The Celestial Sphere, Angles, and Positions, Lecture notes of Calculus

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The Celestial Sphere, Positions, and

Angles

Objectives:

• Develop a coordinate system
• How do you measure distances on a sphere

The Celestial Sphere

 Earth at center of very large sphere  Because sphere is so large, observer, is also at center (figure not to scale).  Stars in fixed positions on sphere

Earth’s Coordinate System

• Latitude (-90 to 90°): A series of full circle arcs which are parallel to the equator. - “up-and-down” or “North-to-South”
• Longitude : A series of half circle lines which run from the N. pole to the S. pole. - “left-to-right” or “West-to-East”
• Meridian: Any half circle arc that connects the poles
• Prime Meridian: The local Meridian line which runs through Greenwich England. Latitude

Extend the Earth’s Coordinate System

• Celestial Coordinate System:
• Declination (0- 90 °) : The north/south positions of points on the celestial sphere. “Latitude”
• Right Ascension (0- 24 hrs) : The east/west positions of points on the celestial sphere. “Longitude”
• These two give the location of any object on the sky Dec=90° Dec=0°

Your Observing Location

• Zenith
  • point directly overhead
• Meridian
  • connects N and S through zenith
• Noon
  • sun is on meridian

TPS (reports?)  Which of the following locations on the celestial sphere is closest to the South Celestial Pole? A. RA= 14 hr dec= +88° B. RA= 14 hr dec= - 88 ° C. RA= 23 hr dec= +02° D. RA= 6 hr dec= +24°

Tip: For Northern Hemisphere

Observers Only

 Altitude of North Star = Approximate Latitude  If you measure the altitude of Polaris in the sky to be 20°, this means you are observing from approximately 20 ° N Latitude (or + 20° Latitude). You could be, for example, in Mexico City…  Laramie: Latitude = + 41° Laramie

Angular Separation & Size

 Two stars are

separated by an

angle of 24 °as

seen by the

observer.

 We say the “angular

separation is 24

degrees.”

The Northern Sky

 What would happen if we walked north (really far)?

 Find a reference star:

• The pointer stars from the Big Dipper point to Polaris (the North Star)

Measure the Circumference of Earth Air Distance: Lar Shively Arpt, Laramie, WY to Natrona Cty Intl Arpt, Casper, WY Distance 108 miles 1.5 degrees Laramie Casper

Lecture Tutorial (LT)  Position

• From a latitude of 90° N, the altitude of the North Celestial Pole is ____ above the horizon? A. 45 ° B. 90 ° C. 20 ° D. 0 °

• Where would the observer look to see the star indicated by the arrow?

A. High in the Northeast

B. High in the Southeast

C. High in the Northwest

D. High in the Southwest

Celestial Sphere Celestial Sphere Rotation Celestial Sphere Rotation Celestial Sphere Star A Star B 1 1 3 2 2 4 4 3 Figure 2 Horizon