Why did the U.S. Apollo 11 lunar spacecraft complete the entire process of launching, landing on the moon, and returning to Earth in 8 days and 3 hours, and is this speed reasonable?
In the past two days, many, many friends have raised questions in the comment area, feeling that this speed is too fast, which obviously violates "common sense" and is another "strong proof" of the US moon landing fraud.
That's a good question, let's do the math.
The distance between the earth and the moon is more than 384,400 kilometers, except for their stay on the surface of the moon for 21 hours and 36 minutes, the time really left for them to be on the road is only 174 hours, that is, in more than 7 days, 380,000 kilometers to fly back and forth, with an average speed of 4,418 kilometers per hour, and about 1,227 meters per second, is it possible?
For example, this old brother complained that "the United States built a manned vehicle 50 years ago that is more than 3 times the speed of sound and can fly continuously for 96 hours (in space)", which he found incredible, and seemed to go against his instincts.
We all know that Yuri Gagarin of the Soviet Union was the first person to fly into space, but in fact he also had the title of the fastest man in the world relative to the Earth at that time.
How fast is it, about 7.9 kilometers per second, this is the first cosmic velocity, and only when the first cosmic velocity is reached, can we get rid of the gravitational pull of the earth and circle around the earth.
Okay, let's open the junior high school physics textbook, and the law of circular motion tells us that at this time, the engine of the spacecraft does not need to be started at all to maintain a circular motion around the earth, because the earth's gravity just provides the centripetal force of the spacecraft.
So what happens if I have to speed up? You'll notice that the ship starts to throw out, and the trajectory becomes an ellipse.
The faster you go, the longer the ellipse gets, and the farthest end will get farther and farther away from the earth, and when your initial speed is fast enough, the farthest end becomes infinite.
Your ellipse can no longer close, and this velocity is the escape velocity at which you completely fly out of the Earth, which is the second cosmic velocity, which is about 11.2 kilometers per second. At this rate, you'll say goodbye to Earth.
But if I just want to go to the moon, I don't need to reach the escape speed of the earth, I just need to make my elliptical orbit long enough, how long, 380,000 kilometers long, just put the moon in, right?
Congratulations, you've discovered a theoretical Earth-Moon transfer orbit, which is the arc edge of an ellipse.
Note that you only need to start at about 10.9 kilometers per second (the following velocities are relative to the Earth's coordinate system), and then, click, you can turn off the engine, and then you can glide to the moon with gravity. This is one of the most simplified states of space dynamics.
The mainland's Long March 5 rocket accelerated Chang'e-6 to an initial speed of 10.9 kilometers per second, and entered an elliptical orbit with a perigee of 200 kilometers and an apogee of about 400,000 kilometers, and then the rocket completed its mission.
However, we only considered the gravitational pull of the earth just now, in fact, there are also the gravitational force of the moon, the sun and some other interference errors, if these factors are added, it will have to be slightly corrected halfway, which is why Chang'e-5 and Chang'e-6 have carried out two orbit corrections in the middle.
Note: This statement is a simplified model that only considers the Earth's gravity, but in fact, after about 66,000 kilometers from the Moon (Lagrange point), the Moon's gravity will dominate and the flight trajectory will become the Moon's ellipse, but the principle is the same.
Then someone has to ask, if I maintain a speed of 10.9 kilometers per second, it will only take 10 hours to fly to the moon?
Very good, let's draw the second important point, when Chang'e-6 flies along this elliptical orbit, the speed is not constant, but has been decreasing.
Why? You can open our freshman physics textbook, Kepler and his three laws.
Kepler's first law is the law of ellipse, the orbit of all celestial bodies (planets) around the central celestial body (the sun) is elliptical, and the orbit of Chang'e-6 to the moon is simplified to a part of the ellipse, and the earth is one of the focal points of the ellipse.
Kepler's second law, also known as the law of area, states that the line between the planet and the sun sweeps over an equal area in equal time.
That is, the closer you are to the focal point, the shorter the connection and the faster the speed of sweeping; The farther away from the focal point, the longer the line is, and the slower the speed of the sweep, so that the area swept per unit time will be equal.
In other words, when the Chang'e-5 rocket sent Chang'e-6 to perigee, it was the fastest, 10.9 kilometers per second, and then in the state of "gliding", the speed has been decreasing. When it reaches apogee, it is the slowest and can be calculated to fall to about 2.7 kilometers per second.
There is another detail here, if you don't brake on the moon, then Chang'e-6 will fly back again. Because the escape speed of the moon is about 2.4 kilometers per second, the speed of Chang'e-6 apogee exceeds this value, and the moon cannot tie it.
Therefore, on May 8, the Chang'e-6 probe carried out ignition braking, reducing its speed by more than 300 meters per second relative to the moon, so that it was lower than the lunar escape speed, so it circled the moon.
Okay, now everyone has an idea of how Chang'e-6 flew to the moon, to sum up, the rocket took off and accelerated, gave Chang'e-6 an initial velocity of 10.9 kilometers per second at perigee, and then followed an elliptical orbit, slower and slower, and finally flew to the moon, and then stepped on the brakes, the process took about four days.
As for Chang'e-6, it will take 53 days, which is the entire mission duration, more than 40 days are in lunar orbit, but the section from the earth to the moon is only four days.
In fact, most of the lunar spacecraft, including the Apollo spacecraft, are flying along similar orbits, but due to the different transition windows of the Earth and the Moon and the different initial velocities, the orbit parameters are slightly different, but it generally takes three to five days.
In addition to the Indian lunar probe, it is because they do not have enough speed in orbit, and the edge of the elliptical is far from the moon, so they circle around it, and each time they circle the earth, they add a little more speed, and it took several months to finally save up enough speed before they set foot on the lunar transfer orbit.
And for the United States, the USSR (Russia) and China, the carrying capacity of the rocket is sufficient, so generally going to the moon is a transfer orbit of three to five days. The difference is that the heavier the spacecraft, the greater the rocket thrust will need to reach about the same initial velocity. Our Chang'e-3 probe is only 3.7 tons, so it is enough to use the Chang'e-3B reinforced version with a thrust of 600 tons. Chang'e-5-6, on the other hand, weighs 8 tons and must be launched using the Long March 5, which has a thrust of more than 1,000 tons.
Photograph of the site of the Apollo moon landing
The total weight of the American Apollo 11 spacecraft plus the lunar module reached 78 tons, but the thrust of the Saturn V rocket exceeded 3,400 tons, which was completely enough to accelerate to an orbital speed of about 11 kilometers per second, so it could reach the moon in more than three days. In fact, it is not only the technology of rockets that determines the length of the flight time of the Earth and the Moon, but also the most crucial gravitation and Newton's laws. As long as you follow this track, the time is about the same.
Can the ship of the future be a little faster? Don't talk about the future, in fact, you can do it now, as long as you don't take this track, bring a big fuel tank up, and keep accelerating on the road, past the middle point, and then keep slowing down, with the current technology of human beings, you can fly to the moon in 10 hours. But the engine was always on, and it was unacceptable to launch at least ten or even a hundred times the extra weight of fuel into space, so no one did it. Don't look at the fact that more than 60 years have passed, and technology has developed so much, but from the launch of the first artificial satellite by the Soviet Union to today, all our human space technology is still based on the law of gravitation and Newton's law of motion more than 300 years ago.
(Fundamental physics dictates space limitations)
and Tsiolkovsky's rocket formula proposed in 1897, when the Qing Dynasty was not dead, but that formula was to strangle the speed of human spaceflight, and there has been no breakthrough of an order of magnitude for decades.
Therefore, flying back and forth in eight days is in line with the technical level of mankind from the late 60s of the last century to the present, and cannot be used as real evidence of "moon landing fraud".
In fact, there is nothing wrong with being a little questioned, this article is not intended to prove the authenticity of the United States manned landing on the moon, we can also take this opportunity to popularize some aerospace knowledge. Of course, if you think I'm, I'm whitewashing Americans, and you want to scold me, then it's okay to scold me, it's good to vent your emotions.
I think it's okay, our predecessors struggled and sacrificed, two bombs and one star to get to the sky, isn't it just for our contemporaries to live a happy life, and it is a kind of fate to be able to read the article here, and you are more happy than anything else.
In our time, it is easy to obtain knowledge, and the decentralization of the network allows everyone to easily access a lot of information; However, in this era, it is difficult to acquire knowledge, because we are easily anxious, easily immersed in the cheap emotional catharsis brought by entertainment short videos, and lose the ability to distinguish information pollution.
Traces of six Apollo moon landings
In addition to "it is impossible to go back and forth in 8 days", there are many such "doubts", such as many friends saying "why are the lunar rover and flag gone", "Pakistan Cubesat was not photographed", "How could there be a live broadcast at that time, and it was so high-definition"...... Many, much more.
Many self-media mistakenly regarded the later moon landing documentary as a live broadcast picture, but in fact, the live broadcast of the earth and moon at that time was not only delayed, but also very blurry, and it was still a black and white picture, which was not "high-definition live broadcast without delay".
If you look it up again, you will know that the United States has long published the exact coordinates of the six moon landings, which are on the official website of NASA. The so-called "why the United States does not dare to announce the coordinates of the moon landing" is nothing more than a rumor.
The same rumor is that "the United States has lost a full set of lunar landing materials." In fact, the data was not lost, and most of it was kept in microfilm by NASA.
There is also such a saying: "If the United States really landed a man on the moon back then, then why can't it go up now?" The logic of this statement is even more problematic, if a person is not good at the age of sixty, can it be proved that he is not good at the age of twenty? The British Navy invented aircraft carriers, catapults, but now they can no longer build catapults, is it also a fake? The Soviet Union has carried out 24 unmanned moon landings, but Russia has not been able to climb on the moon, is it true that the Soviet Union was also a fraud back then?
Therefore, the reason why the United States has failed to explore the moon without one is very simple, because they are not good now, they are in decline, but they can't prove whether it was a fraud back then.
It is impossible to draw correct conclusions from the wrong basis, and if we use rumors to attack the enemy, is that not tantamount to deceiving ourselves? Refuting rumors is not to help the United States testify, but because our self-confidence does not need to be based on smearing the enemy, which is also belittling ourselves.
Questioning needs to have a scientific and reasonable basis, and in any case, seeking truth from facts comes first. That's what we're at the bottom of where we're today. And the United States has gradually lost the scientific spirit of seeking truth from facts, which is also the core reason for their decline and loss of popular support.