Positions in the Sky
Most people are familiar with the idea of plotting a graph. This is one example of a coordinate system, the x and y coordinates (abscissa and ordinate) providing a means of specifying the position of a point within the two-dimensional surface occupied by
- PDF / 911,224 Bytes
- 31 Pages / 439.37 x 666.142 pts Page_size
- 24 Downloads / 225 Views
Positions in the Sky
Spherical Polar Coordinates Most people are familiar with the idea of plotting a graph. This is one example of a coordinate system, the x and y coordinates (abscissa and ordinate) providing a means of specifying the position of a point within the two-dimensional surface occupied by the graph. It is a simple extension of the idea to give completely the position of an object in space using three coordinates, x, y and z (Fig. 4.1). In astronomy there is frequently the need to specify the position of an object; however, neither the two or three-dimensional Cartesian coordinate systems above are convenient. Instead, the three-dimensional position in space of an object is specified in a spherical polar coordinate system. This gives the position of an object, P, with respect to a point in space (the center of the sphere) and a reference direction and plane, and results in coordinates, R, y, f (instead of x, y, z), where y and f are not linear distances, but angles (Fig. 4.2). A familiar example of the use of spherical polar coordinates is to give positions on Earth. Here, however, we normally only specify two of the three coordinates because the radial distance is almost constant at about 6,370 km. Thus only the latitude and longitude need be given in order to fix a point on the surface of Earth. Latitude is measured in degrees north or south of the equator, from 0 at the equator to 90 at the poles. Other systems of spherical polar coordinates may go from 0 to 180 (i.e., from South Pole to North Pole) for this coordinate. Longitude is measured in degrees from 0 to 180 east or west of the Greenwich meridian (Fig. 4.3). In other systems, the equivalent coordinate may go from 0 to 360 . For the latitude and longitude position coordinate system, the reference plane is Earth’s equator, and the reference direction, the direction along the equator through the Greenwich meridian. Thus the old observatory at Greenwich is at a latitude of 51 280 N, and a longitude of 0 , while Mount Palomar Observatory is at a latitude of 33 210 N and a longitude of 116 520 W.
C. R. Kitchin, Telescopes and Techniques, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-1-4614-4891-4_4, # Springer Science+Business Media New York 2013
69
70 Fig. 4.1 Three-dimensional coordinate system based on orthogonal axes
Fig. 4.2 Spherical polar coordinates
Fig. 4.3 Latitude and longitude
4
Positions in the Sky
Celestial Sphere
71
Celestial Sphere Unlike objects on the surface of Earth, those in the sky are distributed throughout the whole of three-dimensional space. Nonetheless we may still use a system of spherical polar coordinates analogous to latitude and longitude. We do this by imagining a huge sphere, centered on Earth and large enough to contain every object in the universe. We then project an object in three-dimensional space on to the surface of that sphere. Then just the two angular coordinates give its position (Fig. 4.4). In other words, we ignore the radial coordinate of an object when it comes to
Data Loading...
