  For a convex body on the Euclidean unit sphere the spherical convex floating
body is introduced. The asymptotic behavior of the volume difference of a
spherical convex body and its spherical floating body is investigated. This
gives rise to a new spherical area measure, the floating area. Remarkably, this
floating area turns out to be a spherical analogue to the classical affine
surface area from affine differential geometry. Several properties of the
floating area are established.
