Read BEFORE coming to class.

1. Read BEFORE coming to class. • Newton’s Laws of Motion 2.7 • Newton’s Gravity 2.7, Box 2-2 • Orbits, including escape velocity 2.8 • Kepler’s Laws of Planetary motion 2.5, 2.8 (focus on Newton’s versions) • Tides 7.6 • Weighing the sun, Box 2-2 • introduction to General Relativity p. 558-560 login and password • Note: • “Box” refers to the “More Precisely” boxed areas in the chapters. • A number like 1.6 refers to Chapter 1, section 1.6. • p.8-9 means pages 8 to 9.

2. The Vastness of the Universe Measurements on the Sky Parallax and Distance

3. Linear Measurements Re-arrange the equation so the calculated parameter is on the left. • The linear diameter is: 2 pi * Distance linear diameter = --------------------- * angular diameter 360 degrees • Measure the angular diameter • Measure the distance • Put these in the equation  Gives the linear diameter!

4. Distances For Step 2. : How we can get distances to objects in our solar system? • We can get the distances to the moon and other planets by bouncing radio waves off them, i.e. by using radar. • http://science.howstuffworks.com/radar2.htm

5. Distances: Bouncing radar or laser beams (re-arrange equation) • Radio waves, along with visible light, are part of electromagnetic spectrum • Light travels at specific speed, c. • c = 300,000 km/s roughly. • Speed = distance/time  distance = speed * time distance = c * time where time is time for radar signal to bounce back to Earth from object in solar system

6. Linear Measurements: Linear Diameter of the Moon Powers of 10 Convert units! • Distance = 384,000 km = 3.84 * 10**5 km • Angular diameter = 31 arcmin (roughly) = 31’/60’ per degree = 0.52 (½ degree roughly) Sothe linear diameter of the moon is roughly 3,485 km. A more precise measurement gives 3,476 km.

7. Check Using Dimensional Analysis and Powers of 10 1. 2. 3.

8. Parallax The apparent motion of a relatively close object with respect to a more distant background as the location of the observer changes. What about for objects further away or another method? Parallax in general terms:

9. Measurements on the Sky Angular Size Exercise

10. Measurements on the Sky Parallax and distance. Use the Earth’s position at 1 time and then ½ a year later. Astronomical Unit == 1 AU == average distance between Sun & Earth

11. Distances to Stars: Parallax • Parsec definition: • The distance that an object would have if its parallax is 1 arcsec. • Written “pc”.

12. Distances to Stars: Parallax 1 pc = = 3.26 ly = 206265 AU 1 kpc = 1 kiloparsec = 1 Mpc = 1 megaparsec =

13. What would happen to parallax of a specific star if measured at planet closer to sun? Smaller baseline  Smaller parallax. Further from the sun? Larger baseline  Larger parallax. We use as our baseline for parallax the distance between Earth & Sun.

14. Distance and Size • parallax distance to solar system objects & nearby stars (< 1000 pc) How do relate parallax to distance? (Good interactive parallax tutorial associated with your book.) Let’s see how.

15. Have you heard these terms? • Start with some definitions

16. Relate parallax to distance

17. Relate parallax to distance D

18. Relate parallax to distance D

19. Relate parallax to distance D Baseline ------------------ Circumference Parallax ------------------ Full revolution =

20. Relate parallax to distance D Baseline ------------------ Circumference Parallax ------------------ Full revolution = Substituting:

21. Relate parallax to distance

22. Relate parallax to distance

23. Relate parallax to distance

24. The distance to an object is inversely proportional to its parallax. For example, if a star’s parallax is 1/50 arcsec, it is 50 parsecs away. • true • false

25. Distance and Size • parallax  distance to solar system objects & nearby stars (< 1000 pc) • Up to ~10 kpc with Gaia in future. (Good interactive parallax tutorial associated with your book.)

26. Gaia – launched Dec 2013 - observations Aug 2014. • Repeatedly scanning the sky, observe a billion stars an average of 70 times each over the five years -> high precision. • “By taking advantage of the slight change in perspective that occurs as Gaia orbits the Sun during a year (parallax!), it will measure the stars’ distances and, by watching them patiently over the whole mission, their motions across the sky.” • also measure brightness, temperature and chemical composition. • motions of the stars can be put into ‘rewind’ to learn more about where they came from and how the Milky Way was assembled over billions of years from the merging of smaller galaxies, and into ‘fast forward’ to learn more about its ultimate fate. European Space Agency

27. Distance and Size • parallax distance to solar system objects & nearby stars (< 1000 pc currently) • If relatively nearby, use parallax distance & angular size linear size (e.g. moon diameter, companion galaxies to the Milky Way) (Good interactive parallax tutorial associated with your book.) Let’s see how.

28. Linear Measurements S • The linear diameter is: 2 pi * Distance linear diameter = --------------------- * angular diameter 360 degrees Note that in this case the linear diameter is directly proportional to the angular diameter.

29. Distance and Size • need other methods beyond 10 kpc • diameter of Milky Way’s gas layer is more than 50 kpc. • using distances • “fuzzy” nebulae are other galaxies • large scale structure of the universe • Knowing distances & angular size measure the linear size

30. Eskimo Nebula Planetary Nebula radius ~ 0.25 ly distance ~ 5*10**`3 ly ~ 1.5 kpc

31. Crab Nebula Supernova Remnant radius ~ 5 ly distance ~ 6.5*10**`3 ly ~ 2 kpc

32. Eagle Nebula Molecular Cloud pillar length ~ 1 ly nodule ~ 5 light-hours distance ~ 6.5 * 10**3 ly ~ 2 kpc

33. Herbig-Haro 47 Jet from a protostar. length ~ 0.5 ly distance ~ 1.5 * 10**3 ly ~ 460 pc Some are a dozen ly long.

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

35. 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)

36. Dark Matter

37. 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.

38. 2.7 Newton’s Laws Newton’s laws of motionexplain how objects interact with each other.

39. 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.

40. 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

41. 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)