Mapping in Astronomy

Sky Mappings

  1. Hammer Projection
  2. Mollweide Projection
  3. Aitoff Projection
  4. Sanson Projection
  5. Lambert Projection
  6. Ortographic Projection
  7. Gnomonic Projection
  8. Stereographic Projection
  1. Hammer Projection
    • equal-area projection
    • first presented by Ernst von Hammer in 1892
    • is also known as Hammer-Aitoff (the Aitoff projection looks similar, but is not equal-area)
    • the border is an ellipse, equator and central meridian are straight lines other parallels and meridians are complex curves.
  2. Mollweide Projection
    • pseudo-cylindrical, equal-area projection
    • developed by Mollweide in 1805
    • Parallels are unequally spaced straight lines with the meridians being equally spaced elliptical arcs.
    • The scale is only true along latitudes 4044' north and south.
    • The projection is used mainly for global maps showing data distributions. occasionally referenced under the name homalographic projection.
    • Like the Hammer projection, outlined above, we need to specify only two parameters to completely define the mapping of longitudes and latitudes into rectangular x/y coordinates: * The central meridian * Scale along equator in inch/degree or 1:xxxxx , or map width
  3. Sanson Projection
    • sinusoidal, pseudo-cylindrical, equal-area projection
    • Parallels are unequally spaced straight lines
    • Simple mapping formulae
        x= r*a*cos(d)
        y= r*d 
      
  4. Aitoff Projection
    • equal-area projection
    • The Aitoff projection is a modified azimuthal map projection.
    • Proposed by David A. Aitoff in 1889,
    • it is the equatorial form of the azimuthal equidistant projection, but stretched into a 2:1 ellipse while halving the longitude from the central meridian:
    • Three years later Ernst Hermann Heinrich Hammer suggested the use of the Lambert azimuthal equal-area projection in the same manner as Aitoff, producing the Hammer projection. Hammer did not cited Aitoff that caused confusion where Aitoff has been attributed to Hammer's projection.
    • WMAP CMB maps are presented in Aitoff projection