 Danish astronomer ( )  Built an astronomical observatory on an island  Measured positions of stars and planets over a period of 20 years

 German astronomer and mathemetician ( )  Used Tycho’s observations to describe planetary orbits using THREE LAWS.

 Planets travel in oval-shaped paths (ellipses), with the Sun at one focus (the other focus is a theoretical point)

 Eccentricity (e): how much an ellipse deviates from a perfect circle  e = distance between foci (d) Length of major axis (L)

 What observations can you make about the motion of the planet as it moves through its orbit around the Sun?

 An imaginary line joining a planet to the Sun will sweep over EQUAL AREAS over EQUAL PERIODS OF TIME  The orbital speed of the planets INCREASES as they get CLOSER to the Sun, and DECREASES proportionally as the get FARTHER AWAY

 Planets closer to the Sun have a shorter period of revolution (year) than those farther away from the Sun  Equation: ____________________  P= orbital period (in Earth years)  D= distance from the Sun (in astronomical units – AU )

 Law of Universal Gravitation  British mathematician, Issac Newton, explained how gravitational forces and inertia interact to produce orbital motion

As mass of two objects increases, the gravitational force between them __________________ ______________________ As the distance between two objects increases, the gravitational force between them __________________ __________________________