No wonder no one believed that the Earth orbits the Sun Galileo's Re-examination of Aristotelean Physics Aristotle said that objects will tend to slow down and stop unless pushed or pulled by some force. Using this idea, he shows that the Earth must be motionless. If the Earth were moving quickly, a ball thrown vertically into the air would slow down ('cuz it's not connected to the Earth anymore), and it would fall behind the Earth, and land off to one side (according to Aristotle). Galileo decides to test this idea by considering what happens inside a moving ship. Galileo's Thought Experiment (in his own words) The Setup: "Shut yourself up with some friend in the main cabin below decks of some large ship, and have with you there some flies, butterflies, and some other flying animals. Have a large bowl of water with some fish in it. Hang up a bottle that empties drop by drop into a wide vessel beneath it." The Control Experiment "With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal distances in every direction." The Test "When you have observed all these things carefully (though there is no doubt that when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will not discover the least change in all the effects named, nor could you tell from any of them whether the ship is moving or standing still...." The Conclusion "The cause of all of these correspondences of effects is the fact that the ship's motion is common to all of the things contained in it..." Galileo's Law of Inertia Rather than Aristotle's principle that objects move only under the influence of a force, Galileo says that objects change their velocity only under the influence of a force. For Galileo, an object will continue moving at the same speed and in the same direction, unless it is pushed. Seemingly in conflict with our everyday experience; after all, a ball rolling on the floor will not roll forever, but will come to a stop. Galileo's response is that frictional forces between the ball and floor push on the ball, slowing it down. In a frictionless environment, the ball would roll forever. Galileo and Relativity The Principle of Inertia leads directly to the Principle of Relativity. If everything is moving at the same speed (as inside the ship), you will not notice any motion at all. Only differences in velocities can be measured. Consider being in an airplane: no sensation of going 600 mph your drink doesn't come crashing back toward you at 600 mph The Effects of Galileo's Physics on Heliocentrism Galileo says that since everything on the Earth is moving with you, you don't notice that the whole planet is moving at 67,000 mph. There's no problem in having the Earth in motion. Removes the last major objection to the heliocentric model. Acceleration Galileo says that changes in velocity are due to a push or pull (e.g., some sort of external force). Acceleration is a measure of the change in velocity. velocity = change in distance per time acceleration = change in velocity per time Example: Accelerating a car from a stop initial velocity = 0 (you're stopped) final velocity = 20 m/s (say) time to get up to that speed = 2 sec acceleration = (change in velocity)/time = (final velocity - initial velocity)/time = (20 m/s - 0 m/s)/2 sec = 10 m/s/s Units are odd -- meters per second per second