Dancin' in the moonlight Everybody's feelin' warm and right It's such a fine and natural sight Everybody's dancin' in the moonlight King Harvest, Dancing in the Moonlight

Assignment: Reading: In Explorations, pp. 81-90, and pay special attention to the boxed text ("Extending our Reach") on p. 84. Also, please re-read the special web page on Newton's Cannonball again. Hopefully, it will make more sense this time. Sign up for a time slot for Observing Lab #2. Start reviewing for Wednesday's Exam.

In Class: Question to Ponder If I'm out in deep space coasting along at constant speed in my fancy new spaceship, and I carelessly throw the wrapper from my ``SpaceBurger Deluxe with Cheese'' out the window, the wrapper will a) fall behind the spaceship as it slows down and eventually stops. b) move along at the same speed as the ship, sitting outside my window and mocking me for being such a litterbug. c) magically gravitate toward the nearest SpaceLitter Recycling Facility. Galileo's Work on Gravity The speed of falling objects increases linearly with time (v = at). This means that the acceleration is constant (e.g., change in velocity per time is constant). He also figures out that the distance fallen is equal to one-half the acceleration times the time squared (e.g., dist = 1/2 a t2). The acceleration objects feel in the Earath's gravity does not depend on the composition of the object. Galileo measured the acceleration due to gravity at the surface of the Earth to be 9.8 m/s/s. Isaac Newton (1642-1727) Takes Galileo's physics and Kepler's planetary laws and constructs a unified theory of gravity. Realizes that Galileo's gravity might also hold the Moon in orbit. Why the Moon Doesn't Fall Down Becuse of its inertia, the Moon "wants" to continue in a straight line. Because of the Earth's gravitational pull, the Moon's trajectory bends into a circle about the Earth. The pull inward is necessary for the Moon (or anything) to move in a circle. Circular motion requires an inward acceleration. Newton's Cannonball Newton calculates the relationship between orbital velocity, orbital size, and the necessary acceleration for circular orbits. See the special web page on Newton's Cannonball for details. How Fast is Newton's Cannonball? v2 = a x r Galileo said a = 9.8 m/s/s at the Earth's surface. radius of Earth r = 6.4 x 106 m so v2 = 9.8 m/s/s x 6.4 x 106 m = 6.25 x 107 (m/s)2 and v = 7.9 x 10 3 m/s Newton Calculates the Acceleration the Moon Feels Since it's going in a circle, the Moon must feel an acceleration Could it be due to gravity? amoon = vmoon2/rmoon v = distance/time time = period = 27.3 days x (86400 sec/1 day) = 2.36 x 106 seconds distance = 2 x pi x rmoon = 2 x 3.14 x 3.84 x 108 m = 2.41 x 109 m vmoon = 2.41 x 109 m / 2.36 x 106 seconds = 1.0 x 103 m/s amoon = (1.0 x 103 m/s)2 / 3.84 x 108 m = 2.7 x 10-3 m/s/s Uh-oh -- this is a lot smaller than the acceleration due to the Earth's gravity at the surface of the Earth. Could Newton be wrong about the Moon feeling the Earth's gravity? -- Could be (but he isn't).