Lagrange Points

Newton's heritage left many unanswered problems, which he himself foresaw.

The three body problem in mathematics - finding the relative position of three bodies under mutual gravitational attraction - has no analytic solution. That is because those positions never form a repeating pattern; there is something that changes all the time. We are left with at best  a series of approximations.

The mathematician Lagrange (and others after him) looked at it another way. He defined identifiable points of equilibrium of forces between two large bodies that a third of negligeable mass could inhabit. In effect, he found points where the third object would follow along with the second in its orbital movement.This is the basis on which we today position observational devices such as  the future James Webb telescope at Lagrange 2.

The German Wikipedia points out that, for Earth, Lagrange 2 is 1/100 the length of the distance between the Sun and Earth: (gravity being a function  of mass and the square of distance , voir Newton). 

Not all the Lagrange points are arrived at in the same manner, and mathematically there is a great deal going on. Newtonian mechanics applies to two bodies in an inertial system ie one that does not move; however, a planetary system does move, and one needs to take centrifugal forces into account (Coriolis). Long story short, the L1 and L2 points are not stable, and this is what we want, because they will not accumulate planetary litter the way other points will. It has estimated that there are some 5 000 planetoids at Lagrange 4 and 5 for Jupiter (so-called Trojan planets). We can maintain an artificial satellite at L2 with a minimal expenditure of fuel.