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# MSTC Physics 2 - PowerPoint PPT Presentation

MSTC Physics 2. Chapter 7 Section 6. Johannes Kepler. Formulated 3 empirical laws from observational data gathered over a 20 year period by Tycho Brahe Laws were initially applied only to Mars First 2 laws announced in 1609 3 rd law announced 10 years later. Johannes Kepler.

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### MSTC Physics 2

Chapter 7 Section 6

• Formulated 3 empirical laws from observational data gathered over a 20 year period by Tycho Brahe

• Laws were initially applied only to Mars

• First 2 laws announced in 1609

• 3rd law announced 10 years later

• Took Kepler 15 years to derive his laws from observed data

• Today they can be derived theoretically in a page or two of calculations

• Laws apply to planets and any 2 body system composed of a body revolving about a much more massive body

• Law of orbits

• Planets move in elliptical orbits, with the Sun at one of the focal points

• In reality, most of the planets orbit in a path closer to a circle than an ellipse

• Law of areas

• A line from the sun to a planet sweeps out equal areas in equal lengths of time

• Tells us that the orbital speed of a planet varies in different parts of its orbit

• Speed is greater when it is closer to the sun

• Law of periods

• The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun; that is, T2 α r3

• Can we derive it?

• Why was it important to make sure that the stopper was traveling in a horizontal circle?

• to make sure we had uniform circular motion

• A small sphere of mass m is attached to the end of a cord of length R, which rotates under the influence of the gravitational force in a vertical circle about a fixed point. Determine the tension in the cord at various locations.

A car of mass m passes over a bump in a road that follows the arc of a circle of radius R. What force does the road exert on the car as the car passes the highest point of the bump if the car travels at a speed v? What is the maximum speed the car can have as it passes this highest point before losing contact with the road?