Universal Gravitation

Brief Astronomical History A.D Ptolemy Greek Astronomer A.D. Believed in Geo- centrism First to latitude and longitude Nicholas Copernicus Galileo Galilei Polish Astronomer Changed societal belief to helio- centric model, though orbits were circular in his model. Tycho Brahe Danish astronomer Built first astronomical observatory Made accurate observations of night sky Catalogued 1000 stars Italian Physicist Continued to promote helio- Centrism Discovered Moons of Jupiter and phases of Venus

Johannes Kepler Johan Kepler, a student of Tyco Brahe, was a German astronomer who lived between He introduced three important laws of planetary motion and helped the Copernican model of the solar system gain general acceptance, but Kepler accurately modeled the path of planets as ellipses.

Kepler’s Laws 1) The paths of planets are ellipses with the sun at a focus. 2) An imaginary line from the sun to a planet sweeps out equal areas in equal times. 3) The square of the ratio of the periods of two orbiting bodies is equal to the cube of their radii ratio.

Ellipse Explanation Major Axis Minor Axis focus dd a b a+b=constant a b a b

Kepler’s First Law

Kepler’s Second Law (Also called the Law of Equal Areas) Equal areas in equal times. t1t1 t2t2 A1A1 A2A2 If t 1 =t 2, then A 1 =A 2 Orbiting bodies move faster near the central mass and slower farther away.

Kepler’s Third Law rArA rBrB r A =orbital radius of Object A (distance from central mass). r B =orbital radius of object B (distance of object B from central mass)

Kepler’s Third Law T A =period of body A T B = period of body B The square of the ratio of the period of two bodies orbiting the same central mass is equal to the cube of their orbital radii ratio.

Kepler’s 3 rd Law Example Saturn’s period of revolution is 29 years. What is the distance of Saturn from the Sun as a multiple of Earth’s distance? T S = 29 years T E = 1.0 years r S = ? r E = ?

Example Continued Saturn is located 9.4 times farther from the Sun than Earth.