The Celestial Sphere

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The Celestial Sphere

• Lab 2

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Celestial sphere
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Geocentric model

• zenith - the point on the celestial sphere that
  is directly over our heads always 90 from the
  horizon
• celestial meridian - the arc that goes through
  the North point on the horizon, Zenith, and South
  point on the horizon

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Geocentric model

• All objects are slowly changing their positions
  on the celestial sphere
• The only noticeable changes (for a human
  lifespan) are diurnal and intrinsic motion
• Diurnal motion of celestial sphere due to
  earths rotation, does not change relative
  positions
• Intrinsic motion the wanderers

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Ecliptic

• Ecliptic road of the sun
• imaginary path that the Sun follows on the
  celestial sphere over the course of a year

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ecliptic
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Celestial Coordinate System

• To measure distances on the imaginary celestial
  sphere, we use angular separations instead of
  miles/km
• There are 360 in a full circle and 90 in a
  right angle
• Each degree is divided into 60 minutes of arc
• Each minute of arc is divided into 60 seconds of
  arc

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Celestial Coordinate System

• Sun and Moon are both 0.530 arc min in
  diameter
• The pointer stars in the bowl of the Big Dipper
  are about 5 apart
• The arc from the N point on the horizon, through
  the point directly overhead, to the S point on
  the horizon is 180, so any object directly
  overhead is 90 above the horizon
• Similarly any object ½-way up in the sky is 45
  above the horizon

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N P
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AK
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LA
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LA example details

• Los Angeles latitude 34 N.
• The NCP is therefore 34 degrees above the north
  horizon.
• Because the Earth's equator is 90 away from the
  north pole, the celestial equator as seen in LA
  will arc up to 90 - 34 56 above the southern
  horizon at the point it crosses the meridian.
• It still intercepts the horizon due east and
  west.
• The stars rise in the E, move in arcs parallel to
  the celestial equator reaching maximum altitude
  when they cross your meridian, and set in the W
  part of the sky
• The star paths make an angle of 90 - 34 56
  with respect to the horizon.

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animation

• http//www.star.ucl.ac.uk/idh/STROBEL/nakedeye/cs
  ph1t5.htm

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Summary so far..

• Meridian always goes through due North, zenith,
  and due South points
• Altitude of zenith always equals 90
• Altitude of celestial pole observer's latitude.
  Observers in northern hemisphere see NCP
  observers in southern hemisphere see SCP
• Altitude of celestial equator on meridian 90 -
  observer's latitude
• Celestial equator always intercepts horizon at
  due East and due West points
• Angle celestial equator (and any star path) makes
  with horizon 90 - observer's latitude
• Stars move parallel to the celestial equator

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RA

• Longitude lines run N-S
• Analogous celestial reference are lines of right
  ascension
• RA is measured in hours, minutes, and seconds,
  instead of degrees, and increases in an easterly
  direction on the sky
• Zero RA is where the Sun crosses the celestial
  equator
• The full 360 degrees circle is broken up into 24
  hours, so one hour of RA 15 degrees.
• The lines of RA all converge at the celestial
  poles, so two stars one hour of RA apart will not
  necessarily be 15 degrees in angular separation
  on the sky (only if they are on the celestial
  equator will they be 15 apart)

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Dec

• Latitude lines run E-W parallel to the equator
• When projected onto the sky, they become lines of
  declination
• Like the latitude lines on Earth, declination
  (Dec) is measured in degrees away from the
  celestial equator, for objects north of the
  celestial equator and - for objects south of the
  celestial equator
• Objects on the celestial equator are at 0 Dec
• objects ½-way to the NCP are 45
• objects at the NCP are 90
• objects at the SCP are -90
• Polaris's position is RA 2hr 31min, Dec 89 15
  arcmin

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RA and Dec
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Altitude and Azimuth

• Azimuth and altitude are usually used together to
  give the direction of an object in the
  topocentric coordinate system.
• We use altitude and azimuth to describe the
  location of an object in the sky as viewed from a
  particular location at a particular time.
• The altitude is the distance an object appears to
  be above the horizon. The angle is measured up
  from the closest point on the horizon.
• The azimuth of an object is the angular distance
  along the horizon to the location of the object.
  By convention, azimuth is measured from north
  towards the east along the horizon

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Altitude

• Altitude is the angle up from the horizon. Zero
  degrees altitude means exactly on your local
  horizon, and 90 degrees is "straight up". Hence,
  "directly underfoot" is -90 degrees altitude.

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Azimuth

• Azimuth is the angle along the horizon, with zero
  degrees corresponding to North, and increasing in
  a clockwise fashion. Thus, 90 degrees is East,
  180 degrees is South, and 270 degrees is West.
  Using these two angles, one can describe the
  apparent position of an object (such as the Sun
  at a given time).

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Azimuth

• We sometimes include the nearest compass
  direction as an abbreviation to help clarify the
  azimuth angles value in degrees. Up to three
  letters are used and they represent azimuth
  angles in the following order
• N (0), NNE (22.5), NE (45), ENE (67.5), E
  (90), ESE (112.5), SE (135), SSE (157.5), S
  (180), SSW (202.5), SW (225), WSW (247.5), W
  (270), WNW (292.5), NW (315), NNW (337.5)

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Horizontal Coordinate System (Alt/Az coordinate
system)

• The horizontal coordinates are
• altitude (Alt), that is the angle between the
  object and the observer's local horizon.
• azimuth (Az), that is the angle of the object
  around the horizon (measured from the North
  point, toward the East).
• The horizontal coordinate system is fixed to the
  Earth, not the stars
• Used for determining the rise and set times of an
  object in the sky.
• When an object's altitude is 0, it is rising (if
  its azimuthlt180) and setting (if its azimuth
  gt180)

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Summary of Celestial Coordinates for Positional
Astronomy

• Altitude varies from 0 to 90. Vertical position
  of object
• Azimuth varies from 0 to 360. Due N 0, due E
  90, due S 180, due W 270. Horizontal
  position of object
• Right ascension varies from 0 to 24 hours.
  Horizontal position of object.
• Declination varies from -90 (at SCP) to 90 (at
  NCP). Celestial equator declination 0
• Meridian altitude of any object 90 -
  (observer's latitude) declination degrees. If
  declination is negative, then addition of
  declination becomes a subtraction