Mapping in Astronomy
Sky Mappings

Hammer Projection

Mollweide Projection

Aitoff Projection

Sanson Projection

Lambert Projection

Ortographic Projection

Gnomonic Projection

Stereographic Projection

Hammer Projection

equalarea projection

first presented by Ernst von Hammer in 1892

is also known as HammerAitoff (the Aitoff projection looks similar, but is not equalarea)

the border is an ellipse, equator and central meridian are straight lines
other parallels and meridians are complex curves.

Mollweide Projection

pseudocylindrical, equalarea 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 40°44' 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

Sanson Projection

sinusoidal, pseudocylindrical, equalarea projection

Parallels are unequally spaced straight lines

Simple mapping formulae
x= r*a*cos(d)
y= r*d

Aitoff Projection

equalarea 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 equalarea 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