What are halo orbits
What is the difference between Halo Orbits and Lissajous Orbits?
Halo orbits are a subclass of Lissajous orbits.
The image showing a simple circular orbit shows only a 1: 1 Lissajous pattern.
These Lagrange point orbits actually orbit the larger body in a way that resonates with the smaller body. When we talk about the earth-sun system, satellites like DSCOVR, SOHO (L1) and the (hopefully) upcoming James Webb Space Telescope (L2) are about 1% closer or farther in heliocentric orbits (orbits around the sun) ( each) than the earth's orbit around the sun.
Earth's gravity is weak there, but strong enough to "pull" the satellites a little faster or slower to keep them in sync.
When you step into the twilight zone of a rotating frame and move with the earth, seems to be move their movement from your point of view in the rotating frame around the points L1 and L2.
Mathematically speaking, the equations become simpler when you do calculations for a simplified one Three-body problem with restricted circles (CRTBP, CR3BP) when using the rotating frame.
In an inertial frame, these satellites appear to drift up and down slightly, making a full cycle about twice a year. Only in the rotating frame sees this movement how forms an orbit around the Lagrange point or is at least connected to it.
This movement has a "horizontal" or left-right component and a "vertical" or up-down component.
In some cases, when this CR3BP movement has a sufficiently large amplitude, these movements can have the same period, and therefore seems the orbit in the rotating frame to be closed, cyclic and periodic. Orbits in this subgroup are called Called halo orbits . SOHO and the future JWST will be in these.
However, there are many orbits in this family where the horizontal and vertical motion do not have the same period, and therefore seem to be they form a criss-cross or lissajous figure in the space in the rotating frame. These are called Lissajous orbits. There is no specific relationship between the horizontal and vertical periods. For example, they don't need to be set in a 4: 3 ratio. Remember, these are not real orbits.
From a satellite's point of view, halo orbits are used because they tend to orbit the sun-earth axis (or the earth-moon axis) and avoid radio interference and power outages due to the darkening of the solar panels. DSCOVR's orbit will bring it to the exclusion zone around 2020, where the communications line of sight is too close to the sun, so an orbit correction is planned there to handle the situation. In the picture, you can see the insertion point labeled LOI and about a dozen cycles in five years. The horizontal and vertical periods are almost the same for this orbit. From the Lissajous Orbit Control for the L1 calibration point mission Sun-Earth L1
After 2020, DSCOVR will need to burn fuel every 3 or 6 months to stay on this ellipse and bypass the exclusion zone, which will then run out around 2028.
For more information on equations for calculating halo orbits and some Python, see
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