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Remember…. What is an AU? (astronomical unit) Approximately the Earth-Sun distance 149.60 x 10 6 km 92.956 x 10 6 mi (92,946,000 mi) HOW BIG IS THIS???. Johannes Kepler (1571-1630). Born and Raised in Germany, went to college at University of Tubingen.
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Remember… • What is an AU? (astronomical unit) • Approximately the Earth-Sun distance • 149.60 x 106 km • 92.956 x 106 mi (92,946,000 mi) HOW BIG IS THIS???
Johannes Kepler (1571-1630) • Born and Raised in Germany, went to college at University of Tubingen. • Extremely strong Christian. Taught math. Passionate about God and Science. • Best known for the Laws of Planetary Motion. • His works provided foundations for Isaac Newton’s theory of universal gravitation.
Ellipse R1-R2 e= R1+R2
Kepler’s First Law • States that the orbit of every planet is an ellipse with the Sun at one of the two foci. • An ellipse is a smooth closed curve which is symmetric about its horizontal and vertical axes. • The distance between antipodal points on an ellipse is between pairs of points whose midpoint is at the center of the ellipse. • maximum along the major axes or transverse diameter • minimum along the minor axis or conjugate diameter. Mechanics' and Engineers' Pocket-book of Tables, Rules, and Formulas. Harper & Brothers.
Eccentricity • A measure of an ellipse’s flatness. • Numerically, it is the distance between the foci divided by the length of the major axis. • Ellipses can have the same major axis but different eccentricities: • Why? http://near.jhuapl.edu/Education/lessonKepler/K1eccentricity.gif
Eccentricity • As the eccentricity approaches 1, the ellipse resembles a straight line. • As the eccentricity approaches 0, the foci come closer together and the ellipse becomes more circular. • A true circle has an eccentricity of 0. http://near.jhuapl.edu/Education/lessonKepler/K1eccentricity.gif
Kepler’s Second Law • A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. • According to Kepler, the time it takes for a planet to get from A to B is equal to the time it takes a planet to get from C to D. • This shows that planets orbit slower as they move further from the sun. http://near.jhuapl.edu/Education/lessonKepler/K2ellipse.gif
Kepler’s Third Law • The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. P2=a3 • Ex. Calculate how long it takes the near-Earth asteroid Eros to orbit the Sun. • The average distance from Eros to the Sun, or the semi-major axis, is 1.46 AU. (a) • Solve for P.
Newton’s Laws of Motion • First Law: states that objects at rest will stay at rest and objects in motion will stay in a straight line unless acted on by an unbalanced force.
Newton’s Second Law • States that the sum of all forces acting upon a body is equal to the body’s mass times its acceleration. Sum (F) = ma
Newton’s Third Law • States that for every action there is an opposite and equal reaction.