Gnomonic Projection

The concept of gnomonic projection requires some explanation. It is the only map projection that shows great circles as straight lines - thus all meteors can be drawn onto gnomonic charts as straight lines too. On other maps, such as those found in "Norton's Star Atlas", most meteors would appear as sections of arcs. Observers who plot meteors on non-gnomonic maps as straight lines coming directly from the radiant classify themselves as unskilled observers. Figure 1 shows what is understood by gnomonic projection. As we mentioned earlier, meteors describe arcs on the celestial sphere that are parts of great circles. Such a circle determines a plane. Plotting a meteor then comes down to determining the intersection between this plane and the plane on which the stars were projected. Figure 1 shows two meteors and their great circles on the celestial sphere. Our gnomonic map is the plane tangent to the sphere at point P. The center of projection is O. From O all stars on the sphere are projected onto the plane of the map.

Figure 1 - Gnomonic projection. The value of R defines the scale of the chart (in the case of Atlas Brno R = 160.43 mm). P is the center of the projection, and thus the center of the chart. The small arrows simulate meteors and their projection onto the map.

The meteor's projection on the map is the intersection between the plane determined by the great circle and the plane of the stellar map. The radiant lies on this intersection as well. Points at more than 90° from the map's center P are not projected on the map. In fact, constellations are strongly distorted near the map's edges. To solve this problem, several maps are necessary. Each of them represents a plane tangent to the celestial sphere at other points P.

Some of the characteristics of gnomonic projection are listed below:

  • As already mentioned, every great circle of the celestial sphere is projected as a straight line. This is the case with meteors (straight trajectory through the atmosphere) as well as with the hour circles, the equator, the ecliptic, the horizon and the galactic equator.
  • Small circles are projected as conic sections.
  • Gnomonic projection is not true to area or angle. This results in very distorted constellations towards the edges of the maps. Because of the overlap of the existing charts, this problem is reduced to choosing the most appropriate map.
  • Photographs obtained with standard lenses can be well approximated by gnomonic projection. Since only a small part of the sky is photographed, the distortion is not noticeable.