ASTRONOMY. 



I. The Celestial Sphere. Planes and Circles of Reference. 



The celestial sphere is a sphere to which it is convenient to refer stars and 

 other celestial objects. Its centre is assumed to be coincident with the eye of 

 the observer, and the objects referred to it are supposed to lie in its surface. 

 The orientation of this sphere is defined by its equator, which is assumed to be 

 parallel to the earth's equator. The equator is thus the principal plane of refer- 

 ence. Other planes of reference are the plane of the horizon, which is perpen- 

 dicular to the plumb line at the place ; the meridian, which is a plane through 

 the place and the earth's axis of rotation ; the prime-vertical, which is a vertical 

 plane at the place at right angles to the meridian ; and the ecliptic, which is a 

 plane parallel to the plane of the earth's orbit. These planes cut the surface of 

 the sphere in great circles called the equator, the horizon, the meridian, etc. The 

 points on the sphere defined by the intersection of the meridians, or the points 

 where the axis of the equator pierces the sphere, are called the poles. Similarly, 

 the prolongation of the plumb line upwards pierces the sphere in the zenith, and 

 its prolongation downwards pierces the sphere in the nadir. Great circles pass- 

 ing through the zenith are called vertical circles. 



2. Spherical Co-ordinates. 



a. Notation. 



The position of a celestial body may be defined by several systems of co-ordi- 

 nates. The most important of these in practical astronomy are the azimuth 

 and altitude system and the hour angle and declination system. In the first of 

 these the azimuth of a star or other body is the angle between the meridian 

 plane of the place and a vertical plane through the star. It is measured, in gen- 

 eral, from the south around by the west through 360°. The altitude of a star is 

 its angular distance above the horizon, and its zenith distance is the complement 

 of the altitude. In the second system the hour angle of a star is the angle 

 between the meridian plane of the place and a meridian plane through the star. 

 It is measured towards the west through 360°. The declination of a star is its 

 angular distance above or below the equator ; the complement of the declination 

 is called the polar distance. 



The angular distance of the pole above the horizon is equal to the zenith dis- 

 tance of the equator, or to the latitude of the place. Likewise, the altitude of 

 the equator and the zenith distance of the pole are each equal to the comple- 

 ment of the latitude at any place. 



