The Japanese needed help. On 24th January 1990 the country’s Institute of Space and Aeronautical Science had launched its first lunar probe, Hiten. It was supposed to fly close to the Moon before launching a second probe, Hagoromo, which would orbit the Moon and transmit data back to Earth.

Every part of the launch had gone according to plan with one exception — Hagoromo was silent. ISAS could see Hagoromo but they couldn’t speak to it, meaning the first Japanese probe to orbit the Moon would be an embarrassing dud. Somehow the mission needed to be salvaged.

A plan was hatched — if they could find a way to get Hiten out of its flyby trajectory and into the Moon’s orbit then the mission could still be a success. However, there were two problems with this plan: the probe’s engines were too small, and it didn’t have enough fuel. Hiten hadn’t been designed to reach the Moon by conventional means.

The team contacted NASA’s Jet Propulsion Laboratory for help. The answer that came back surprised them. They could get Hiten to the Moon but they needed to fly 1.5 million kilometres in the opposite direction.

Going the wrong way to get there

The idea was Edward Belbruno’s and was the first ever example of a Low Energy Transfer, a technique that has revolutionised space travel, paving the way for our first manned mission to Mars. It also opened up the prospect of what some scientists call the Interplanetary Transport Network.

Belbruno had been hired by JPL five years earlier in 1985. “I arrived at JPL new to the engineering world and I was thrown into designing trajectories for the Galileo mission to Jupiter,” he told me. “The first year there didn’t work out quite as I had planned.” His job on the mission was calculating hundreds of different routes for NASA’s probe. It was mechanical work and not particularly rewarding. “I was more of a creative thinker and I got bored pretty easily.”

After a year he was taken off the Galileo mission and moved to a pet project of General Lew Allen, director of JPL at the time. It was a theoretical project, Allen wanted to see if you could get a very tiny spacecraft, a “Getaway Special Cannister”, to the Moon using electric engines only. “The people working on it at the time found that when it got to the Moon it was simply going too fast, namely a kilometre a second, to achieve a stable orbit and the little engines were too small to slow it down.” In each simulation it would either smash into the Moon or whizz past.

“I realised that to get a little spacecraft like that captured by the Moon, we would have to use a new method,” he explained. “The engines were too small to get it captured using thrust to slow it down. They can only get 14 m/s for a day and it would need 1,000 m/s. The spaceship was very much deficient for doing it with classical means. The only way to have it captured by the Moon was to have it fall into the Moon and capture automatically with no engines at all.”

Everyone working on the project thought it was impossible.

“Well, I found a way to do it.”

Image from Lunar Capture Orbits, A Method of Constructing Earth Moon Trajectories and the Lunar Gas Mission by Edward Belbruno

Belbruno calculated that if you launched the probe from the Earth while the Moon was on the far side of the planet and then allowed the Earth’s gravity to start pulling the probe back towards our planet it would drag it into the path of the Moon’s orbit around the Earth, transferring it from the Earth’s gravitational pull to the Moon’s. The probe would be going fast enough and travelling at an angle that would allow it to be captured into the Moon’s orbit without the probe firing its engines at all, something called a ballistic capture.

What’s more, the trajectory Belbruno had designed used a fraction of the fuel that a direct launch to the Moon would use, a trajectory called the Hohmann transfer. The downside was it took much longer than the three days that a Hohmann transfer traditionally takes — Belbruno’s trajectory took two years. “A year and a half to spiral away from the Earth and six months to spiral down to the Moon using this little engine,” he told me.

That first 18 months takes the cannister out to 100,000 km from the Earth, at which point the engines are turned off for two weeks, letting it coast for 70,000 km under the influence of the Moon’s gravitational pull. When it’s 30,000 km from the Moon you switch the engines back on and direct it into a complete capture. “That coasting part is a low energy transfer,” explains Belbruno.

There was still a lot of work to be done on the theory, Belbruno didn’t fully understand the capture region around the Moon — the area where you aimed the probe to intersect with Moon and begin orbiting. At the time he called it the “Fuzzy Boundary” but we now know it as the “Weak Stability Boundary”. He would continue his research till 1990.

His discovery wasn’t much appreciated by the JPL. “They thought it was ridiculous at the time,” he said. “It took so long and the methods were brand new, they just didn’t understand them.” But they recognised that, in theory, it could work. This worried them.

“They thought the ideas I was working on weren’t going to come to fruition,” Belbruno explains. “I was called into one of the associate directors offices at the JPL and he told me not to work on the ballistic capture methods anymore. That was in 1989. I asked why and he said ‘We like to make large rockets. They employ a lot of people, we have 7,000 people that work here and we would like to make larger rockets. If you succeed in finding shorter routes for these ballistic transfer trajectories then we’ll make smaller rockets and employ fewer people.’ They knew the ballistic capture worked because they’d seen it work [in my paper] but they were definitely worried that I’d find a flight time that was short. That threatened them. A year later I was asked to leave.”

That was in January 1990, the same month that Japan launched Hiten.

The first spacecraft on the superhighway

“It was an engineer who told me about the Hiten mission,” Belbruno told me. “Japan had, in January when I had all my problems at the JPL, launched two spacecraft into Earth’s orbit Hagoromo and Hiten. Hiten was a relay, it was never designed to go to the Moon, Hagoromo was and it went off on a Hohmann transfer on a standard three day route and, as far as I knew, it didn’t get there. He’d been asked by the Japanese quietly to see if he could get the other craft, Hiten, to the Moon. He’d looked at a Hohmann transfer and it wouldn’t work, there was too little fuel for anything like that. It had enough for 100 m/s and to use the Hohmann transfer to get capture it would need 1,000 m/s. Ten percent of what they needed.

“He said ‘I’ve heard about your work and I’m desperate, at this point I’ll try anything.’ I didn’t like this guy very much. But as soon as he said that it was like a light went off, all this stuff from the previous five years I couldn’t figure out, suddenly I knew how to do it. In all previous work I’d never modelled the sun’s gravity because it was so far away.”

Belbruno got Hiten to the Moon by spiralling it out 1.5 million km from the Earth, allowing our planet’s gravity to slow the probe. It manoeuvred into position and the engines were turned off. Hiten was then pulled back towards Earth and into a capture trajectory with the Moon.

But the Earth and Moon weren’t the only variables in this calculation. Hiten had to be manoeuvred so far from the Earth because it was being moved into a region where the Sun reduced the influence of Earth’s gravity. When explaining the procedure to the LA Times, James K. Miller, who helped Belbruno with the Hiten trajectory, likened it to throwing a ball high into the air. Near the peak of the ball’s ascent, where it’s moving slowest, it’s most susceptible to other forces, a light wind, say. When Hiten was so distant from the Earth and moving in a region where it was little affected by gravity it’s engines could manoeuvre into a new trajectory more cheaply than when it was near the Earth.

“Instead of the two years flight time I had planned previously, I did exactly what the [associate director] didn’t want to happen, I did it in four months.” Unsolicited, Dr Belbruno faxed his flight plan to ISAS. “Luckily, because the JPL was cooperating with the Japanese on this, the Japanese were more than interested to see the solution we found. They looked at it seriously and they verified it that weekend, it was sent the first weekend of June. They faxed back a note saying ‘we’re going to do it.’ Over the next couple of months they got it approved by the Ministry of Science and they fired the engines up in April of 1991. It got there on October 2nd 1991. That was the first demonstration ever of a Low Energy Transfer to the Moon using the so-called Interplanetary Super Highway.”

Where the Weak Stability Boundary can take us

The Interplanetary Superhighway, or Interplanetary Transport Network, simply refers to the many possible Low Energy Transfer routes between large planetary bodies in our solar system. “This transfer is really the magic trajectory that unlocks space exploration near the Earth,” says Belbruno. For you to understand why it works, I’ll need to explain the Weak Stability Boundary.

The Weak Stability Boundary is a region around any large body where objects will be “weakly captured” by the body orbited. These regions are huge, even around relatively small bodies. In the case of our Moon it extends out to about 100,000 km from the surface. It’s not as simple as directing an object at the Moon to get an automatic capture, “you have to arrive at the Moon at the correct position and at the correct velocity,” says Belbruno. If you do that that “you automatically capture.”

The reason this region exists is because of large bodies’ competing gravitational fields. Whenever you’re moving about the Moon your spacecraft is being pulled towards the surface by its gravity but the Earth is also pulling you away. There are a few places where these forces balance exactly, known as Lagrangian Points, but more often one bodies’ gravity will have dominance over another. “It’s a very delicate motion,” says Belbruno. “If you have a spaceship on the way to the Moon and you get captured in the Weak Stability Boundary it’s very tenuously captured and it won’t stay captured for very long. It’ll stay captured for maybe a week or two, or a few days or a few hours. The beauty of these applications, and this is the miracle of a Weak Stability Boundary trajectory, is that you can stabilize your orbit around, say, the Moon with a very tiny amount of fuel.”

So, once Hiten had been weakly captured by the Moon’s gravity, ISAS was able to adjust the probe’s position and velocity with its small engines to place it into a more stable orbit. It stayed in the Moon’s orbit from October 2, 1991 until it was deliberately crashed into the surface on April 10, 1993.

The Weak Stability Boundary and Low Energy Transfers don’t just allow for cheap space travel. It also has implications for the history of the solar system. Going back to Belbruno’s paper in 1986, he suggested then that “it is conceivable that [Mars’ moons] Phobos or Deimos could have been captured by Mars by such orbits. Similarly, some of the satellites of Jupiter, as well as those of the other outer planets, could have been captured in the same way. For this to be the case, these satellites must have not only been simply captured but captured in such a way that the motion about [the planet] is stable. These conditions are difficult to achieve, but the chances of achieving them were probably much higher at the early stages of the solar system formation due to a possible large number of objects throughout the solar system.”

A very unusual orbit

Besides automatic capture, the Weak Stability Boundary includes two points of particular interest — the Lagrangian points L1 and L2. They’re two points where, Belbruno tells me, “if you put something there it will stay there, relative to the Moon and Earth, forever.”

Lagrangian Points aren’t actually fixed points in space, they’re a particular orbital trajectory, and they exist between every large body and the body it orbits.

Normally, the closer an object is to a large body the faster it must travel to maintain its orbit. Mercury travels much faster than Earth to keep itself from being drawn into the Sun. This isn’t the case with an object that’s at a Lagrangian point. A probe at Earth-Sun L1, the Lagrangian Point between our planet and the Sun, will orbit the Sun at the same velocity as Earth. This means that the probe will maintain its position in relation to the Earth throughout its orbit of the Sun.

There are five Lagrangian Points about any two large bodies, L1 through L5, but only L1 and L2 are within the Weak Stability Boundary.

In his paper on the Interplanetary Transport Network, Shane. D. Ross illustrates how L1 and L2 work using a toy gravity well. You might have seen them before, they’re a funnel where you run a marble round the exterior. The marble will move round the slope of the funnel, in an ever-tightening spiral till, eventually, it falls down the hole in the centre. That is, unless it is moving fast enough to maintain its position on the funnel. A marble moving at the right speed would orbit the hole in the centre. The closer it is to the centre the faster it has to go to maintain its orbit. All the planets in our solar system that orbit the Sun are examples of these fast-enough marbles. They are moving at a velocity that keeps them from moving towards the Sun.

A gravity well at Rueben H. Fleet Science Center

However, our solar system is more complex than that — every large body has its own gravity well, too. Replace those planet-marbles with smaller funnels embedded into the plastic of the larger funnel. They’re moving around the surface of the funnel at the same speed as the marble they replaced were. These smaller funnels represent each planet’s own gravity well. If you were to drop a new marble into the funnel, representing an asteroid, say, it would spiral towards the centre as before but it might sometimes come into contact with one of these smaller planet-funnels. Sometimes the asteroid-marble will fall down these smaller funnels, not able to escape the incline of their slope.