Reading about geological history of Mars and coming across the Martian dichotomy, which is about having the two hemispheres' geography differ in elevation by 1 to 3 km.
Does this mean that Mars' center of mass is slightly shifted to the south? and if so, more generally, what is the influence of a concentration of mass aligned with the rotational axis of a planet that is not tidally locked?
Yes, by about 3 kilometers, and it is also shifted by about 1.5 km along the y axis in the direction of Tharsis. See Table 4 in Smith et al. (2001), which shows, among other geodetic parameters, the ellipsoid offset of COF (center of figure) from COM (center of mass):
| parameter | value |
|---|---|
| Δx | −233 m |
| Δy | −1428 m |
| Δz | −2986 m |
According to the same source, this morphology have impacted sediment transportation:
The 3-km offset along the z axis between Mars' COM and COF (cf. Table 4) results in a non-zero $C_{1,0}$ term in the spherical expansion of topography (equation (8)). [...] While this zonal elevation change is complicated by both large- and regional-scale topographic features, it is apparent that this fundamental aspect of Martian topography has controlled the surface and subsurface flow of volatiles and sediments throughout much of Martian history. As discussed more below, the global-scale elevation change associated with the $C_{1,0}$ term of the topography field resulted in the northern hemisphere becoming a global-scale sink for transported material.
