1. Universal Gravitation

2. Objectives for today Introduce Newton’s Universal Law of Gravitation Applications Historical context Scientific Process Problem solving with circular motion and gravitation

3. Applications Apollo Space probes Satellites, TV, GPS, XM, Sirius

4. Names in History Ptolemy (Claudius Ptolemaus) –Greek, 2d Century A.D. –Geocentric still use in navigational astronomy “Sunrise”, “Moonrise” earth Sun Moon Mercury Venus Mars epicycle

5. Names in History Copernicus (Nicolas, 1473 -1543, Poland) –Heliocentric –More elegantly explains Retrograde motion of Mars –But, still used epicycles earth Sun Moon Mercury Venus Mars (Columbus) http://www.lasalle.edu/~smit hsc/Astronomy/retrograd.ht ml

6. Names in History Tycho Brahe(1546 -1601) –Controversy between Ptolemaic and Copernican views –Made observations without a telescope (Galileo 1609) –Had an assistant named…

7. Names in History Johannes Kepler (1571 -1630) –Analyzed data over 20 years –Identified regularities in the motions of the planets –Three Laws (empirical)…

8. Kepler’s Three Laws 1)All planets move in elliptical orbits having the sun as one focus. 2)A line joining any planet to the sun sweeps out equal areas in equal times. 3)The square of the period on any planet about the sun is proportional to the cube of the planet’s mean distance from the sun. P 208

9. Three Laws Very Low eccentricity Equal Areas T^2 proportional to r^3

10. Names in History Issac Newton (1642-1727) –Cambridge “Plague days” 1665 –Began to think about gravity extending to the moon –Tea under an apple tree His work built on those before him. He was able to derive Kepler’s Laws, p 208.

11. F=GmM r 2 Cavendish exp. – solve for G, p 203 Knowing period, and radius of the moon’s rotation, calculate the mass of the earth. Knowing G and mass of the earth find the altitude a satellite will orbit over a constant longitude. Given the general form of gravitational potential energy, find the “escape velocity” from the earth. P 201

12. What if? Orbital Radius doubles…T Velocity doubles….R Mass of satellite changes… Masses same order… Surface radius and mass changes… Why do Directv and Dish antennas stay pointed in the same direction? How? How do we find Black Holes?...they’re called black because….

13. “To infinity and beyond!” 3 Escape velocity 3 Buzz Lightyear, Toy Story, Disney-Pixar, 1995