Satellite-to-Satellite Tracking in the Three-body Problem

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The acceleration vectors in the Three-body problem can be seen above. In this plot, the rotating frame is sychronized with the motion of the Earth and Moon, so they stay stationary. The dynamics in the regions immediately surrounding the Earth and Moon appear just like the two-body problem seen in the last slide, but in the region between the Earth and Moon where the L1 point would be, you can see some very asymmetric accelerations. In this region, orbits such as halo orbits cannot have any arbitrary orientation. Each halo orbit has a unique size, shape, and orientation. Because of these unique dynamics, the problems of SST observability do not occur as long as one spacecraft in a constellation is near these regions of gravitational asymmetry. For example, a spacecraft in a halo orbit could track a spacecraft in a lunar orbit using SST. With only those SST measurements, it is possible to estimate the relative AND absolute position and velocity of both spacecraft simultaneously.

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