1. Constellations & Astronomy as a Science

2. Conclusion: Earth’s coordinates projected onto Sky
The Celestial Sphere
An imaginary sphere surrounding the earth, on which we picture the stars attached
Axis through earth’s north and south pole goes through celestial north and south pole
Earth’s equator 
Celestial equator
Relative positions of stars do not change -> attached to sphere
In ancient times was often literally thought of as a physical sphere rotating about the earth

3. Celestial Coordinates
Earth: latitude, longitude
Sky:
declination (dec) [from equator,+/-90°]
right ascension (RA) [from vernal equinox, 0-24h; 6h=90°]
Examples:
Westerville, OH °N, 88°W
Betelgeuse (α Orionis) dec = 7° 24’ RA = 5h 52m
Relative positions of stars do not change -> attached to sphere
In ancient times was often literally thought of as a physical sphere rotating about the earth

4. For Homework use Simplified Diagram
Zenith
Cel. Eq.
CNP
90⁰ A
latitude
Altitude of objects on the celestial equator is thus A = 90⁰ – latitude

5. Position II: Once you know where the Celestial Equator is, add declination δ of object
Zenith
Cel. Eq.
CNP δ
Aobj
90⁰
latitude
ACEq
Altitude of objects on the celestial equator is thus A = 90⁰ – latitude + δ

6. Examples: Position I Observing from:
Frankfurt (50°N latitude): Celestial equator is inclined 40° with respect to horizon
Equator (0°N latitude): Celestial equator is inclined 90° with respect to horizon
North Pole (90°N latitude): Celestial equator is inclined 0° with respect to horizon
Longitude of city does not matter!

7. Examples: Position II
Observing from Frankfurt (50°N latitude): Celestial equator is inclined 40° with respect to horizon. Then observe:
Star A (Declination 22.4°): Culminates with altitude angle of 62.4° in Frankfurt
Star A (Declination –12.4°): Culminates with altitude angle of 27.6° in Frankfurt
Star C (Declination – 45°): Culminates with altitude angle of – 5° ???  Is not visible in Frankfurt! Always below horizon.
RA (celestial longitude) of star does not matter!

8. Complicated! Let’s go with Patterns in the Sky!
We can group specs of light together to form triangles, squares, etc.
This allows us to find them the next night and follow their motion
Talk to other observers, and give them names: Bear, Bull, Lion, Hunter, Queen, etc.
 The Constellations

9. Constellations of Stars
About 5000 stars visible with naked eye
About 3500 of them from the northern hemisphere
Stars that appear to be close are grouped together into constellations since antiquity
Officially 88 constellations (with strict boundaries for classification of objects)
Names range from mythological (Perseus, Cassiopeia) to technical (Air Pump, Compass)

10. Constellation 1: Orion Orion as seen at night Orion as imagined by men
Also the Chinese and Egyptians; most constellations today (88) have Greek origins
Basically the constellations of the zodiac (12 in number)
Pattern not really meant to resemble Orion or whatever; likely named in honor, picture fit later
Orion as seen at night Orion as imagined by men 10

11. Orion “from the side”
Note naming scheme
Stars in a constellation are not connected in any real way; they aren’t even close together! 11

12. Constellation 1: Orion “the Hunter” Bright Stars: D) Betelgeuze
E) Rigel
Deep Sky Object:
i) Orion Nebula

13. Constellation 2: Gemini
“the Twins”
zodiacal sign
Brightest Stars:
I) Castor
J=K) Pollux

14. Constellation 3: Taurus
“the Bull”
zodiacal sign
Brightest Star:
F) Aldebaran
Deep Sky Object:
iii) Plejades

15. Constellation 4: Ursa Major
Other name:
Big Dipper
Stars:
B) Dubhe
C) Merak
Navigation: go 5 times the distance from Merak to Dubhe and you are at Polaris.

16. Constellation 5: Ursa Minor
Other name:
Little Dipper
α Ursa Minoris is
Polaris [A], the pole star

17. Constellation 6: Canis Major
“Big Dog”
Stars:
H) Sirius
(brightest fixed star)

18. Constellation 7: Cancer
“Crab”
No bright Stars

19. Constellation 8: Leo “the Lion” zodiacal sign Brightest Star:
G) Regulus

20. Astronomy as a Science
The science dealing with all the celestial bodies in the Universe
Cosmology is the branch of astronomy that deals with the cosmos, or Universe as a whole
The medieval list of the Liberal Arts: grammar, rhetoric, logic (trivium); arithmetic, music, geometry and astronomy (quadrivium)
Is an “exact science” for ~5000 yrs
Most rapid advancements in astronomy have occurred during the Renaissance and the 20th century
Success has been a result of development and exploitation of the scientific method
Will start at the earth and work outwards
At each step, we will find distances that dwarf all previous distance scales.
We will also discover the principle of mediocrity: not only is the Earth insignificant in size, but it's just an average planet orbiting an average star in an average galaxy.
In the end our study will return to Earth and the relationship of humanity to the Universe.

21. Astronomy and Culture
Astronomy had and has an enormous influence on human culture and the way we organize our lives
For example:
The year is the rotation period of the Earth around the Sun
The year is subdivided into months, the period of the Moon around the Earth
The weeks seven days are named after the seven bodies in the solar system known in antiquity: Sunday, Monday, Saturday (obv.), Tuesday=Mardi, Wednesday = Mercredi, Thursday=Jeudi, Friday=Vendredi

22. Position: Angles vs. Distances
Locations in the sky are easy to measure: 2 angles
Distances from observer are hard (one length)
 Together they give the location of an object in three-dimensional space

23. Angles and Angular Size
Angles measured in degrees
full circle = 360; right angle = 90
1 = 60' (minutes of arc or arc minutes)
1' = 60" (seconds of arc or arc seconds)
Typical angular sizes:
Moon 0.5, Sun 0.5, Jupiter 20”, Betelgeuse (α Ori) 0.05”
Size of image depends on actual size as well as distance away (thumb example) 23

24. Typical Values for Angles in the Sky

25. The Trouble with Angles
Angular size of an object cannot tell us its actual size – depends on how far away it is
Sun and Moon have very nearly the same angular size (30' = ½) when viewed from Earth
Actual Rsun/Rmoon ~ 400
Hence ratio of distances from earth also ~400 25

26. Angles and Size

27. Without Distances … We do not know the size of an object
This makes it hard to figure out the “inner workings” of an object
We can’t picture the structure of the solar system, galaxy, cosmos

28. The most important measurement in Astronomy: Distance!
The distances are astronomical!
The distance scales are very different
Solar system: light minutes
Stars: light years
Galaxies: 100,000 ly
Universe: billions of ly
Need different “yardsticks”

29. Performing Experiments
Experiments must be repeatable – requires careful control over variables
Possible outcomes of an experiment:
The experiment may support the theory
We then continue to make predictions and test them
The experiment may falsify the theory
We need a new theory that describes both the original data and the results of the new experiment
Since we cannot do every possible experiment, a theory can never be proven true; it can only be proven false
Or the experiment may be wrong!
Variables = the quantities on which the outcome of the experiment depends 29

30. Making Measurements Errors
Random
Systematic
With every measurement, it is essential to provide an estimate of the uncertainty – the likely range of errors
Example:
Using a ruler marked in mm, we round to the nearest marking – at most off by half a division, or 0.5 mm
Cite a measurement of 15 mm as 15  0.5 mm to indicate that the real value of the length is likely to be anywhere between
14.5 mm and 15.5 mm
If a theory predicts a value of mm, then a reading of
15  0.5 mm is in agreement with the theory but a reading of
15  0.1 mm is probably not

31. Relative Uncertainty
If you have a small error and the measured length is also small, you might have a huge error!
Use percentages:
Percent error = (estimated error)/(result) x 100%
Example: 51.3 cm ± 0.2 cm gives
Percent error = (0.2 cm)/(51.3cm) x 100 % = 0.4 %
(This is a pretty small error)

32. Is our result precise or accurate or what?
Two different concepts: precision and accuracy!
High precision means small error
High accuracy means close to an accepted value
Examples:
* * * * high precision, high accuracy
* * * * high precision, low accuracy
* * * * low precision, high accuracy
* * * * low precision, low accuracy
accepted value

33. When Do Results Agree?
Results agree, if they are within the error margins of each other
Examples:
| O | | O |
values very different, but errors large: agreement!
| O | | O |
values closer, but errors smaller: no agreement!