Ulybyshev Yu.PWhat are these points, why does their use in space projects seem to be so attractive, and has there been any experience in their use? Those were the questions the editorial board of the Korolev’s Planet website addressed to Doctor of Engineering Science Yuri Ulybyshev.

The interview is conducted by Oleg Volkov, deputy head of the Great Start project.

Volkov O.N.: Today’s guest of the Korolev’s Planet website is deputy director of a scientific and technological center of the Rocket and Space Corporation Energia, the head of the Space Ballistics department, Doctor of Engineering Science Yuri Petrovich Ulybyshev. Mr. Ulybyshev, good day!

Ulybyshev Yu.P.: Good day!

V.: Manned space systems in low-Earth orbit are no longer big news. In fact, they are quite routine. Recently, the world space community has been showing interest in a different kind of space projects, which propose to place space systems, including manned space systems, in so-called Lagrange points. This includes a man-tended space station project, a project of stations looking for dangerous asteroids monitoring the Moon.

What are Lagrange points? What is their advantage from the standpoint of celestial mechanics? What is the story of theoretical studies on this subject? What are the main results of the studies? 

U.: There are many natural phenomena in our Solar system which have to do with the motion of the Earth, Moon and planets. These include the so-called Lagrange points. In scientific literature they are more often called libration points. To explain the physics of this effect, let’s first consider a simple system. Imagine that there is Earth and there is the Moon flying around it in a circular orbit. And there is nothing else in the universe. This is the so-called restricted three-body problem. And its within the framework of this problem that we a going to consider a spacecraft and its possible motion.

The first thing that comes to mind is to consider what will happen if the spacecraft is on the line connecting Earth and the Moon. If we move along this line, we have two accelerations that are due to gravity: attraction of the Earth, attraction of the Moon, and in addition to this there is also centripetal acceleration due to the fact that this line continuously rotates. It is evident that at some point all these three accelerations, due to the fact that they are all differently directed and are all on the same line, may cancel each other out, in other words, this will be and equilibrium point. That’s a point which is called a Lagrange point or a libration point. In fact, there are five such points: Three of them are on the rotating line connecting the Earth and the Moon and they are called collinear libration points. The first one, which we have just discussed, is denoted by L1, the second is behind the Moon - L2, and the third collinear point - L3 is on the opposite side of the Earth with respect to the Moon. In other words, it lies on the same line, but in the opposite direction. Those are the first three points.

There are two more points which lie to both sides outside this line. These are called triangular libration points. All these points are shown in this figure (Fig.1). That’s a kind of an idealized picture.

Libration points in the Earth-Moon system
Fig.1 Libration points in the Earth-Moon system

Now, if we place a spacecraft at any of these points, within the framework of such a simple systems it will stay there forever. If we move a little bit away from these points, there might exist periodic orbits in their vicinity, which are also called halo orbits (see Fig.2), and the spacecraft might follow such peculiar orbits around that point. If we talk about libration points L1, L2 in the Earth-Moon system, the period of these orbits will be about 12 - 14 days and they can be selected in various ways.

Halo orbits in the Earth – Moon system
Fig.2 Halo orbits in the Earth – Moon system

In fact, if we come back to real life and this time consider the exact problem statement, everything turns out to be much more complicated. That is, a spacecraft cannot stay in such an orbit for a long time, let’s say for longer than one period, because:

- first of all, the Moon’s orbit around Earth is not circular – it is slightly elliptical;

- in addition to this the spacecraft will be affected by Sun’s gravity and sunlight pressure.

As a result, the spacecraft will not be able to remain in such an orbit. Therefore, from the standpoint of making a spacecraft fly in such an orbit, the spacecraft needs to be first put in the desired halo orbit and then periodically perform station-keeping maneuvers to maintain it.

Compared to interplanetary missions, propellant requirements for maintaining such orbits are fairly small, no more than 50 – 80 m/s per year. For comparison, I could say that station-keeping of a geostationary satellite also requires 50 m/s per year. But in that case we are keeping a geostationary satellite near a fixed point – that problem is much simpler. Here, we will have to keep a spacecraft close to such a halo orbit. In principle, this is doable. Moreover, this is doable using low-thrust engines, and each burn it’s just a fraction of a meter or a few m/s. This suggests a possible use of orbits around these points for space missions, including manned missions.

And now let’s consider why these points are so advantageous and interesting from the standpoint of practical applications to space flight.

You may all remember the US project Apollo, where they used a circumlunar orbit to descend from it a spacecraft to the lunar surface, which after landing and spending some time on the surface returned to the circumlunar orbit and then they flew back to Earth. Circumlunar orbits are of some interest, but they are not always convenient for manned spaceflight. We may have all kinds of contingencies, and besides, it is only natural that we want to study the Moon not only in some particular area, we want to study the entire Moon. Eventually, it turns out that the use of circumlunar orbits places a number of constraints. The constraints are put on the launch dates, on the dates of return from the circumlunar orbit. The circumlunar orbit parameters may depend on the available propulsion performance. For example, polar regions may turn out to be inaccessible. But what is probably the most important argument in favor of space stations in the vicinity of libration points is that:

- first of all, we can launch from Earth at any moment in time;

- if the station is in a libration point, and cosmonauts are supposed to fly to the Moon, from the libration point, or, to be more precise, from the halo orbit they can reach any point on the surface of the Moon;

- now, after the crew has arrived: From the standpoint of manned spaceflight, it is very important to provide a quick crew return capability in the event of some contingencies, crew illness, etc.. If we are talking about a circumlunar orbit, we may have to wait, let us say, 2 weeks for the launch window, but here we can launch at any moment – from the Moon to a station at a libration point and then to Earth, or, in principle, we could launch directly to Earth. Such advantages are clearly visible.

We can choose which one to use: L1 or L2. There are certain differences. As you know, the Moon always shows us the same side, because the period of its axial rotation is the same as period of its orbital revolution around Earth. As a result, the far side of the Moon can never be seen from Earth. Under these circumstances, we can select such a halo orbit, that there’ll always be line of sight between the spacecraft and the Earth, and the spacecraft will always be able to communicate with the far side of he Moon, observe it or perform some experiments related to it. Thus, space stations stationed at either L1 or L2 point may have certain advantages for manned spaceflight. It is also interesting to note that it is possible to perform a so-called low-energy transfer between halo orbits of L1 or L2, requiring literally just 10 m/s, and we’ll fly from one halo orbit to another.

V.: Mr. Ulybyshev, I have a question: L1 lies between the Moon and the Earth, and, as far as I can understand, is more convenient from the standpoint of communications between the space station and the Earth. You said that L2, the point which is behind the Moon is also of interest for space missions. But how can communications with Earth be provided, if the station is placed at L2? 

U.: Any station staying in orbit in the vicinity of L1 has the capability to communicate with Earth at all times, in any of the halo orbits. For L2 it’s a little bit more complicated. This has to do with the fact that a space station travelling along a halo orbit may get hidden from Earth by the Moon, and then communications become impossible. But it is possible to establish such a halo orbit that will always provide the capability to communicate with Earth. This is a specially selected orbit.

V.: And it isn’t difficult to do? 

U.: Yes, it is doable, but since you can’t get something for nothing, this would require a little bit more propellant. Let’s say that instead of 50 m/s it will be 100 m/s. This is probably not the most critical issue.

V.: I just want to make sure. You mentioned that it doesn’t take much energy to fly from point L1 to point L2 and back. Is it right to assume that it would make no sense to construct two stations in the vicinity of the Moon, that it would be sufficient to have one station which it would take very little energy to move to the other point? 

U.: Yes, in fact our partners in the International Space Station propose for discussion as one of the options for further development of the ISS project a space station capable of flying from L1 to L2 and back. It is quite feasible and manageable from the standpoint of the transit time (let’s say, two weeks) and it can be used for manned spaceflight.

I would also like to say that in actuality the missions in halo orbits have at present been implemented by the US under project ARTEMIS. That was two or three years ago. In that case, two spacecraft were flying in the vicinity of L1 and L2 points maintaining that kind of orbits. One spacecraft did make a transfer from L2 to L1. All this technology has been implemented in practice. Of course, I wish that had been done by us.

V.: Well, for us, the best is yet to come. Mr. Ulybyshev, the next question. From what you said, I understand that any space system consisting of two planets has Lagrange point, or libration points. Are there any such points in the Sun-Earth system, and what might be the attractive aspects of those points? 

U.: Yes, that’s absolutely correct. The Earth-Sun system also has libration points. Their total number is also five. In contrast to the circumlunar libration points, the missions to those points might be attractive from a standpoint of achieving a different kind of objectives. To be more specific, of the greatest interest are L1 and L2 points. The L1 point lies in the direction from the Earth to the Sun, while L2 point lies in the opposite direction on the line connecting the Earth and the Sun.

And the first mission to L1 point in the Sun-Earth system was accomplished in 1978. Since then, several space mission have been carried out. The recurring theme in such projects had to do with sun observations: solar wind and solar activities, among other things. There are systems, which use warnings about solar activity that has an effect on Earth: on our climate, on people’s well-being, etc. That’s what L1 point is all about. It is of interest to mankind first of all because it provides an opportunity to observe the Sun, its activity and processes that occur on the Sun.

Now, about L2 point. The L2 point is also of interest, first of all, for astrophysics. This has to do with the fact that a spacecraft placed in the vicinity of this point can use, for example, a radio telescope that will be shielded from the solar radiation. It will be pointed away from the Earth and the Sun, and may provide clearer astrophysical observations. They won’t be corrupted by interference from the Sun or some reflected emissions from Earth. It is also interesting to note that since we move around the Sun and make a full revolution in 365 days, such a radio telescope can survey any direction in the universe. Such projects also exist. Currently the Physics Institute of the Russian Academy of Sciences is developing one such project called Millimetron. A number of missions has also been carried out to this point and the spacecraft are flying.

V.: Mr. Ulybyshev, from the standpoint of searching for dangerous asteroids which might threaten Earth, which point is best suited for placing into them the spacecraft watching out for dangerous asteroids? 

U.: Generally speaking, I do not think there is a straightforward and obvious answer to this question. Why? Because asteroids moving through the solar system are sort of grouped into a number of families, they have very different orbits and, in my opinion a spacecraft for observing one type of asteroids could be placed in a circumlunar point. As for the Sun-Earth libration points, this could also be studied. But it seems to me that it would be difficult to give such a straightforward and clear-cut answer as: "such and such point in such and such system”. But in principle, libration points could be attractive from the standpoint of protecting Earth.

V.: Did I get it right, the solar system has many more interesting places, not only Earth-Moon, Earth-Sun systems. What other interesting places in the solar system could be used in space projects? 

U.: The fact is that the solar system the way it is now, in addition libration point effects, has a number of effects that are due to the relative motion of the bodies in the solar system: of Earth, planets, etc. Unfortunately, I don’t know of any studies on this subject done here in Russia, but, primarily Americans, and also Europeans, have found that in the solar system there exist the so-called low-energy transfers (these studies, being very complicated both in terms of the math and the amount of computation, require large supercomputers).

For example, coming back to the L1 point in the Earth-Moon system. With reference to this point it is possible to construct (and this is attractive for unmanned spacecraft) transfer trajectories covering the entire solar system, requiring burns that are small in terms of interplanetary travel, somewhere on the order of several hundred m/s. And then this spacecraft will be set in slow motion. And the trajectory can be constructed in such a manner that it will visit a series of planets.

In contrast to direct interplanetary flights, this will be a time-consuming process. Therefore, it isn’t well-suited for manned spaceflight. But it could be very attractive for unmanned spacecraft.

Here in the picture (Fig.3) you can see an illustration of these transfers. The trajectories sort of interlink with each other. Halo-orbit transfer from L1 to L2. It doesn’t cost very much. It’s the same thing there. We are sort of sliding along this tunnel and at the point where it interlinks, or is close to interlinking, with another tunnel we perform a small maneuver and fly over to the path to another planet. Actually, it's a very interesting field of research. They call it the Superhighway (at least, that’s the term used by the Americans).

Our solar system is riddled with low-energy transfer tunnelsFig.3 Our solar system is riddled with low-energy transfer tunnels
(the picture is borrowed from a foreign publication)

It was actually partially implemented by the Americans within the framework of the GENESIS project. They continue to work in that area. I think this is one of the most promising areas for advancement of space flight. Because with those engines or thrusters that we currently have, I mean both high-thrust engines and electrical propulsion thrusters (which for now have very low thrust and require plenty of power), we cannot make any significant advances in the solar system exploration. And these transfers that take many years or even decades might be of great interest for exploration. Just as it is in the case of Voyager. It has been in flight, as far as I can remember, since 1978 or 1982 (since 1977 – Ed.), and it is now beyond the boundaries of the solar system. This area or research is very complex. First of all, it’s complex from the standpoint of math. In addition to this, the flight mechanics analysis and computations require a huge amount of computing resources, in other words, it’s doubtful that you can do this on a personal computer, you need to use supercomputers.

V.: Mr. Ulybyshev, is it possible to use a system of low-energy transfers to organize a space solar patrol – a permanent system for solar system monitoring with the existing propellant constraints? 

U.: Even between the Earth and the Moon, as well as, for example, between Earth and Mars, and Earth and Venus there exist so-called quasi-periodic trajectories. Similarly to our discussion of the halo-orbit, which exists in the case of the idealized statement of the problem without perturbations, as soon as real perturbations are applied, we need to correct the orbit in some way. These quasi-periodic orbits also require small delta Vs in terms of interplanetary missions, where characteristic velocities are hundreds of m/s. They can be attractive from the standpoint of space patrol for asteroid observations. Their only drawback is that they are ill-suited for today’s manned space flight because of the long-duration transfers. But from the standpoint of energy requirements, even with the engines that are available now in this century, it is possible to implement some fairly interesting projects.

V.: Let me make sure I got you right: you propose to use libration points in the Earth-Moon system for manned vehicles, and the points you just mentioned for automatic probes? 

U.: I would like to add one more thing, a space station at L1 or L2 can serve for launching small spacecraft (the Americans call such an approach a gateway to the universe). The spacecraft may use low-energy transfers to move around Earth in some periodic manner at very large distances, or travel to other planets or even fly around several planets.

V.: If we give free play to our imagination for a moment, in the future the Moon will become a source of space fuel, and the lunar fuel will be delivered to a libration point in the Earth-Moon system, where spacecraft will be fueled and sent on space patrol all over the solar system. 

Mr. Ulybyshev, you told us about some very interesting phenomena. They were studied in the US (at NASA), but does anybody in our country work on these projects? 

U.: As far as I know, probably nobody is working on the projects related to libration points in the Earth-Moon system. But they do work on projects related to the libration points in the Sun-Earth system. In our country a great deal of experience in this field is accumulated at the Keldysh Institute for Applied Mathematics belonging to the Russian Academy of Sciences, the Institute for Space Research, some universities in Russia are trying to do some work on these problems. But there is no systematic approach, no big program, because such a program should start with personnel training, very highly skilled personnel at that. In the traditional curricula for space ballistics and celestial mechanics, the very subjects of spacecraft motion in the vicinity of libration points or low-energy transfers are virtually absent.

I should note that back in the days of the Soviet Union such programs were more or less actively pursued, and, as I have already, there were specialists at the Institute for Applied mathematics, IKI (Space Research Institute), FIAN (Lebedev Physical Institute). Today many of them are already at an advanced age… And I don’t see too many young people working on these problems.

I mentioned Americans not because I just wanted to praise them. The matter is, in the United States these problems are studied by very large teams. First of all, there is a big team at NASA’s JPL lab, and they have carried out probably most of the US interplanetary spaceflight projects. In many US universities, in other centers, in NASA, there is a large number of specialists with good training, with good computing facilities. Working on this problem, in this area, they advance on a very wide front.

Unfortunately, in our country, this subject is sort of neglected. So even if such a program appeared in Russia, and it would be of great interest, it would have taken quite a lot of time to organize such work, starting with personnel training and ending with studies, analyses, development of the proper type of spacecraft.

V.: Mr. Ulybyshev, which universities in our country train specialists in celestial mechanics? 

U.: As far as I know, they have chairs of celestial mechanics at Moscow State University, at St. Petersburg University. They do have the specialists there. How many, I’m not certain.

V.: Because in order to implement it in practice you need to become an in-depth specialist, and for that you need to have special training. 

U.: And to be very well instructed in mathematics.

V.: OK. And could you give a list of literature, which would help those people who at the moment do not have the specialized mathematical training? 

U.: As far as I know, there has been one monograph on libration points in Russian written by Markeev. If I remember right, it is called “Libration Points in Celestial Mechanics and Space Dynamics". It was published somewhere around 1978. There is a reference book edited by Duboshin called “Handbook on Celestial Mechanics and Astrodynamics”. It went through two print runs. As far as I can remember, it also covers these subjects. The rest can be found, first of all, on the web site of the Institute of Applied Mathematics, where they have an electronic library and their own preprints (papers published separately) on this subject. These can be freely accessed on the Internet. Using a search engine, you can find and view the relevant preprints. There is plenty of material in English available on the Internet.

V.: Thank you for a very interesting discussion. I hope that this subject will be of interest to the readers of our web site. Thank you very much! 

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