Which way to the moon?

Recently, the "Artemis 1" has come to a successful conclusion. Although the preparation stage was full of twists and turns, the entire implementation process was exceptionally smooth. As the saying goes, "there are thousands of roads, but safety comes first", so how many roads are there to fly to the moon? To understand this question, we must start from the total number of steps from the earth to the moon.

Generally speaking, there are three steps to get from the Earth to the Moon: the first step is to break free from the Earth's gravity and become a satellite, that is, to enter the Earth's orbit; the last step is to land on the Moon, before which you must first be captured by the Moon's gravity, that is, to enter the Moon's orbit. The third step can be regarded as the reverse process of the first step, similar to the takeoff and landing of an airplane. The second step between these two steps is to fly from the Earth to the Moon. The flight trajectory connects the Earth's orbit at one end and the Moon's orbit at the other end, so it is also called the Earth-Moon transfer orbit.

There are many things to know about choosing this transfer track, which is very similar to the dilemma we have when choosing flights. Although the departure and destination are the same, the shortest flight is the most expensive, and the longest flight is the cheapest. Sometimes, in order to save money, we even have to fly to a farther place first and then transfer to the destination. Let's take stock of the transfer methods between the earth and the moon.

"Direct transfer" takes the shortest time

Direct transfer is the fastest and most commonly used transfer method to the moon. The carrier first sends the spacecraft (probe or manned spacecraft) to the moon into a near-Earth parking orbit, and then the spacecraft's own main engine or upper stage rocket sends it into the Earth-Moon transfer orbit. This orbit looks like a steep curve connected to the Earth and Moon orbits at both ends. It is straight and the path is very short, so it is called "direct transfer". Since the pursuit is the shortest path, the spacecraft must constantly correct its flight direction and increase its flight speed during the flight to the moon, which requires the spacecraft to carry a lot of fuel. The more fuel the spacecraft carries, the heavier the launch weight, the larger the tonnage of the carrier required, and the higher the cost of the entire space mission to the moon. In order to save the spacecraft's fuel as much as possible, the Hohmann transfer orbit is a more suitable economical direct transfer orbit that can be used by unmanned lunar probes. Using different direct transfer orbits, the flight time varies from two days to five days. Since there is a certain angle between the lunar orbit and the Earth's orbit, it is more appropriate to launch direct transfer spacecraft at launch sites in mid- and high-latitude areas. This is why most of China's lunar probes are launched in Xichang.

Direct transfer is very suitable for manned lunar landing activities due to its short flight time. Astronauts can minimize their exposure to cosmic radiation. It is also understandable that the initial lunar exploration activities to verify the subsequent manned lunar landing activities also use direct transfer. After all, astronauts cannot be used as guinea pigs. Unmanned probes must first run the route proficiently. Therefore, the Soviet Union's "Luna" probe series, the spacecraft in the "Probe" series that perform lunar exploration missions, the United States' "Ranger" series, "Prospector" series, and "Lunar Orbiter" series probes, and China's "Chang'e" series probes all use direct transfer orbits to fly to the moon. At present, all spacecraft in the "Apollo" series, the only successful lunar landing by humans, not only use direct transfer orbits, but also directly give birth to the largest and heaviest launch vehicle-"Saturn V".

Economical “indirect transfer”

The higher the spacecraft is sent into the Earth's orbit, the more energy it consumes. Although the orbital speed of the high orbit is very low, the orbital energy is very high. Flying to the moon from here will save a lot of fuel carried by the spacecraft itself.

Of course, if we send a lunar exploration spacecraft to a high orbit, it will be a bit of a loss, but if we use the "residual capacity" of the high orbit launch to carry it, it will be "economical and applicable". The European Space Agency highly respects this kind of "indirect transfer" and has conducted a lot of research and attempts. The altitude of the geosynchronous orbit is 360,000 kilometers, and the average distance between the earth and the moon is 380,000 kilometers. It seems very suitable to fly to the moon from here.

However, due to the large angle between the geosynchronous orbital plane and the lunar orbital plane, the spacecraft has to spend an astonishing amount of fuel to change its flight trajectory when transferring between these two planes. Its economy is not outstanding compared to direct transfer. Therefore, ESA scientists have come up with another indirect transfer method, which is to fly to a higher Earth orbit, so high that the orbital apogee reaches the Earth-Sun Lagrange L1 point, which is 1 million kilometers away from the Earth, more than twice the farthest distance between the Earth and the Moon. The spacecraft completes the transfer from the Earth's orbital plane to the lunar orbital plane there, and then switches to the lunar high elliptical orbit, which will save a lot of fuel. This process is very similar to climbing a difficult but not too high mountain. You have to take a cable car to the halfway point of a higher mountain that is easy to climb, then climb to the top of the mountain by yourself, and then use a parachute to land from the top of the higher mountain to the not too high mountain.

On September 27, 2003, the European Space Agency's "Intelligence 1" lunar probe was launched on the "Ariane 5" launch vehicle. This lunar probe is very small, with a cross-section of only 1 square meter, and it carries only 80 kilograms of fuel. This fuel is not traditional hydrocarbon rocket fuel but liquefied xenon. After reaching the geosynchronous orbit, "Intelligence 1" began to use its own ion thrusters to slowly accelerate along an increasingly flat elliptical orbit, circling the earth. After more than a year, it finally successfully passed the Lagrange L1 point on November 11, 2004, and began to "descend" toward the lunar orbit. Finally, four days later, it successfully reached the near-moon orbit of the moon and began to conduct remote sensing measurements of the moon along the polar orbit. During the more than ten months of flying to the moon, "Intelligence 1" only consumed 60 kilograms of xenon fuel, which fully verified the feasibility and sufficient economy of using the geosynchronous orbit for "indirect transfer" between the earth and the moon.

The magical "weak equilibrium boundary transfer"

On the basis of the above "indirect transfer", if we want to further squeeze the economy, we must save the energy used to change the orbit from the transfer orbit to the lunar orbit. As we all know, energy can only be converted and cannot disappear, so where does this saved energy come from? We need to use a little dark force, that is, at the "weak equilibrium boundary", borrow a little force from the gravity of the sun or the moon. This "weak equilibrium boundary" refers to the area where the gravity of "Earth-Sun" or "Earth-Moon" is balanced. A very small disturbance can change the trajectory of an object. This area is also often used as a "chaotic orbit" area, and it is easy to produce orbital changes. Since the previous "indirect transfer" orbit plan has already flown to the Lagrange point, it is better to use the power of the sun or the moon, use gravity to complete the transition to the lunar orbit, and save some fuel for the transfer from the apogee to the lunar orbit. This is the "weak equilibrium boundary" transfer that sounds quite mysterious. In fact, Japan has successfully used this method of flying to the moon when it launched the "Hiten" lunar probe in 1990. This probe, which is smaller than the "Smart 1", not only successfully completed the lunar polar orbit after more than half a year of flight, but also released a sub-satellite called "Hagoromo" in the lunar orbit, which shows how fuel-saving this Earth-Moon transfer orbit is.

Back to the manned lunar mission at the beginning of this article, in order to shorten the time on the road and reduce the impact of many uncertainties on astronauts, this type of mission often uses a direct transfer orbit, which is the safest and most convenient.