Circular Motion: Understanding Kepler's Laws

1. Do Now (on a new sheet please): • What net force must act on a 5 kg mass that is moving at a constant speed of 4 m/s around a circle with a radius of 2 m?

2. Objective/Homework • Objective: • Homework: • Circular Motion – due Tuesday 12/14 • Quiz: Circular Motion – Tuesday 12/14 • Lab: Circular Motion – Friday 12/17 • Kepler’s Laws Worksheet: Monday 12/20 • Test: 2-D Motion – Tuesday December 12/21

3. What are some things you know about the universe?

4. Keplar’s Laws and Universal Gravitation 12/13/10

5. Do Now (12/19): • What are the three views of the universe that changed over time? • Who are the men who developed each? • Which is our current view?

6. History of Views of the Universe Aristotle: Geocentric (everything rotates around the Earth in perfect circles) • Patterns of stars in the sky never change • Planets drift with respect to background stars

7. History of Views of the Universe Nicolas Copernicus: Heliocentric (everything rotates around the sun in perfect circles) • Accurately predicts the rising and setting Sun, moon, and stars • Accounts for retrograde motion of Mars, Jupiter, and Saturn

8. History of Views of the Universe Johannes Keplar: Heliocentric • Used the accurate recorded observations of Tyco Brahe to develop a new planetary model and three laws • Planets rotate around the sun in ellipses with the sun at one focus

9. Keplar’s Laws • First law: The path of each planet about the sun is an ellipse with the sun at one focus

10. Keplar’s Laws • Second Law: Each planet moves so that the planet sweeps out equal areas in equal periods of time • http://www.physicsclassroom.com/mmedia/circmot/ksl.cfm

11. Keplar’s Laws • Third Law: The ratio of the squares of the periods (time of rotation: T) of any two planets revolving around the sun is equal to the ratio of the cubes of their radius R from the sun

12. Variables and constants: • T=period of orbit • R or r= radius of orbit • G=universal gravitational ; G= 6.67x10-11 Nm2/kg2 • m=mass • F= force • K=Kepler’s constant

13. Newton’s Law of Universal Gravitation • Fg = force of gravity • G = 6.67x10-11Nm2/kg2 • r = distance between two objects • m = mass 1 or 2

14. Equations:

15. Practice/Review: • Please use the rest of class to work on “Kepler’s Laws and Universal Gravitation.” Make sure your test trial results are in by the end of the day!!!

16. Example: • A 3 kg mass and a 2 kg mass are placed with their centers 5 m apart. What is the force of attraction between them?

17. Do Now: • A 5 kg mass and a 6 kg mass are placed with their centers 0.5 m apart. What is the force of attraction between them? • Turn in your Circular Motion worksheet and your Do Now’s from last week (starting with 12/6)

18. Quiz: • Clear your desks except for a piece of paper and a writing utensil

19. Quiz: • A 9800 N car is driven on a circular track with a diameter of 600 m at 30 m/s. Calculate the car’s centripetal acceleration & its centripetal force.

20. Do Now (12/20): • A 5 kg mass and a 6 kg mass are placed with their centers 0.5 m apart. What is the force of gravitational attraction between them?

21. Law of Universal Gravitation: The gravitational force between two objects

22. Period of a planet orbiting the sun • ms: the mass of the sun (constant) • r: radius of orbit

23. Speed of a satellite orbiting earth • me= mass of the earth • r=radius of orbit

24. Period of a satellite orbiting the earth • r=radius of orbit

25. Practice/Review: • Please use the rest of class to work on “2-D Forces Review.” Make sure your test trial results are in!!! Once you finish, you may work on your notecard for tomorrow’s test.

26. Do Now: • What is the speed of the planet Jupiter around the sun? • hint – look on page 178 of your classroom textbooks • Hint – look for the radius of the ORBIT not the radius of the planet

27. Do Now: • What is the period of the planet Neptune around the sun? • hint – look on page 178 of your classroom textbooks