Rocheworld: Lagrange Points
The Lagrange point phenomenon exists in any system wherein the gravitational fields of two large bodies interact to create five “sweet spots”, within which lies the exact centripetal force necessary for a smaller object to remain in a constant orbit with the larger objects. There are five Lagrange points within the Sun-Earth orbit, as well as five Lagrange points within the
Earth-Moon orbit. These points will vary according to the mass of the two larger objects, as well as the distance between them. The first three of these points (commonly referred to as L1,
L2, and L3) were discovered by Swiss physicist Leonard Euler; the remaining two were discovered a few years later by Italian physicist Joseph Louis Lagrange, who first published his findings in a 1772 publication entitled “Essay on the three-body problem.” The first three of these points are considered “unstable” while the remaining two are “stable,” based on their positions within the two gravitational fields. Taking advantage of these points enables a small object, like a satellite built by NASA, to remain in orbit within a two-body system in order to make observations from a constant position relative to those two bodies. Robert Forward makes use of this concept quite frequently in Rocheworld to describe the activities of the human space travelers as they explore the binary planet system of Roche and Eau, and the unique qualities of these binary planets raise the possibility for Lagrange points that are quite unlike those we observe in our own Solar System.
The first Lagrange point, called L1, is located between the two larger masses. For example, in the Sun-Earth system, anything orbiting between the Sun and Earth will experience the gravitational forces of both masses pulling it in opposite directions (toward
each respective mass). The closer an object rotates to the sun, the faster it will move, because it has to maintain a higher velocity to remain in orbit, counteracting the
Earth-Moon orbit. These points will vary according to the mass of the two larger objects, as well as the distance between them. The first three of these points (commonly referred to as L1,
L2, and L3) were discovered by Swiss physicist Leonard Euler; the remaining two were discovered a few years later by Italian physicist Joseph Louis Lagrange, who first published his findings in a 1772 publication entitled “Essay on the three-body problem.” The first three of these points are considered “unstable” while the remaining two are “stable,” based on their positions within the two gravitational fields. Taking advantage of these points enables a small object, like a satellite built by NASA, to remain in orbit within a two-body system in order to make observations from a constant position relative to those two bodies. Robert Forward makes use of this concept quite frequently in Rocheworld to describe the activities of the human space travelers as they explore the binary planet system of Roche and Eau, and the unique qualities of these binary planets raise the possibility for Lagrange points that are quite unlike those we observe in our own Solar System.
The first Lagrange point, called L1, is located between the two larger masses. For example, in the Sun-Earth system, anything orbiting between the Sun and Earth will experience the gravitational forces of both masses pulling it in opposite directions (toward
each respective mass). The closer an object rotates to the sun, the faster it will move, because it has to maintain a higher velocity to remain in orbit, counteracting the