Lecture 3

1. Lecture 3 ASTR 111 – Section 002

2. Terms • Apogee/Perigee • Subtend • Parsec, light-year, AU • Parallax • Solar and Sidereal time • Small angle formula • Ecliptic • Zenith • Tropic of Cancer, Capricorn, Artic and Antarctic Circle • Equinox, Solstice • Zodiac

3. Notes on Lecture Notes • Sent out Tuesday afternoon/evening • I suggest that you print them out and bring them to class • I will also post PowerPoints • If you have problems with the file, email me!

4. Outline • Quiz Discussion • Rotation – review generally • The Seasons – finish lecture tutorial • The Moon in its orbit • Math Review – converting units and scientific notation

5. #3 • In class, we estimated the angular separation of two points on the screen that were separated by 10 feet. Suppose that these two points were separated by 1 AU. How far away from the screen would you need to walk so that the dots appeared to subtend 1 arc-second?

6. B A

7. Gods-eye view Observer’s view “

8. #4 • How many light-years are in 10 parsecs? • How many parsecs are in 5 light-years?

9. Units conversion • Start with a relationship like • 1 degree = 60 arcminutes • To convert from degrees to arcminutes, set up a ratio so the unit you want to get rid of cancels • Example: how many arcminutes is 0.5 degrees?

10. Units conversion • Start with a relationship like • 1 parsec = 3.26 light-years • To convert from parsec to light years, set up a ratio so the unit you want to get rid of cancels • Example: How many light-years are in 5 parsecs?

11. #6 • In the image, suppose that a star in the constellation Cygnus appears exactly at an observer's zenith (the dotted line) at 8 pm local time. After 24 solar hours have passed, where would the constellation appear to be?

12. Outline • Quiz Discussion • Rotation – review generally • The Seasons – finish lecture tutorial • The Moon in its orbit • Math Review – converting units and scientific notation

13. Thinking about rotation With parallax, we learned that the position of a near object relative to a distant object can change if the observer moves. With rotation, the time it takes for the position of a near object to change relative to a distant object can be different if the observer moves.

14. Thinking about rotation In the last lecture I had you do an experiment with a quarter to illustrate this point: When one object “B” rotates about another object, the number of times it rotates with respect to something in the distance depends on if “B” is rotating on its axis.

15. Slippage Meaning • When you skid a tire, there is slippage – same part of tire always touches ground • When you roll a tire, there is no slippage – different parts of tire touch ground

16. George B looking straight to the left (at a distant object) B Table

17. I can get him across the table by “skidding” or “slipping” – the 9 always touches the table. In this case he always is looking to the left at the distant object. B Table

18. Instead of “skidding” or “slipping”, he can “roll”. On a flat table, he will look at same place in distance after 1 revolution – or after he has “rolled” the distance of his circumference B Table

19. Group Question • Rotate B around A with slippage. How many times does George B look straight to the left? • With slippage, the 9 on the top quarter always touches the bottom quarter • Rotate B around A without slippage (like a gear). How many times does George B look straight to the left? • Without slippage, first the 9 in the 1993 on the top quarter touches the bottom quarter, then 1 then the “In God We Trust”. B A (A is glued to the table)

20. Group Question • Rotate B around A with slippage. How many times does George B look straight to the left? • With slippage, the 9 on the top quarter always touches the bottom quarter • Rotate B around A without slippage (like a gear). How many times does George B look straight to the left? • Without slippage, first the 9 in the 1993 on the top quarter touches the bottom quarter, then 1 then the “In God We Trust”. One time B A Two times (A is glued to the table)

21. B B A B B With slippage The nine on B always touches A

22. Without slippage Note: George B only looks directly at George A’s center one time right about here B “rolls” on A, in the same way a tire rolls on the ground. B B A B B George B is looking to the left again here!

23. Summary • When the coin slipped across the table, it did not rotate at all. When a coin slipped around another coin, it rotated once with respect to the “distance”. • When a coin rolled across a table the distance of its circumference, it rotated once. When it rolled the same distance, but around another coin, it rotated twice with respect to the “distance”.

24. What to know • When thinking about rotation, you need to account for rotation about its own axis and rotation about another object. • The number of times you see something in the distance will be different than the number of times you look at the object that you are rotating around.

25. Top view of classroom Someone in back of room (distant object) Stage Student Instructor

26. Or Sidereal Time = star time Sidereal Day = the length of time it takes for a star to repeat its position in the sky. Solar Time = sun time Solar Day = the length of time it takes the sun to repeat its position in the sky.

27. Sidereal Time = star time Solar Time = sun time At 1, line points at sun and distant star Line 1 goes through sun and distant star

28. At 2, 24 sidereal hours since 1, line is now pointing at distant star only • Sidereal Time = star time • Solar Time = sun time Line 1 goes through sun and distant star At 1, line points at sun and distant star Line 1 goes through sun and distant star

29. At 2, 24 sidereal hours since 1, line is now pointing at distant star only • Sidereal Time = star time • Solar Time = sun time • Which is longer? • Sidereal day • Solar day At 1, line points at sun and distant star At 3, 24 solar hours since 1, line points at sun only

30. At 2, 24 sidereal hours since 1, line is now pointing at distant star only • Sidereal Time = star time • Solar Time = sun time • Which is longer? • Sidereal day • Solar day by ~ 4 min. At 1, line points at sun and distant star At 3, 24 solar hours since 1, line points at sun only

31. Key • A solar day is longer than a sidereal day • This means it takes longer for the sun to repeat its position in the sky than a distant star

32. Which way is Andromeda at 8:00 pm local time for the person in California? • West • East • Vertical • West • East • Vertical

33. Where is Cygnus 24 sidereal hours later? • West • East • Vertical

34. Where is Cygnus 24 solar hours later? • West • East • Vertical • West • East • Vertical

35. Outline • Quiz Discussion • Rotation – review generally • The Seasons – finish lecture tutorial • The Moon in its orbit • Math Review – converting units and scientific notation

36. What causes the seasons? • Distance of the sun from earth • Tilt of Earth with respect to the ecliptic • Both • None of the above • Primarily 2., but with a small contribution from 1.

37. What causes the seasons? • Distance of the sun from earth • Tilt of Earth with respect to the ecliptic which causes • Change in length of time sun is visible • Change in height of sun in sky • Both • None of the above • Primarily 2., but with a small contribution from 1.

38. The ecliptic is the imaginary plane that the Earth moves on as it rotates around the sun

41. The Celestial Sphere • Sometimes it is useful to think of the stars and planets as moving along a sphere centered on Earth

43. Important! The angle of the light to the ground.

46. The two circled yellow arrows point to the same line of latitude. The right arrow is perpendicular to surface. The left arrow is less than perpendicular to surface.

47. Thinking about light • It is often useful to think of photons as very small particles. • When I point a flashlight at you, you are getting hit with a bunch of little pellets. • Suppose you were hit by 10 pellets in an area the size of a quarter. • How does this compare with getting hit with 10 pellets over an area the size of a book?

49. See Seasons Lecture Tutorial at end D A F

50. Outline • Quiz Discussion • Rotation – review generally • The Seasons – finish lecture tutorial • The Moon in its orbit • Math Review – converting units and scientific notation