Lecture 3

1. Lecture 3 ASTR 111 – Section 002

2. Eventually we want to be able to explain things like this

3. 16" Dobsonian 2 Meade 12" SCTs 2 telescopes from Mason's original observatories Observing Sessions http://physics.gmu.edu/~hgeller/observing.html Fall schedule to be posted … Research I Building

4. Outline • Suggested Reading Note • Quiz Discussion • Angular Measurements Review • Precision, Accuracy, and Bias Review • Another Parallax Problem • Rotation • The Seasons

5. Suggested Reading • In general, the quiz and exams will be based on material that I cover in class. Almost all of this material is also covered in the book. • Ideally you should review notes and read suggested sections in book and then take quiz. • Suggested Reading for this quiz: Chapter 2.

6. Outline • Suggested Reading Note • Quiz Discussion • Angular Measurements Review • Precision, Accuracy, and Bias Review • Another Parallax Problem • Rotation • The Seasons

7. Quiz (aka Homework) Discussion • The quiz counts as 10% of your Lecture grade • Your lecture and lab are independent. You will receive a separate grade for lab and for lecture on your report card • I will post the quiz within a few hours of the end of lecture, typically on Thursday.

8. Quiz Question Apogee – farthest distance Perigee – nearest distance

9. Where does the “hand rule” come from?

10. R S

11. a is always in radians! R D S

12. Close enough! S D R

13. Close enough! S D R When will this approximation break down?

14. Two points on screen separated by distance D D Your finger a is angular size. D is linear size.

15. Group question What is the ratio of the width of your index finger to the distance of your finger from your arm? Answer in degrees.

16. Outline • Suggested Reading Note • Quiz Discussion • Angular Measurements Review • Precision, Accuracy, and Bias Review • Another Parallax Problem • Rotation • The Seasons

17. Center of red dot is true value • Accuracy – all measurements or values are clustered around the true value (you’ll get an A for accuracy, because you are on the true value) • Precision – all measurements are clustered but are not centered on true value • Bias – measurements are not centered on true value No bias

18. Group question • Can you have high accuracy and high bias? • Can you have low precision and high accuracy? • Suppose many people used the small angle formula to estimate the linear distance between two dots on the screen. They all sat in the same seat while making the measurements. Will there be a bias in their measurements?

19. Outline • Suggested Reading Note • Quiz Discussion • Angular Measurements Review • Precision, Accuracy, and Bias Review • Another Parallax Problem • Rotation • The Seasons

20. Group question • How many light-years are in 10 parsecs? • How many light-years could a human travel in a space craft? • Which is larger, a parsec or an AU? • Why do you think we have two units, the parsec and the light year, when they are so close to each other? (1 parsec = 3.26 light-years)

21. To describe the distances to stars, astronomers use a unit of length called the parsec. One parsec is defined as the distance to a star that has a parallax angle of exactly 1 arcsecond. Distant Stars PA Earth (July) Earth (January) Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

22. To describe the distances to stars, astronomers use a unit of length called the parsec. One parsec is defined as the distance to a star that has a parallax angle of exactly 1 arcsecond. Distant Stars 1 parsec PA Earth (July) Earth (January) Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

23. If the parallax angle for Star A (PA) is 1 arcsecond, what is the distance from the Sun to Star A? (Hint use parsec as your unit of distance.) Label this distance on the diagram. Is a parsec a unit of length or a unit of angle? As Star A moves outward, what happens to its parallax angle? Group Question

24. Outline • Suggested Reading Note • Quiz Discussion • Angular Measurements Review • Precision, Accuracy, and Bias Review • Another Parallax Problem • Rotation • The Seasons

25. 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.

26. 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

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

28. 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

29. 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

30. 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)

31. 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)

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

33. 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!

34. Question • Rotate B around A without slippage (like a gear). How many times does B rotate? • Same as when B was a quarter • More than when B was a quarter • Less than when B was a quarter A B (A is glued to the table)

35. Question • Rotate B around A without slippage (like a gear). How many times does B rotate? • Same as when B was a quarter • More than when B was a quarter • Less than when B was a quarter A B (A is glued to the table)

36. Sidereal Time Definition • From text: “A sidereal day is the time between two successive upper meridian passages of the vernal equinox. By contrast, an apparent solar day is the time between two successive upper meridian crossings of the Sun.”

37. 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.

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

39. 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

40. 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

41. 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

42. 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

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

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

45. Outline • Suggested Reading Note • Quiz Discussion • Angular Measurements Review • Precision, Accuracy, and Bias Review • Another Parallax Problem • Rotation • The Seasons

46. Seasonal Stars • Where do the names of the zodiac come from? During certain months, a constellation is (approximately) behind the sun • Approximately, because precession has caused things to shift a bit. http://historyday.crf-usa.org/1708/images/zodiac.jpg

47. 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.

48. Group question At summer solstice, when the sun is highest in the sky, who is closer to the sun • A person on Tropic of Capricorn • A person on Tropic of Cancer?

49. Group question At summer solstice, when the sun is highest in the sky, who is closer to the sun • A person on Tropic of Capricorn • A person on Tropic of Cancer?