Re: What is the Earth Moon neutral point?

The neutral point is defined as the point between the Earth and the Moon where the gravitational forces of the Moon exactly equal the gravitational forces of the Earth. Since they are pulling in opposite directions, this point is a point where something with no velocity will stay without falling to either the Earth of the Moon. It is also an important point in flights to the Moon because if the spacecraft reaches the neutral point with any forward velocity, it can then fall to the Moon without expending additional fuel for thrust.

Knowing that the ratio of the masses of the Earth and Moon is approximately 81:1 and the gravitational forces vary inversely with the square of the distance, the approximate neutral point can be calculated. It turns out the neutral point is about nine times further from the Earth than the Moon or approximately 340,000 km from the Earth. An accelerometer on the Apollo Command Module should have discerned the exact point where each spacecraft went through the neutral point on their journey to the Moon, but no explicit reference could be found to confirm this.

Note that in the above paragraph the distance is given as an approximate value. Newton's work assumes point masses or objects that are perfectly spherical and have a uniform density. As a quick glance around the Earth and up into the sky can tell you, neither the Earth or the Moon are points or perfectly smooth spheres. Furthermore, the density of both bodies varies with the type of rock that predominates within a region. Also, the orbit of the Moon is not circular but elliptical. As the distance varies, the attractive forces acting upon a spacecraft also vary. Under those conditions the neutral point actually moves constantly around a mean value. Seemingly meaningless things such as the direction the Himalayas are pointing actually become important.

A closely related concept are the Lagrangian or L points. Joseph-Louis Lagrange was a mathematician who lived between Jan. 1736 and April 1813. During this time a considerable amount of work was done on the o rbits of the Moon and planets. One of the key concepts was the mathematical description of the motion of a three body problem, i.e., the Earth, the Moon and the Sun. His work showed that there are places 60° in front of and behind a planet in its orbit where the gravitational forces between the Sun and the planet cancel each other out. These became known as the Lagrangian or L points. While Lagrange did not believe these points had any special significance in the Solar System, astronomers have since discovered several asteroids in the Lagrangian points for the Earth and Jupiter. The ones for Jupiter are called the T rojan asteroids. Achilles was the first one discovered in 1908.

The Lagrangian points also exist in the Earth-Moon system as well. They move about a central point as the Earth and Moon orbit one another and rotate on their axes. The Lagrangian points may become important in the future as they are excellent places to build communication satellites and potentially even space colonies. Several of the L5 Societies and related organizations can be accessed through the National Space Society.

Reference: Concise Encyclopedia of Astronomy, Paul Muller, Follett Publishing, Chicago, (1968) pp. 166-167