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Geometry and time line for an L2 halo orbit. The L2 Lagrange point is on the Sun-Earth line of syzygy at about 0.01 AU (1.5 x 10 6 km) from the Earth. A halo orbit about this point is three dimensional, with coupled two-dimensional periodic motion in the ecliptic plane and independent periodic motion out of the ecliptic, thus describing a three-dimensional Lissajous figure. The amplitudes can be chosen such that the frequencies become equal and with appropriate phasing, the spacecraft will appear to be orbiting about the line of syzygy. The minimum in-plane amplitude must be of the order of 670,000 km, about 24° from the line of syzygy. The halo orbital period of 180 days is somewhat less than half the Earth's orbital period. Injection into a large-amplitude halo orbit requires a ∆V~50 m/s, far less than that needed for placement at L2 (~300 m/s). Orbital maintenance requires a ∆V~10 m/s/yr. Locations along the trajectory from Earth orbit are indicated in days.

Geometry and time line for an L2 halo orbit. The L2 Lagrange point is on the Sun-Earth line of syzygy at about 0.01 AU (1.5 x 10 6 km) from the Earth. A halo orbit about this point is three dimensional, with coupled two-dimensional periodic motion in the ecliptic plane and independent periodic motion out of the ecliptic, thus describing a three-dimensional Lissajous figure. The amplitudes can be chosen such that the frequencies become equal and with appropriate phasing, the spacecraft will appear to be orbiting about the line of syzygy. The minimum in-plane amplitude must be of the order of 670,000 km, about 24° from the line of syzygy. The halo orbital period of 180 days is somewhat less than half the Earth's orbital period. Injection into a large-amplitude halo orbit requires a ∆V~50 m/s, far less than that needed for placement at L2 (~300 m/s). Orbital maintenance requires a ∆V~10 m/s/yr. Locations along the trajectory from Earth orbit are indicated in days.

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