1. PHY134 – Introductory Astronomy
Ronen Plesser: (PHY134 in subject line please)
Ryan Kozlowski
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2. To Flip or not to Flip? Normal Class 2.5hrs of classroom lecture
HW Assignments
Review Sessions
Observations
Flipped Class
2.5hrs of video lectures
Discussion/Demos/HW solving in class
Review Sessions
Observations
Vote through Sakai by Friday, 9/1/17

3. Introductory Astronomy
Week 1: Positional Astronomy

4. Laws for the Heavens
“The ancients gave to the Gods the heaven or upper place, as being alone immortal; and our present argument testifies that it is indestructible and ungenerated. Further, it is unaffected by any mortal discomfort, and, in addition, effortless; for it needs no constraining necessity to keep it to its path... Such a constrained movement would necessarily involve effort…-and would be inconsistent with perfection. Hence we must not believe the old tale which says that the world needs some Atlas to keep it safe” Aristotle (350 BC) We seek Universal laws governing heaven and Earth This week: Understand apparent motion of the sky; what we can see when and where. Intuitive and mathematical description
Celestial Sphere

5. The Celestial Sphere
Pattern of stars unchanging: can imagine them fixed on a sphere surrounding Earth
Celestial Sphere is large and rigid
Celestial Sphere rotates daily about axis through poles from East to West
Equivalently, Earth rotates from West to East inside stationary Celestial Sphere
Stars occupy fixed positions on Celestial Sphere: use Celestial coordinates to specify this with mathematical precision
Lat/Long Demo

6. Latitude - Declination
Terrestrial Poles are where rotation axis meets Earth
Terrestrial Equator lies midway between Poles
Latitude is angle from equator (at center)
Rotation moves observer East along a parallel
Celestial Poles lie directly above terrestrial poles – along axis of relative rotation
Celestial Equator lies midway between Poles
Declination is angle from equator (at center)
Rotation moves star West along a celestial parallel
Observer looking up sees a star whose declination is equal to observer’s latitude
Observer sees pole at angle above horizon (altitude) equal to latitude – Celestial Navigation

7. L

8. Longitude – Right Ascension
Meridians run between poles
Longitude measured East from prime meridian (Greenwich) in degrees
Rotation moves observer from one meridian to the next, East at 15°/hr
Celestial meridians run between poles
Right Ascension measured East from prime meridian (Pisces) in hours
Rotation moves star from one meridian to the next, West at 15°/hr
Right Ascension of the Meridian seen overhead is observer’s Sidereal Time – Celestial Clock

9. Summary Stars fixed on large Celestial Sphere concentric with Earth
Sphere rotates daily from East to West
Declination is Celestial Latitude
RA is Celestial Longitude measured in hours to the East

10. Local Coordinates
To find a star, need to know what direction to look. Use
Altitude: angle above horizon
Zenith Angle: angle from Zenith 90°-Altitude
Azimuth: angle from North (clockwise)
Alt/Az Demonstrator

11. Sky Charts Pole N Zenith Fixed RA Fixed Azimuth Horizon Fixed Decl.
Equator
Fixed Altitude E W S

12. What We Can See
As sky rotates about celestial pole stars near North (South) pole never set (circumpolar)
Stars near South (North) celestial pole never visible
Stars near celestial equator rise, move West across sky, and set
Rotating Sky Demonstrator

13. Sidereal Time Zenith at Decl = Latitude RA = Sidereal Time
Sidereal Time is celestial meridian coinciding with local meridian
Changes with time: 24 sidereal hours = One full rotation of Earth
Can use stars to measure time! In one (sidereal) hour Celestial sphere shifts by one hour of RA
Changes with longitude at 1h/15°
Athens, looking South, both coordinates.
Find Alpheratz, watch it move an hour at a time

14. Finding a Star Star: Observer: Define: Find:
Right Ascension:
Declination:
Observer:
Latitude:
Sidereal time:
Define:
Hour Angle:
Colatitude:
Codeclination:
Find:
Azimuth:
Zenith Angle:
Idea: Local system obtained from Celestial by:
Rotation by about z
Rotation by about y

15. Rotation Matrix

16. Summary: Finding A Star
Star is highest at meridian crossing when sidereal time is its RA
At this time Zenith angle is |Decl-Latitude|
Altitude is 90° - Zenith angle
Azimuth is 0° if Decl > Latitude
180° if Decl < Latitude
To find star earlier/later, rotate East/West by 15°/h
Need to know how to tell sidereal time

17. An Example Look for Sadr: RA 20h 22m Dec 40° 19’
Crosses meridian at ST 20h 22m (22:07)
At Zenith Angle 4° 19’ or altitude 85° 41’
And Azimuth 0°
Try Antares: RA 16h 30m Dec -26° 26’
Crosses meridian at ST 16h 44m (18:29)
At Zenith Angle 62° 26’ or altitude 17° 34’
And Azimuth 180°
We have ST ~ LT - 1h 45m

18. Angles and Distances Small-Angle Approximation
Error of order (α/57.3°)2

19. An Application How large is Celestial Sphere?
Every point on Earth can be taken to be in center to within accuracy of measurement
AB arc is red
AB is green
In our e.g. AB can be two points on Earth, O a star. Lines should be parallel, a~0.

20. The Sun Also Rises (and Sets)…
The Sun, like anything off Earth, is somewhere on Celestial Sphere
When sidereal time near RA of Sun it is daytime
Stars near Sun not visible
Where is the Sun?
How is sidereal time (ST) related to local time (LT)?

21. …But Slower
As it spins once a day, Earth also orbits Sun once a year in the same sense
Seen from Earth, Sun orbits once a year, so not fixed on Celestial Sphere
Sun moves along Celestial sphere from West to East (increasing RA) completing full revolution in a year
Visible (night) part of sky changes over the year
This means Sun moves across sky from East to West slightly slower than stars – one less revolution per year
Sidereal and Solar Time Demonstrator

22. Clocks
This means time from noon to noon is a bit (1/365 of a day or about 4min) longer than time it takes Earth to turn 360°
A (mean) solar day is longer than a sidereal day
Our clocks (LT) keep solar time so run slower than sidereal clock (ST)
24 sidereal hours = 23h 56m 4s

23. Finding Sidereal Time
By convention ST ≅ LT on September 21 (Sun at 12h)
D days later (earlier)
ST ≅ LT +/- D×4m
This is approximate. In any event ignores time zones and Daylight Savings Time
On December/March/June 21
ST ≅ LT + 6/12/18 h
Sun is at /0/6 h
Today (8/28) is ~24 days before 9/21 so ST = LT - 24*4m = LT - 96m = LT - 1h 36m

24. Summary - Example When is Vega (in Lyra) RA 18h 36m high at midnight?
Vega is high when ST = 18h 36m
This is midnight (LT = 24h) when
ST = LT - 5h 24m
= LT – 81*4m
or 81 days before September 21: on July 3
ST = LT – 5h 24m = LT – 81*4m so 81days before September 21 – July 3 (midsummer)
Note that on June 21 ST = LT +18h so get 18h + 4Dm = 18h 36m or D = 9…
Closer: 9 days after June 21

25. Summary So Far
Stars are fixed on celestial sphere, which rotates once each sidereal day from East to West.
Positions on celestial sphere are given by Declination (Latitude) and Right Ascension (RA - Longitude, in hours)
Sidereal time of an observer is the Right Ascension of her zenith. This changes with time, repeating once each sidereal day
When a star’s RA is the same as local sidereal time the star is on local prime meridian. Its azimuth is then 0 (if it lies North of zenith) or 180 (if it is South of zenith). Its Zenith Angle is then|Decl – Lat|.
When RA is 12h away from local sidereal time it again lies on same local meridian but Zenith Angle is now 180° - |Decl + Lat|
If |Decl – Lat| > 90° star never rises
If |Decl + Lat| > 90° star never sets (circumpolar)

26. It Tilts Earth’s axis is tilted 23.5° from perpendicular to orbit
Celestial equator tilted 23.5° from plane of orbit – ecliptic
Sun’s orbit along Celestial sphere – ecliptic - tilted 23.5° from Celestial equator
Sun’s Declination changes between 23.5 and -23.5
Ecliptic meets equator at Vernal/Autumnal equinox at 0h/12h RA
Seasons Simulator

27. Seasons When Sun North/South of equator
Days longer in North/South
Sun higher in the sky in North/South
Climate warming in North/South cooling in South/North
Inside Arctic circle Sun becomes circumpolar/never rises (reverse for Antarctic circle)
At equinox day/night equal everywhere
Between tropics Sun is at Zenith once a year

28. How High is Sun at Noon? We are at Latitude 36°N At equinox
At summer solstice
At winter solstice
54°
77.5°
30.5°

29. Why Mean? 24h is an average Solar day
Sun’s RA increases over the year but not uniformly
Sun moves around ecliptic almost uniformly but ecliptic is tilted near equinoxes and parallel to equator near solstices. So Eastward motion fastest near solstices.
Almost… Earth very slightly nearer Sun in January

30. It Also Wobbles
The Earth’s axis wobbles like a spinning top – precession
Celestial axis wobbles.
North pole moves to the West in a circle of radius 23.5° every 26,000 years relative to stars
So does celestial equator hence precession of the equinoxes
Coordinates of stars change too – epoch J2000
Age of Pisces gives way to age of Aquarius ca. 2600
Precession SN

31. Moon Moves Too
Like Sun, Moon moves around celestial sphere as it orbits Earth West to East
Moon is faster: orbits in a sidereal month (27.32 days)
RA increases by 52min per day
Spin locked to orbit – same side always faces Earth
Moon moves relative to Sun by 48min per day
Full rotation relative to Sun in synodic month (29.53 days)
Position relative to Sun controls rise/set times as well as phases
Lunar Phases Simulator/GoPro?

32. Moon’s Declination New/Full Moon highest in Summer/Winter
Moon’s orbit inclined 5° to ecliptic about line of nodes
Twice a year line of nodes aligns with Sun: Eclipse Season
Tilt precesses to the West every 18.6 years so twice an eclipse year of days
At New/Full Moon during eclipse season have Solar/Lunar eclipse
Shadow simulator

33. Solar Eclipse Moon almost same angular size as Sun
With near perfect alignment can completely obscure Sun – from up to 250km shadow – total eclipse
More common – partial eclipse
When Moon farthest from Earth – annular eclipse
2001 Solar Eclipse series taken near Zimbabwe

34. Shadow of Moon on Earth taken from Mir spacecraft, August 11, 1999

35. January 4, 2011 Annular eclipse from Hinode satellite

36. Lunar Eclipse Moon enters Earth shadow from West
Eclipse can be total or partial. Penumbral eclipse when Moon in partial shadow – dims slightly
During totality Moon illuminated through atmosphere looks red

37. Fun with the Moon Moon appears larger near horizon
This is a psychological illusion not shared by optical instruments
Various theories as to mechanism
Can see dark part of crescent Moon – “old moon in new moon’s arms”
This is physical viewing dark part by reflected Earthlight

39. Signs of the Times
Astronomy and timekeeping are always closely related – we want our time to match what happens.
Our 24-hour days are adjusted to mean solar day.
Our months are approximately lunar.
Our years match orbit – days is a sidereal orbit.
Tropical orbit is days (precession).
Julius Caesar got so invented leap years.
Pope Gregory XIII (1582) corrected for the .0078

40. Summary Our cosmos now has moving parts
Sun moves around Celestial Sphere to the East, completes one revolution in a year. The ecliptic tilted relative to celestial equator by 23.5° about equinoxes and precesses West every 26,000 years
Moon moves around Celestial Sphere to the East, completes one revolution in a month. Moon’s orbit tilted relative to ecliptic by 5° about line of nodes and precesses West every 18.6 years
The model now explains day/night, lunar phases, eclipses
What else moves?