Technology invades the modern world

Chapter 92: Lessons for Comrade Korolev

You are actually gay?

I've worked in the Soviet Union for so many years, and with my authority, I shouldn't be unaware that we still have a comrade fighting on the secret front. Now it was Korolev's turn to be surprised and confused.

He didn't ask the other party why he knew he was a Russian. After all, the name was Sergei and Viktoria, and it sounded like it came from the Soviet Union.

"Professor Lin, how do you speak Russian?" Korolev was quite curious about this question, and it didn't matter even if he lost the initiative.

Lin Ran was not playing tricks. He originally wanted to find an opportunity to convey important information of his plan to the Soviet side.

It is better to choose a day than to hit it.

Korolev himself has come, which means the timing is right.

"I studied Russian in college," Lin Ran replied.

Korolev nodded. "Göttingen?" he asked. "They do teach Russian there."

Göttingen was rebuilt 45 years later. Because the Soviet Union was the victorious country, German universities gradually paid more attention to the study of Russian language and Slavic culture.

Considering history, it is normal for Lin Ran to learn Russian in Göttingen, but Korolev could never have imagined that Lin Ran learned Russian on the campus of Huaguo University 60 years later.

"Randolph, congratulations to NASA on the successful moon landing. I saw the news in Moscow and felt that the moon landing was no longer just a game for the Soviet Union.

NASA is finally able to join the race.

I also think your design for the space station is very good, and we have similar plans internally.

I really like the idea that space stations are just bigger satellites, and space cities are just bigger space stations.”

Korolev said that these were not secrets. All members of Congress participated in the hearings, and NASA's ambitions had long been announced to the world through reports from the American media.

"I'm getting old, and the Russian Space Agency needs a successor. Do you have any thoughts on becoming the next chief designer?"

That’s right, the purpose of taking the risk to come to London in person was to recruit talents for the Soviet Union.

Lin Ran has fully demonstrated his abilities, and the title of great mathematician adds to his glory.

From Moscow's perspective, Lin Ran is simply a combination of Euler and Korolev. If they can recruit him to Moscow, it is worth taking some risks.

"If I just go with you guys like this?" Lin Ran asked doubtfully, "Won't we be intercepted by London or America?"

Korolev ignored them and said, "You don't need to worry about that.

As long as you are willing to come to Moscow, we will naturally find a way to bring you back safely."

Korolev did not take London's security seriously. In his view, this was a public place and he could come and go as he pleased.

"Rather than becoming the next chief designer, I would rather be the one and only Randolph." Lin Ran's words were a polite refusal.

Lin Ran was not worried that the other party would attack him if he refused. After all, if they attacked and made noise, Korolev would not be able to leave.

"Sir, how long can you guarantee that we will have this conversation?" Lin Ran asked.

Korolev glanced at the Kirov watch on his wrist. "At least 20 minutes."

Lin Ran stood up and looked outside. Although there were still two security guards standing at the door, their appearance had changed from Germans to Slavs.

After Lin Ran closed the door, he said, "We don't have much time, so let's make it short.

Is it possible to launch tens of thousands of satellites into low Earth orbit with current technology?

Korolev said without hesitation: "Impossible, the cost is too high."

Lin Ran asked: "What if it can create benefits?"

Korolev thought for a moment and said, "That's impossible. The cost is still too high. I can't imagine what kind of revenue satellites must generate to encourage countries to launch tens of thousands of satellites."

Lin Ran asked, "What if the cost of rocket launches could be reduced to one-fifth, one-fiftieth, or one-five-hundredth of what it is now?"

Although Korolev didn't know what Lin Ran was trying to say, he couldn't help but follow his logic. "If it's one in fifty, it's possible."

Because the temptation is too amazing.

"Okay, let's assume that in the future we need to use tens of thousands of satellites to build a network that can be used by all of humanity, and everyone can exchange information through this network." Lin Ran said, "Then because the cost of rocket launches is too high, we need to develop a technology called reusable rockets.

We designed the rocket to have a multi-stage ignition structure, with three stages: one, two, and three. The first two stages ignite to send the rocket into the predetermined orbit and then return it to the ground, where it can be used again.

Later on, even the first, second, third and third stage boosters will be recoverable.”

Korolev thought for a moment and said, "It's theoretically possible, but it's still too difficult."

Lin Ran continued, "That's right. I am now trying to prove that it is possible from a mathematical point of view. This is my latest research result, and I call it:

Lossless convergence of nonconvex control bounds and pointing constraints."

Lin Ran didn't expect that before coming to London and discussing number theory with London mathematicians, he would have to give Korolev a math lesson first.

"We simplified rocket stage recovery into a benchmark problem in optimal control theory.

That is how to make the spacecraft reach a designated location on the surface of the planet in a limited time in the best way, usually by minimizing fuel consumption, while satisfying various state and control constraints.

The soft landing problem can be modeled as a finite-time horizon optimal control problem, which includes state constraints, such as altitude and speed, and control constraints, such as thrust magnitude and thrust direction.

The core difficulty of this problem lies in the non-convexity of the control constraints, which is specifically manifested as: non-convex constraints on thrust size: the thrust size has a non-zero lower bound and an upper bound, which makes the feasible control set non-convex.

Non-convex constraints on thrust direction: The thrust direction is often subject to pointing constraints, for example the thrust vector must lie within a non-convex geometric region such as a cone.

These non-convex constraints make it difficult for traditional optimal control solutions to guarantee a global optimal solution, and may even fail to converge to a feasible solution.

Therefore, we need to transform the non-convex problem into a convex problem and prove that this transformation is lossless, that is, the solution to the convex problem is consistent with the global optimal solution of the original non-convex problem.

I call this approach lossless optimization."

This mathematical paper, which laid the foundation for the successful development of SpaceX's reusable rocket, was taken out by Lin Ran in advance as a gift to Korolev and even the Soviet Russian space industry.

As long as the other party can remember, with Korolev's ability, the Soviet Union will be able to achieve manned lunar landing in three years at most.

Because it goes straight to the heart of soft landing.

However, allowing the Soviet Union to land on the moon was not the most important goal. His real purpose was to prepare for the more distant future.

Korolev had completely forgotten why he came and was concentrating on listening to what Lin Ran was going to say:
"Where's down there?"

(End of this chapter)