Die on Mars

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

Tang Yue nodded.

The old cat then clicked a small dot on the circle, "This is the location of our Kunlun Station and the Eagle spacecraft. It is located in the northern hemisphere of Mars, in the Isidis Planitia. The specific location is 87 East Longitude. Degrees, 12 degrees 54 minutes north latitude, close to the equator, and to the northeast of us is Utopia Planitia."

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

Tang Yue watched Old Mao draw another big circle on the paper and put the first circle inside, "This is the orbit of the United Space Station. The perigee is 380 kilometers and the apogee is 480 kilometers. It is an elliptical orbit that is approximately circular. , its operation cycle is one hour and twenty minutes, which means that the Joint Space Station passes above our heads every more than an hour."

Tang Yue nodded.

The old cat drew a small rocket in the blank space next to the big circle, "This is the Eagle spacecraft, and what will be launched will be its ascent stage..."

Lao Mao framed the upper part of the rocket, "There are two stages of the rocket in the ascent stage. The first stage is two SpaceX Raptor 3C engines. Their working time is only two hundred seconds, which is more than three minutes. Here Within three minutes, the engines have to push the payload bay into orbit."

The old cat drew an arc from Mars and slowly extended it to represent the Eagle spacecraft taking 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 away, and the payload module will begin flying around Mars." Lao Mao continued, "My original plan was to dock quickly Plan, select a suitable launch window, allow the lander to launch at the right time, and synchronize with the joint space station as soon as possible... The second-stage rocket in the ascent stage is responsible for adjusting the orbit, a Russian-made RD-0172 engine, which is very mature. Bullshit."

Tang Yue was reassured. Lao Mao was experienced and made a very safe plan.

"But this plan has been scrapped now." Old Cat shrugged.

"Because of the weather?"

Old Cat frowned, "Yes, because of this troublesome weather, we can no longer choose the launch time based on the location of the space station, but must decide whether to launch based on changes in wind speed. When the wind speed drops, we will launch... …But that creates another problem.”

"what is the problem?"

"The changes in wind speed are random. We don't know when this damn storm will weaken, so we can't preset the rendezvous trajectory between the Eagle spacecraft and the space station before launch. The space station may be above our heads when the lander lifts off. , or it may be on the other side of Mars." Lao Mao said, "So we can only use the slow docking method, first put the lander up, and then let it stay in the orbit for a long time, and we will see each step step by step."

"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 cheerfully, "What kind of big problem is this? The spacecraft has already entered orbit, and finally The difficult stage has been passed. At most, we will fly around Mars twice more. Anyway, one circle only takes an hour or two. It is better to be slower than to be more prudent and slowly maneuver the orbit."

The old cat was silent for a long time, staring at the pen and paper on the table, "That's the problem."

Tang Yue was startled.

"Maneuvering orbit requires propellant." Old Cat whispered.

"I know."

The old cat raised his head. The cat's face was illuminated by the light and looked expressionless.

"But our propellant remaining situation may be... less optimistic."

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Old Mao and Tang Yue got together. Old Mao wrote quickly and was calculating quickly. The paper was full of densely packed numbers and formulas. Although Tang Yue couldn't understand it, he stood nervously waiting for the results. Knowing what lies behind these cold numbers can mean the difference between life and death.

"According to aerodynamics, the air resistance encountered by the aircraft when operating in low orbit is D=1/2Cρv∧2, C is the drag coefficient, ρ is the atmospheric density, and S is the effective windward area..."

"Then the atmospheric drag only causes negative acceleration along the tangential direction of the orbit. The equation is f=-1/2mCSρv∧2. From the perturbation equation, we can get dr/dt=2vfr∧2/μ...Use Taylor series to expand..."

"Assume that the initial orbit radius is R1. During rendezvous and docking, the orbit radius is reduced to R2, where R1 is greater than R2, and the corresponding atmospheric densities are ρ1 and ρ2. After the rendezvous and docking is completed, Hohmann transfer is used to raise the orbit to... 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 various Greek letters and higher-order equations are piled up layer by layer. In fact, he has gone through these equations and calculations hundreds of times in his mind, and wrote them down just to show Tang Yue. .

"Drawing paper." The old cat didn't even look up.

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

"Scrap paper!"

Tang Yue handed over the paper.

"Scratch paper, scratch paper, scratch paper!"

Manuscript papers filled with calculation processes soon filled the table. The old cat's hand speed was so fast that Tang Yue couldn't see clearly. The cat's eyes were fixed on the paper, from Mars to Storm to the Eagle spacecraft. All the parameters of the United Space Station form calculations in Lao Mao's mind. Its computer is performing calculations at a rate of billions of times per second, simulating the trajectory of the lander after launch, and then outputting it on paper through the pen in his hand.

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

He prayed for a good result in his heart, but Tang Yue himself also knew that physics and mathematics are the most indestructible things in the world. As long as the initial parameters are given, the result is determined and will never change based on human will. , no matter how tortuous the calculation process is, no matter how many times you calculate it.

Just when there were only three pieces of white paper left in his hand, the old cat stopped writing, and the swishing sound of writing stopped. The huge calculation that was as long as a waterfall in the clouds suddenly ended like a sharp knife cutting through the hemp, and finally only Leave a concise and cold number at the end of the scratch paper.

Old Mao put the paper up and showed it to Tang Yue.

2.15547.

"Twice." Old Cat said slowly. "Assuming that when the Eagle spacecraft takes off, the United Space Station is on the other side of Mars, then the propellant of the RD-0172 engine is only enough to change the orbit of the lander twice at most."

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

"In other words, the Eagle spacecraft can only try to rendezvous with the Joint Space Station twice at most. If both attempts fail, the lander will lose all power and will no longer be able to dock with the space station." Lao Mao gave the final problem. Tang Yue pointed it out. It turned its head and looked into Tang Yue's eyes. Those cat-like eyes were menacing.

"And the sandstorm outside makes it impossible for us to maintain contact with the space station, monitor the real-time status of the Eagle spacecraft, and guide the lander and Ophiopogon japonicus... Do you know what this means?"