About 71% of the Earth's surface is covered with water and the remaining 29% is landmass*. If you could theoretically cut the planet in half, with the objective of producing a half with the most landmass possible (and another with the most water possible), where would the cut be? More specifically, where would the centers (in the surface) of both halves be located?
A quick google search yielded this result which states in the paragraph before "Continents and Oceans" that 'this land hemisphere is centered on Western Europe.' You could validate this and get the precise location with functions in PostGIS by finding the centroid of a polygon (landmass). Then you can do some math to find the cut line based on the centroid.