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, 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”
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 B A One time Two times
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. With slippage A B
The nine on B always touches A

22. Without slippage B B A B B
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. Someone in back of room (distant object)
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. Sidereal Time = star time
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. Sidereal Time = star time
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. Sidereal Time = star time
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

42. Figure 2-16 The Sun’s Daily Path Across the Sky
This drawing shows the apparent path of the Sun during the course of a day on four different dates. Like Figure 2-10, this drawing is for an observer at 35° north latitude.

43. Important! The angle of the light to the ground.
Figure Tropics and Circles
Four important latitudes on Earth are the Arctic
Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude),
Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2°
south latitude). These drawings show the significance of these latitudes
when the Sun is (a) at the winter solstice and (b) at the summer solstice.
Important! The angle of the light to the ground.

44. Figure 2-17 Tropics and Circles
Four important latitudes on Earth are the Arctic
Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude),
Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2°
south latitude). These drawings show the significance of these latitudes
when the Sun is (a) at the winter solstice and (b) at the summer solstice.

45. Figure 2-17 Tropics and Circles
Four important latitudes on Earth are the Arctic
Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude),
Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2°
south latitude). These drawings show the significance of these latitudes
when the Sun is (a) at the winter solstice and (b) at the summer solstice.

46. The two circled yellow arrows point to the same line of latitude.
Figure Tropics and Circles
Four important latitudes on Earth are the Arctic
Circle (661⁄2° north latitude), Tropic of Cancer (231⁄2° north latitude),
Tropic of Capricorn (231⁄2° south latitude), and Antarctic Circle (661⁄2°
south latitude). These drawings show the significance of these latitudes
when the Sun is (a) at the winter solstice and (b) at the summer solstice.
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?

48. Figure 2-13 Solar Energy in Summer and Winter
At different times of the year, sunlight strikes the ground at
different angles. (a) In summer, sunlight is
concentrated and the days are also longer, which
further increases the heating. (b) In winter the
sunlight is less concentrated, the days are short, and
little heating of the ground takes place. This
accounts for the low temperatures in winter.

49. See Seasons Lecture Tutorial at endF

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

51. Eventually we want to be able to explain …

52. A simple model Moon executes circular orbit
Moon orbit is in Earth’s ecliptic plane

54. What is wrong with this picture?

55. Fill in the dark and light parts of the Moon for A-D (from this perspective)
From the perspective of someone on Earth what position of A-E best fits the Moon view in the lower-left-hand corner?
In the blank boxes below, sketch how the Moon would appear from Earth from the four Moon positions that you did not choose for Question 2. Label each box with a letter. A E
Sun’s rays
Earth D B C
View of Moon from Earth at one of the
positions (A-E) above.

56. Shade in the part of the Moon that is not illuminated by the sun when it is at positions F-I.
Which Moon position (F-I) best corresponds with the Moon phase shown in the lower-left corner?
How much of the Moon’s surface is illuminated by the sun during this phase?
How much of the Moon’s illuminated surface is visible from Earth for this phase of the Moon? G
Sun’s rays F H
Earth I
View of Moon from Earth from one of the positions (F-I) above.

57. Model can explain the phases of the Moon
The phases of the Moon occur because light from the Moon is actually reflected sunlight
As the relative positions of the Earth, the Moon, and the Sun change, we see more or less of the illuminated half of the Moon.

58. What does the Earth look like from the Moon at
Full Moon
New Moon
First Quarter
Third Quarter

60. What are 2 observations simple model does not predict?

61. What are 2 observations simple model does not predict?
Why there are not eclipses every month
Why there are “annular” and “total” eclipses

62. Eclipses occur only when the Sun and Moon are both on the line of nodes

64. What are 2 observations simple model does not predict?
Why there are not eclipses every month
Why there are “annular” and “total” eclipses of the sun

65. Solar eclipses can be either total, partial, or annular, depending on the alignment of the Sun, Earth, and Moon

68. Lunar eclipses can be either total, partial, or penumbral, depending on the alignment of the Sun, Earth, and Moon

69. Question
If you were looking at Earth from the side of the Moon that faces Earth, what would you see during
A total lunar eclipse?
A total solar eclipse?

70. The Moon’s rotation always keeps the same face toward the Earth due to synchronous rotation

71. Time and the Moon
Two types of months are used in describing the motion of the Moon.
With respect to the stars, the Moon completes one orbit around the Earth in a sidereal month, averaging days.
The Moon completes one cycle of phases (one orbit around the Earth with respect to the Sun) in a synodic month, averaging days.

73. sidereal month, averaging 27.32 days.
sidereal day – 23 hr 56 min
synodic (lunar) month, averaging days.
solar day – 24 hr

74. Question
On a certain date the Moon is in the direction of the constellation Gemini as seen from Earth. When will the Moon next be in the direction of Gemini?
One year later?
days later?
One sidereal month later?
One synodic month later?