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Is it possible to have a 'figure 8' orbit around the Earth and the Moon? I'm looking for a non-decaying orbit that will not require significant rocket fuel to maintain, unlike the orbits used in the Apollo missions which (I think, not 100% sure) would decay if it was maintained for more that one orbit.

I'm looking for an orbit that can be used for lunar cyclers, so that one lobe of the figure-8 is around the Earth, and the other lobe is around the moon.

For such an orbit, what are the criteria required? What are the different apogees and perigees? What velocities will be involved at different points in the orbit? Where will such an orbit be specifically spaced?

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In addition to my above question(s), is it possible for such an orbit to be always facing sunlight, similar to a heliosynchronous dawn/dusk orbit?

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Yes, it would be possible to have a figure-8 shaped orbit around the Earth/Moon system.

In a two body system like the Earth/Moon or Sun/Earth system, there are five known points where the gravity of the two objects balances out. These are known as Lagrange points. It is possible for a spacecraft to orbit these points. Orbits around Lagrange points are called Lissajous orbits.

One type of Lissajous orbit is a halo orbit. Halo orbits are shaped like a partially flattened ellipse, and are utilized by a number of spacecraft already. Other types of Lissajous orbits include a nearly vertical orbit that looks like a tall figure-8. These orbits are not currently utilized by spacecraft, but unlike halo orbits, figure-8 shaped Lissajous orbits are more stable over a longer period of time without as many small correction burns. This makes them potentially attractive for some types of missions.

The Deep Space Gateway (DSG) lunar space station currently in development by NASA is likely going to use one of these orbits. Besides stability, this type of orbit allows for relatively easy access to a large number of locations on the surface of the Moon. This would allow crewed and uncrewed landers to use the DSG as a staging point for surface missions.

The shape of the orbit depends on the frame of reference, and I do not know what reference frame these orbits would have to be viewed from to appear as a figure-8.

An object in such an orbit would spend most of its time above and below the orbital plane of the Earth/Moon system, so it would be in sunlight most of the time, if not all the time. I do not know what, if anything, would be required to ensure that an object in a nearly vertical orbit spent all of its time in sunlight. Hopefully someone more knowledgeable than me will be able to answer that question.

Here is a link to a Desmos visualization of these orbits: https://www.desmos.com/calculator/eenppc2miu

Here is a link to a paper about 8-shaped lissajous orbits: msia.cedram.org/cedram-bin/article/MSIA_2011__4_1_1_0.pdf

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  • $\begingroup$ Is such an orbit a cycler orbit? $\endgroup$
    – user20905
    Feb 10, 2018 at 12:23
  • $\begingroup$ I could be wrong, but I believe OP is asking more about a free-return orbit than a lissajous $\endgroup$
    – Anton Hengst
    Jul 20, 2019 at 2:06
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If you are asking if a free-return trajectory is a stable orbit, the answer is no. A circumlunar free-return trajectory is one such that you will return in a "figure eight with one lobe around the moon and one lobe around the earth", but it is a trajectory and not an orbit because the same path cannot be taken again without dropping back into a circumterrestrial low parking orbit and boosting yourself into a new free-return trajectory. Why? Simply, because the moon has moved.

It's worth noting that while a circumlunar free-return trajectory looks very much like an earth-weighted figure eight in a earth-centered coordinate frame, in the earth-moon barycentric reference frame, where the positions of the earth and moon are fixed to the line that runs between them, it is obvious that the return orbit, if continued, will send you far behind the advancing moon. enter image description here

Image source

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