Reactionless Thrust Station Keeping at L2

The L2 point is defined for two bodies in circular orbit about each other. The sun-Earth and Earth-Luna systems do not exactly match the definition, but they come close enough that the model is a useful model. Calculations^[1] put the Earth-Luna L2 point at 64500 km beyond Luna's center. If masses are depended from this point along a line connecting the centers of mass of Luna and Earth, one depended away from Luna and one toward Luna, these masses can be adjusted to provide thrust toward or away from Luna. If one mass is depended by tidal force to 5.25*10^7 meters from Luna's center and another depended by tidal force to 7.65*10^7 meters, then when these masses are both reeled in 2*10^6 meters toward L2 the forces needed to move the masses are balanced and the net acceleration on the system changes by an 8% of the previous acceleration on the depended masses directed upward. This force results because the rate change of gravitational intensity per meter change in altitude is greater for the mass hung closer to Luna than it is for the mass hung farther from Luna. By combination with a pair of angular rate control wheels at L2 this can provide all of the stationkeeping needed by a satellite at L2.

In this concept there is no reaction mass expended from the station at L2, but there is an immeasurably small reaction in the moon to which the station is coupled by gravitational force. The station keeping thrust results from the change in the strength of the gravitational coupling by changing the geometry of the station.