Lecture 5 Phys 1810

1. Lecture 5 Phys 1810 • Read BEFORE coming to class: • Electromagnetic Radiation 3.1 to 3.4 • Energy • Thermal Radiation Box 3-2 • Flux and Luminosity (L equation in Box 17-2) • Spectra 4.1, 4.2 • Kirkhhoff’s Laws • Radio Emission 18.4 • Doppler shift: 3.5, Box 3-3, 4.5 MONDAY! Tutorial/Office hour 3:00 pm Allen 514. 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. Examples of the Effects of Gravity: Tides Tides at the Bay of Fundy Effect of the Moon on Earth

3. 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)

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

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

6. Split apart Comet Shoemaker-Levy

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

9. Peculiar Galaxies

11. Tidal Tail

15. Tides • Make note of your prediction. • There is a difference in the gravitational force on each side of an object. Splitting the object into 3 parts, which is going to feel the most force? • The red (closest) ball? • The blue (middle) ball? • The yellow (furthest) ball?

16. Tides • Make note of your prediction. • Which ball moves the least? • The red (closest) ball? • The blue (middle) ball? • The yellow (furthest) ball?

17. Tides: • Movie about motion of the balls. • Note perspective from someone sitting on centre ball

18. Tides • Difference in on each side of an object.

19. Tides • On centre ball: appears other 2 balls have moved in opposite directions. These 2 opposing forces == tidal forces. • Tidal forces: cause distortion of an object by pull of another object. • Can occur when • Objects close (e.g. Earth & Moon) • 1 object is very massive (e.g. Jupiter & Io; Sun & Earth.)

20. Tides • Moon pulls on Earth & tides effect water more than land. • Make a prediction about how Earth’s ocean is distributed due to moon.

21. Tides • Note 2 tidal bulges at one time!

22. Apply what we know: • If the Earth had no Moon, then the tides would occur twice a day but would not be as strong. (Think of the objects in the Solar System.)

23. Tidal Locking: Tidal Drag Why does the moon always show the same face to us? Synchronous Orbit: P == Period

24. What happens to Earth Tidal Locking: Tidal Drag Misalignment due to friction between ocean & crust  crust drags ocean Moon pulls back on tidal bulge  Earth’s spin slows down. 100’s of billions of yrs  tidal locking

25. Tidal Locking: Tidal Drag Moon’s tidal bulge formed when moon solidified & Earth’s tidal pull on moon’s bulge is larger  tidal locking faster for moon. P == Period

26. Tidal Locking: • Summary – Examples: Tidal forces cause 1) Synchronous Orbits

27. 2) Fragmenting Comets

28. 3) Structures in Interacting Galaxies Note: there is structure on each side of an individual galaxy – the bridge and the tail.

29. 2.7 Newton’s Laws Gravity Kepler’s Laws of Planetary Motion from Newton’s perspective.

30. Description of Ellipse

31. Objects orbit a common centre of mass. Centre of mass == average position of all matter making up the 2 bodies. Equal mass 1 object more massive 1 object very massive Notice “wobble” of sun!  large planets around stars are easier to detect because they cause star to “wobble”.

32. Kepler’s 1st Law : Kepler I • Orbit of a planet around the sun is an ellipse with the center of mass of the planet-sun system at one focus • Note: r = radius of circle = distance. O.k. since r == average distance, which equals semi-major axis a

33. Kepler II An imaginary line connecting the sun to any planet sweeps out equal areas of an ellipse in equal intervals of time.

34. Area of A, B, and C are the same. • Note Arc of A, Arc of C and Arc of B • v = distance/time and time remains constant. Therefore planet travels a different speeds when at different distances from the sun.

35. Kepler III The square of the planet’s orbital period (P) is proportional to the cube of its semi-major axis (a) divided by the combined mass in the system (Mtotal) Solar mass = 99.85% of Mtotal Note proportionality. If distance from sun increases so does time to go around sun. Relationship is NOT 1-to-1. Note P in earth years A in AU M in solar masses

37. Example: Planet A and Planet B. Distance between star and B is twice that of A. Long does it take for B to orbit compared to A?

38. Example: Planet A and Planet B. Distance between star and B is twice that of A. Long does it take for B to orbit compared to A?

39. Compare planets’ velocities  Keplerian Rotation Curve And since • Works for: • Earth’s satellites • Jupiter’s moons • planets

40. Plot Velocity Equation for planets the Solar System: a v 1 1 25 1/5 36 1/6 64 1/8 100 1/10 Keperlian motion  Keplerian rotation curve. Important when we study Dark Matter.

41. Derive v using Newton’s Laws Notice how m of smaller object cancels out. So hammer and feather have same acceleration! For Earth’s gravity: accel = g

42. Derive v using Newton’s Laws Kepler’s v is empirical with no reason for formula. Newton’s version provides reason – Forces in balance for an object to be in orbit. Since r = semi-major axes “a” and G & M are constant:

43. v to little, fall back • v enough, go into orbit • v to much, unbound ==escape Escape Velocity

44. Let’s weigh the sun! • Re-arrange the velocity equation and substitute. • Exercise – weigh the Earth using the moon.(Look relevant values in textbook.)

45. Weighing the sun

46. Weighing the sun Many ways to calculate co-efficients. How does this compare with the Earth’s mass? What else can we “weigh” with this equation?