Just a fact. Libration points. Part one. If we place a small object on the surface of the Earth, exactly on the line between the center of the Earth and the center of the Sun, and begin to move it along that line from the Earth towards the Sun, the gravitational pull of the Earth will be gradually reducing, and the gravitational pull of the Sun will be gradually increasing. At a certain point, both gravitational pulls will become equal, while oppositely directed. The resultant of two gravitation forces in this point is zero, and a much smaller object placed in it will not move either to the Sun or to the Earth. Instead, it will move together with the line between the Earth and the Sun, as the Earth will move on its orbit. This point was discovered by Joseph-Louis Lagrange. He also discovered four more such points, where the resultant force of gravitational attractions is such that a small object placed in it will move together with the Earth on its orbit without motion relative to the center of the Earth. Now we call these points either Lagrangian points or libration points. The obvious point described above is L1. Other such points are less obvious and were found from solving complicated equations describing interaction of the gravitational fields of two massive objects, of which one is far more massive than the other, and their influence on a third object, which is much less massive than the smaller of the two (the so-called three-body problem). L1 is about 1.5 million km from the Earth towards the Sun. L2 is located on the same line between the Sun and the Earth, only in the opposite direction from the Earth, again, about 1.5 million km from the Earth. L3 is located on the opposite side of the Sun. It is slightly closer to the Sun than the respective opposite point of the Earths orbit, approximately by 1.5 million km. L4 and L5 are so-called triangular Lagrangian points. They move together with the Earth on an orbit with slightly larger distance from the Sun than the orbit of the Earth, 60 degrees ahead and 60 degrees behind the current position of the Earth on its orbit. Similar Lagrangian points exist in the system of the Earth and the Moon and in any system of two big celestial bodies, one of which is much bigger than the other. ====
Posted on: Mon, 27 Jan 2014 07:08:19 +0000