Two-Sphere Model & Constellations

WebAssign Username: your Otterbein email address Password: first initial plus last name plus IS2(IS3), no space Uwe Trittmann  utrittmannIS2, utrittmannIS3 HW #1 due Friday 8pm Question: Circumference of circle = pi*r^2

More names, now that we’ve observed the Sun’s position in the Sky Observer Coordinates Horizon – the plane you stand on Zenith – the point right above you Meridian – the line from North to Zenith to south

Modeling the Universe During the night, it looks like all “specks of light” in the sky travel around us, like the are fixed to an (invisible) sphere that turns around us So the apparent daily motion of the stars can be modeled by assuming they are fixed to a gigantic transparent ball Call it the Celestial Sphere

What you see depends on where you are! Celestial Sphere Your local sky – your view depends on your location on earth

Two-sphere Model The Celestial Sphere is observed from the “Earth sphere” Where an object appears in the local sky, depends on its position on the Celestial Sphere AND on the location of the observer on the Earth-sphere

Observation Location Matters If we move to a different observing place on Earth, the pattern remains the same (bright light rises & sets, etc.), but: Position of North Star changes Maximal altitude of Sun, special stars changes Latitude-Longitude coordinates of Earth

Observation Time Matters If we observe at a different time, the relative positions of the stars stay the same, but the sky dome apprears rotated: Each hour it rotates 15°, so 360° in 24 hr Later: counterclockwise Earlier: clockwise Latitude-Longitude coordinates of Earth

Timezones – 15°= 360°/24 strips

The Sky From 40°N From 50°N From a longitude 90° further west Plus 6 hours later  same as (a)!

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

Celestial Coordinates Earth: latitude, longitude Sky: declination (dec) [from equator,+/-90°] right ascension (RA) [from vernal equinox, 0-24h; 6h=90°] Examples: Westerville, OH 40.1°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

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

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

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!

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!

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

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)

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 19

Orion “from the side” Note naming scheme Stars in a constellation are not connected in any real way; they aren’t even close together! 20

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

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

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

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.

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

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

Constellation 7: Cancer “Crab” No bright Stars

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

Constellation 9: Cassiopeia Greek mythological figure: mother of Andromeda the big “W” in the sky No bright stars

Constellation 10: Pisces “the Fishes” Zodiacal sign No bright stars

Constellation 11: Pegasus Greek mythological figure: the winged horse big rectangle in the sky No bright stars

Constellation 12: Andromeda Greek mythological figure: Daughter of Queen Cassiopeia and King Cepheus rescued from Cetus by Perseus Deep Sky Object: Andromeda Galaxy