Latitude in Snyder (page 15): For the "normal" Mercator projection (on the ellipsoid) this function defines the spacing of the parallels: if the length of the equator on the projection is (units of length or pixels) then the distance, , of a parallel of latitude from the equator is The isometric latitude is closely related to the conformal latitude : The formulae in the previous sections give the auxiliary latitude in terms of the geodetic latitude. The expressions for the geocentric and parametric latitudes may be inverted directly but this is impossible in the four remaining cases: the rectifying, authalic, conformal,
Latitude dependent mantle depth over the whole planet for the water locked up in the north and south polar caps. Mantle forms when the Martian climate is different than the present climate. The tilt or obliquity of the axis of the planet changes a great deal. The Earth’s tilt changes little because our rather large moon stabilizes the Earth. Mars only has two very small moons that do not possess enough gravity to stabilize its tilt. When the tilt of Mars exceeds around 40 degrees (from today's 25 degrees), ice is deposited in certain latitude bands where much mantle exists today. Latitude dependent