Several space agencies plan to send astronauts, cosmonauts and taikonauts to the Moon in the coming years, with the long-term goal of establishing a permanent human presence there. This includes the NASA-led Artemis program, which aims to create a “sustained program of lunar exploration and development” by the end of the decade. There is also the competing effort by the Russian-Chinese International Lunar Research Station (ILRS) to create a series of facilities “on the surface and/or in orbit of the Moon” that will enable lucrative research.
Beyond these programs run by government agencies, many companies and non-governmental organizations (NGOs) hope to make regular trips to the Moon, either for “lunar tourism” and mining, or to build a “village”. lunar international”. which would act as a spiritual successor to the International Space Station (ISS). These plans will require a lot of cargo and freight between Earth and the Moon over the next decade, which is no easy task. To solve this problem, a team of American and British researchers recently published a research paper on the optimal trajectories for traveling between the Earth and the Moon.
The team consisted of Professor Emeritus Thomas Carter of Eastern Connecticut State University and Professor of Mathematical Sciences Mayer Humi of Worcester Polytechnic Institute. For the purposes of their study, the preprint of which is available online, Carter and Humi examined how a shuttle could transport supplies to a lunar outpost and bring back resources mined from the surface. Based on their calculations, they concluded that a trajectory placing the shuttle in an elliptical orbit and minimizing thrust requirements would be optimal.
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During the space race, NASA and the Soviet space program relied on free return trajectories to send missions to the Moon. This involved using the Moon’s gravitational pull to perform a figure-eight maneuver, which allowed the spacecraft to return home with only minimal orbit adjustments (minimizing the amount of propellant needed). The orbits of the Artemis missions will be similar to those of their Apollo predecessors in that they will also perform figure-eight flights that end in a “splash” in the ocean.
In other words, these missions will be one-way trips. But beyond returning astronauts to the Moon, assembling the Lunar Gateway, and establishing Artemis Base Camp on the surface, the long-term goal is to use the Artemis infrastructure to create a permanent human presence on the Moon. It’s also necessary to keep things profitable, which makes launching heavy payloads from the surface to the Moon inefficient. As co-author Professor Humi explained to Universe Today via email, their proposal envisions a shuttle that would orbit the Earth and Moon:
“One of [the ISS’] ‘functions’ is to avoid sending large payloads into low earth orbits. Instead, we send “capsules” with supplies and replacements for the astronauts. Accomplish [lunar settlements] with minimum cost, we need something similar to the ISS but with an orbit around the Earth and the Moon. This shuttle will never land on Earth or the Moon. Capsules from the Earth will mate with it when it is close to the Earth, and likewise, capsules from the Moon will mate with it when it is close to the Moon. This will avoid having to lift heavy loads from Earth or the Moon, and it will save a lot of money and resources.
However, the shuttle will need engines and propellants to keep this shuttle in orbit because it is subject to gravitational disturbances (from the Earth, the Moon and the Sun). While the Shuttle won’t require the massive thrusters and propellant tanks needed to free itself from Earth’s gravity, the engines and propellant add significant amounts of mass to a mission, driving up costs. To solve this problem, Humi and Carter considered maneuvers that would minimize fuel consumption while allowing the shuttle to circle the Earth-Moon system in a reasonable amount of time.
“The process we used to get our results was to develop appropriate mathematical models based on the gravitational forces of the Earth, Moon (and Sun) that impact the orbit of the shuttle,” said Humi. From there, they determined that a circular, elliptical orbit with perigee near Earth and apogee beyond the Moon would be the optimal trajectory. Only minimal thrust would be needed for trajectory corrections, negating the out-of-plane effects of solar gravity, which could be further reduced by ensuring that the orbital eccentricity remains close to zero.
This type of shuttle and trajectory, Humi said, is necessary for any plan to establish a permanent human center.
presence on the Moon, but could also lead to a thriving Earth-Moon economy:
“Currently there are plans for a permanent ‘outpost’ on the moon. This outpost will need supplies from Earth to function properly (food, medical computers, spare parts for the Robots, etc.) and an astronaut replacement mechanism). At the same time, it will send back to Earth elements that are very rare on Earth (for example, helium-3) which, according to all theoretical calculations, is the necessary fuel for a fusion reactor.
With the signing of the U.S. Commercial Space Launch Competitiveness Act of 2015 and the U.S. Commercial Space Launch Competitiveness Act Ordinance of 2020, the U.S. government has clarified that commercial activities on the Moon will include the resource extraction. In addition to securing mineral resources (such as rare-earth metals that are vital for electronics and digital devices), scientists have dreamed of the day when lunar sources of helium-3 would be within reach as this would allow the widespread use of fusion reactors. to meet our energy needs. Humi and Carter included a caveat in their study, saying their results would require further testing and verification. As they noted in their conclusions:
“It should be possible to design a control system that returns the craft to the designated orbit in order to compensate for disturbances that have not been taken into account in the analysis. It could be argued that one could guess that the shuttle’s circular orbit provides the optimal orbit in terms of thrust. Now this orbit has a maximum length trajectory. It therefore follows that the result obtained in this article, although it may be “intuitively clear “, is not necessarily obvious.
Further reading: arXiv
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