Lagrange
What Lagrange is
Lagrange is a crater — a circular depression, almost always an impact scar — on The Moon, 162 km across, centred at 32.6° S, 71.4° W in the Vallis Inghirami quadrangle. It is the 160th largest named feature on The Moon and the 55th largest of its class there.
Where the name comes from
Joseph Louis; Italian mathematician (1736-1813). The International Astronomical Union approved the name in 1935, under the theme it applies to every crater on The Moon. Of the 1615 features of this class catalogued on The Moon, the naming categories run Germany (234), American (229), France (163), Great Britain (160).
What it would take to settle Lagrange
The Moon scores 29.1 as a world. That number is the same for every square metre of it — but sunlight, water, radiation and the ground under your feet are not. This is the same question asked at 32.6° S, 71.4° W.
What this spot has going for it is earth link — near side — Earth stands 16° above the horizon and never moves. What works against it is water — outside the ice-bearing latitudes.
Computed from Lagrange's catalogued latitude, longitude and feature class — 84% of the model's weight had a basis here, and one axis was dropped as not applicable to The Moon (radiation geometry). Gravity, pressure, delta-v and distance from the Sun are the same everywhere on The Moon and are already counted in the world's own index, not again here.
What this cannot see: elevation. Slope, local shadowing and the polar “peaks of eternal light” — ridge tops near the poles of a barely tilted world that catch sun almost continuously while a crater floor kilometres away never does — need a terrain model this does not have. Where a real mission targets a pole, that is usually why.
Lagrange's satellite craters
The IAU names smaller craters around a major one by letter. Lagrange has 19, and each shares the parent's namesake rather than carrying one of its own.
What is next to it
The largest crater features on The Moon
All 1,615 craters on The Moon — mapped together, with the naming theme and the size distribution.