Lecture 4 Phys 1810

1. Lecture 4 Phys 1810 Read BEFORE coming to class: • Kepler’s Laws of Planetary motion 2.5, 2.8 (focus on Newton’s versions) • Tides 7.6, Chapt 8 (P. 195-196) • Weighing the sun, Box 2-2 • Orbits, including escape velocity 2.8 • introduction to General Relativity p. 558-560 Syllabus at http://www.physics.umanitoba.ca/~english/2014fallphys1810/ (Google “Jayanne English teach”) along supplemental material. REVISE DATE IS Wed. Sept 15 (Do Honours rather than General Science 3yr degree)

2. Laws of Motion and Gravity • The moon produces tides on Earth using the force of gravity.

3. Tidal Forces: •  Distortion of an object by the gravitational pull of another object. • -- nearby (e.g. Earth and Moon) • - or very massive (e.g. Earth and Sun)

4. Dark Matter

5. Laws of Motion and Gravity Need these to explain: Effect of Moon on Earth (Tides) Orbits of the Planets Comet Crashes Measure stellar mass Black Holes Peculiar Galaxies Dark Matter Start with Newton’s Laws and introduce General Relativity.

6. 2.7 Newton’s Laws Newton’s laws of motionexplain how objects interact with each other.

7. Newton’s 1st Law Every body continues in a state of rest or in a state of uniform motion in a straight line, unless it is compelled to change that state by a force acting on it.

8. 2.7 Newton’s Laws Newton’s First Law: Object at rest will remain at rest. Object moving in a straight line at constant speed will not change its motion, unless an external force (e.g. push or pull) acts on it.

9. The tendency of an object to keep moving with the same speed in the same direction is inertia. Demonstrate with a cart. Note change in speed. A measure of an object’s inertia is its mass. Mass is the total amount of matter contained in an object. Demonstrate with a cart and mass. (Ignoring friction.) Harder to push the cart with weight.

10. Velocity: An object’s velocity includes both speed (e.g. m/s) AND direction. Acceleration: Rate of change of an object’s speed OR direction. Units: m/s2 1 N (==Newton) is F to accelerate 1 kg to 1 m/s2

11. 2.7 Newton’s Laws Newton’s second law: When a force is exerted on an object, its acceleration is inversely proportional to its mass: a = F/m . Or F = ma F == force m == mass a == acceleration = a 

12. What happens if the F = 0 ?

13. What happens is the F = 0 ? a= 0  v = constant travel in straight line If sun & its mass were suddenly to disappear, Earth would fly off into space!

14. What happens when a constant force is applied? • Cart with a constant force applied. • Cart with same force & more mass.

15. What happens when a constant force is applied? 1) The speed changes  a. 2) If m increases, a decreases.  

16. 2.7 Newton’s Laws Newton’s third law: To every action there is an equal and opposite reaction. When object A exerts a force on object B, object B exerts an equal and opposite force on object A. (2 carts pushing equally on each other) (Glass of water)

17. 2.7 Newton’s Laws Gravity • Look up: • how astronauts experience gravity. • feather & hammer landing in vacuum • On supplemental page

18. 2.7 Newton’s Laws Gravity For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them:

19. Newton’s Law of Gravity • G • == Gravitational Constant • measured experimentally G = (will give G on a test but you may have to convert units) Since units of Newton: Homework: Convert to units used by textbook Appendix 3

20. 2.7 Newton’s Laws Gravity The constant G is called the gravitational constant; it is measured experimentally and found to be: G = 6.67 x 10-11 m3/s2/kg • If we keep the distance the same (r = constant) • m F • 2 * m1 2 * F • 3 * m1 3 * F • The force felt on m1 due to m2 is equal to the force felt by m2 due to m1.

21. Gravity is inversely proportional to DISTANCE! The closer the object the stronger the Fg. Keep m constant: • r F 1  1 2  ¼ 3  1/9 etc.

22. Question: • The mass of the Earth is a few millionths that of the Sun. Therefore • The gravitational force of the earth on the sun will be roughly 1/1,000,000 that of the gravitational force of the sun on the earth. • The gravitational force of the earth on the sun will be equal to the gravitational force of the sun on the earth.

23. Example:

24. Example:

25. Example: 7) calculate Practise Exercise: What is gravitational force between the Earth & Moon? Is it smaller or larger than between the Earth & Sun? By how much?

26. Examples of the effects of Gravity: Orbits NASA’s Solar System Simulator

27. Define Orbit: The balance between tendency of an object to move in a straight line (inertia) and gravitational pull from a massive body, can cause the object to move in a continuous path around that massive body. This path is called an orbit.

28. Examples of the effects of Gravity: Orbits How fast is the earth going around the sun?

29. Example: collect powers of ten calculate

30. 2.7 Newton’s Laws Escape speed: the speed necessary for a projectile to completely escape a planet’s gravitational field Escape speed: needed for projectile to escape gravitational field. We will do an example in one of the following classes.

31. ESA’s Rosetta Mission to Comet: • Uses orbital assists.

32. Rosetta’s Comet • 67P/Churyumov-Gerasimenko from a distance of 285 km. The image resolution is 5.3 metres/pixel.

33. Examples of the Effects of Gravity: Tides Tides at the Bay of Fundy Effect of the Moon on Earth

34. Gravity ( )  Tidal Forces: • == Distortion of an object by the gravitational pull of another object. • -- nearby (e.g. Earth & Moon) • OR • - very massive (e.g. Earth & Sun)

35. Tidal Force Examples: Asteroid Belt –tidal force of Jupiter prevented formation of planet between Mars & Jupiter.

36. Tidal Force Examples: The tidal force of Jupiter (and Europa) cause • - deformation of Io’s interior • -> heat •  volcanism

37. Split apart Comet Shoemaker-Levy

39. q Saturn raises tides on its moons. Gravity  orbits of material in rings.

40. Peculiar Galaxies

42. Tidal Tail