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MSTC Physics 2

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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?