Where is the L1 Lagrangian point?

Orbital mechanics is a very difficult and complex science, because we do not have a generalized way to compute the gravitational attractions between a large number of objects. But in any system with two large masses, such as the Earth and the Moon, or between the Sun and the Earth, there are five relatively stable points. These are called Lagrange Points.

Lagrange points maintain their positions in respect to two large masses throughout the entire orbital period.

The L1 point is between the Earth and the Sun where the pull of gravity from each body is cancelled out. Because of the higher gravity from the Sun, the L1 point is closer to the Earth than the Sun.

The first Lagrange Point, L1, is directly between the two masses, but closer to the smaller mass, where the pull of gravity from each body is more-or-less cancelled out. In the Earth-Moon system, the L1 point is about 38,000 miles from the Moon. The L2 point is along the line from the Earth to the Moon, about 38000 miles past the Moon.

The L3 point is in the Moon's orbit, directly opposite the Earth from the Moon.

The L4 and L5 points lie in the Moon's orbit, 60 degrees ahead of and 60 degrees behind the Moon in its orbit. Many science fiction stories depict space stations in the L5 point, because this would be a stable location in the system; things would tend to "fall into" the L4 or L5 points and tend to remain there.