The old cat drew a circle on the white paper, "This is Mars, with a radius of 3,389 kilometers, about half the size of the Earth, and the length of the equator is 21,330 kilometers, which is also half the size of the Earth." ”

Tang Yue nodded.

The old cat then dotted a small dot on the circle, "This is the location of our Kunlun station and the Eagle spacecraft, located in the northern hemisphere of Mars, in the Isidis Planitia, specifically at 87 degrees east longitude, 12 degrees 54 minutes north latitude, near the equator, and to the northeast of us is the Utopia Planitia. ”

"The Eagle spacecraft will be launched at this location." The old cat tapped the paper with the tip of his pen.

Tang Yue watched the old cat draw another big circle on the paper, and put the first circle into it, "This is the orbit of the Joint Space Station, with a perigee of 380 kilometers and an apogee of 480 kilometers, it is an elliptical orbit that is approximately circular, and its operating cycle is one hour and twenty minutes, that is, the United Space Station passes over our heads every hour or so." ”

Tang Yue nodded.

The old cat drew a small rocket in the blank space on the edge of the big circle, "This is the Eagle spacecraft, and it will be its up-and-down ...... that will be launched."

The old cat framed the upper part of the rocket, "There are two stages of rockets in the ascent stage, the first stage is two SpaceX Raptor 3C engines, and their working time is only two hundred seconds, that is, more than three minutes, and in these three minutes, the engines must push the payload bay into orbit." ”

The old cat drew an arc from Mars, slowly extending it to represent the Eagle spacecraft that had lifted off, and then began to fly around Mars.

"If the Eagle spacecraft can be successfully launched, then after entering orbit, the Raptor 3C engine and main fuel tank will be thrown off, and the payload bay will begin to fly around Mars." Lao Mao continued, "My original plan was to quickly dock the plan, select the appropriate launch window, let the lander be launched at the right time, and synchronize with the joint space station as soon as possible...... Responsible for adjusting the trajectory is the second-stage rocket of the ascent stage, a Russian-made RD-0172 engine, a very mature Mao Zi cargo. ”

Tang Yue is very relieved, the old cat is experienced, and it is very safe to make a plan.

"But that plan is now scrapped." The old cat shrugged.

"Because of the weather?"

The old cat frowned, "That's right, because of this troublesome weather, we can no longer choose the timing of the launch according to the location of the space station, but decide whether to launch according to the change in wind speed, and when the wind speed drops...... But this poses another problem. ”

"What's the problem?"

"The wind speed changes randomly, and we don't know when the damn storm will abate, so we can't pre-set the rendezvous trajectory of the Eagle spacecraft with the space station before launch, which could be above our heads or on the other side of Mars when the lander lifts off." "So we can only use the slow docking method, first hit the lander, and then let it stay in orbit for a long time, step by step." ”

"Do you mean to put the Eagle spacecraft into orbit first, and then slowly adjust it according to the situation?" Tang Yue's tone was very relaxed, and he turned his chair happily, "What kind of big problem is this?" The spacecraft has entered orbit, the most difficult level has passed, it is a big deal to fly around Mars twice, anyway, it will only take an hour or two to circle around, it is better to be slower, but also to be safe, and slowly maneuver and change orbits. ”

The old cat was silent for a long time, it stared at the pen and paper on the table, "This is the problem. ”

Tang Yue was stunned.

"Maneuvering orbit changes consume propellant." The old cat whispered.

"I know."

The old cat looked up, and the cat's face was illuminated by the light, and it looked expressionless.

"But we may not have enough propellants."

·

·

·

The old cat and Tang Yue got together, the old cat was flying like a pen, calculating quickly, the paper was full of dense complex numbers and formulas, although Tang Yue couldn't understand it, he was also nervously standing on the side and waiting for the result, he knew that behind these cold numbers might be a matter of life and death.

"According to aerodynamics, the air resistance of the aircraft in low orbit is D=1/2Cρv∧2, where C is the drag coefficient, ρ is the density of the atmosphere, and S is the effective windward area ......"

"Then the atmospheric drag only causes negative acceleration along the tangent direction of the orbit, and the equation is f=-1/2mCSρv∧2, and dr/dt=2vfr∧2/μ...... can be obtained from the perturbation equation Using Taylor series to expand ......"

"Assuming that the initial orbital radius is R1, during rendezvous and docking, the orbital radius is reduced to R2, where R1 is greater than R2, and the corresponding atmospheric density is ρ1 and ρ2...... δ=√（μ/r）(1-√(2r/R1+R2)+√(u/r)[(1-√2r/R1+R2)-1]……”

The old cat's calculation speed is getting faster and faster, and all kinds of Greek letters and higher-order equations are piled up layer after layer, and these equations and equations have actually been written hundreds of times in his head, just to show Tang Yue.

"Scratch paper." The old cat doesn't lift his head.

Tang Yue held a stack of white paper in his hand and immediately handed over the scratch paper.

"Scratch paper!"

Tang Yue handed the paper.

"Scratch paper, scratch paper, scratch paper, scratch paper!"

The manuscript paper full of the calculation process was soon piled up on the desktop, and the old cat's hand speed was finally so fast that Tang Yue couldn't see it clearly, the cat's eyes stared at the paper, from Mars to the storm to the Eagle spacecraft to the United Space Station, all the parameters formed an equation in the old cat's brain, and its computer was calculating at a speed of hundreds of millions of times per second, simulating the trajectory of the lander after launch, and then outputting it on the paper through the pen in his hand.

Tang Yue stood on the side, feeling apprehensive, like a student waiting for the results of the college entrance examination.

He prayed in his heart for a good result, but Tang Yue himself knew that physics and mathematics were the most indestructible things in the world, as long as the initial parameters were given, then the result would be dead, and it would never be transferred by human will, no matter how tortuous the calculation process was, no matter how many times you counted it.

Just when there were still the last three sheets of white paper in his hand, the old cat stopped writing, and the sound of the pen clattering stopped, and the huge calculation that was as long as a waterfall of clouds came to an abrupt end like a quick knife, and finally left only a simple and cold number at the end of the scratch paper.

The old cat put up the paper and showed it to Tang Yue.

2.15547。

"Twice." "Assuming that the United Space Station is on the other side of Mars when the Eagle spacecraft lifts off, then the propellant of the RD-0172 engine will only be enough for the lander to change orbit twice at most. ”

Tang Yue's brain froze, and he didn't realize what this number meant for a while.

"That is, the Eagle spacecraft and the Joint Space Station can only attempt to rendezvous twice at most, and if both times fail, then the lander will lose all power and will no longer be able to dock with the space station." The old cat pointed out the last problem to Tang Yue, and it turned its head to look at Tang Yue's eyes, the cat's eyes were terrifying.

"The sandstorm outside made it impossible for us to keep in touch with the space station, monitor the real-time status of the Eagle spacecraft, and guide the lander and Mai Dong...... Do you know what that means? ”