Lagrange Points Make Science Fiction Factual
Robert Forward Uses L Points in Rocheworld
Sep 14, 2008
A Lagrange Point is mathematical name for an area in an orbital system between 2 bodies where a third mass can seemingly stand still, relative to the two other bodies. In this “magic area,” the combined gravity of the two larger objects provides just the right amount of force to ‘cancel out’ the centripetal force required to have a third object rotate "with" them.
In this sense, the Langrage point is analogous to a geosynchronous orbit, whereas the third object is “fixed” with respect to the orbits of the two larger objects.
Lagrange Points in a Two Body System: Where Are They?
Barring other physics phenomena, there are always 5 Lagrange points in every 2 body orbital system. Three provide largely unstable fixed orbits, white the remaining 2 allow for more general, seemingly stationery fixed orbits.
The 3 unstable points are often referred to as L1, L2, and L3. The 2 remaining stable points form the apex of an equilateral triangle with the large bodies as vertices. The differing in stabilities is due to the gravitational strengths of the two large objects creating the Lagrange Point. The Lagrange point can be likened to a ball at the top of a hill: if the gravity is slightly greater in one direction, the ball will roll off the top of the hill in that direction. But if the ball is in just the right spot, it won’t roll in either direction.
NASA's Use of Lagrange Points for Satellites
NASA scientists take advantage of the L1 Lagrange point in the Earth-Sun orbital system to fix the SOHO satellite in position to observe the Sun. Lagrange points are ideal for satellites that require a fixed position relative to orbiting bodies, in order to make observations and calculations. L4 and L5 are areas where asteroids and other small bodies often accumulate, due to the long-term stability that is free from the Sun and Earth’s gravity.
Lagrange Points in Rocheworld
In Robert Forward's Rocheworld, scientists calculate Lagrange points depending on the mass and velocity of the two large bodies. The L points will be much closer to the smaller of the two bodies, to account for the larger gravitational pull of the larger body. In the end of the Rocheworld, on p. 431, Dr. Philipson explains this difference by stating “For the Earth-moon system, where the Earth is much more massive than the Moon, those stable points are in the orbit of the Moon, at plus and minus sixty degrees from the Moon. In the Rocheworld system, where the two bodies are the same mass, the stable points are at plus and minus 90 degrees.”
The crew on Rocheworld not only calculated these points as real astronauts would, but also placed communication satellites in the stable L4 and L5 points. Here, the satellites synchronously orbit the double system and allow the crew to remain in contact with each other, even on opposite sides of the system.
Stability and Stationery Objects in Lagrange Points
As the scientists explain on p. 185, the Lagrange Points are much more stable when one mass is much larger than the other, but will still exist in the Rocheworld similar-mass system. In these points, the crew’s ship experience zero G’s. Thomas, the astrodynamicist of the crew, decides right away to place the communication satellites at the L4 and L5’s, since these are the most stable synchronous points and the satellite can stay there with minimal fuel consumption. They also decide to put a third satellite opposite their orbit to maintain as full coverage as possible for communication.
Lagrange points are an example of real science used by Forward in Rocheworld. Their particular nature allows for a plausible explanation and scenario for the placement and use of communication satellites.
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