I kidnapped an alien civilization

What affects the orbits of the dwarf planets in the Kuiper belt? If a planet’s orbit is abnormal, there must be a planet with a large enough mass to generate gravitational force on them.

Li Mo knew that he had caught the figure of an unknown planet. If he had the specific data of the orbit of the affected star, he could make a mathematical model based on the theory of space quantization (orbit quantization) proposed by Boer.

Only planetariums have the specific orbital data of space stars, with such an idea. Li Mo called Professor Wu and explained that he wanted to make a mathematical model about the operation of planets in the solar system. As a result, he was reprimanded. Professor Wu believed that Li Mo was not doing his job properly at this time, but he still provided a valid message, that is, the School of Astronomy of Yanda University is doing a measurement project, and there may be data he needs there.

Li Mo picked up his mobile phone and dialed the number of Professor Tian from the School of Astronomy that he got from Professor Wu, and the call went through. Hi, hello, Professor Tian, ​​I'm Li Mo, a student of Professor Wu in the Department of Mathematics. Li Mo straightforwardly named himself, because he knew that these professors are usually very busy.

Old Wu's student, didn't the old man always look down on those of us who do actual measurements, why did he let you contact me? There seemed to be a big gap between the other side and Professor Wu.

Li Mo hurriedly explained: It's my personal idea to contact you. I plan to make a mathematical model of the movement of stars in the solar system. I lack actual measurement data, so the teacher introduced you.

A mathematical model for the movement of stars? Professor Tian was a little surprised, Only you?

Li Mo said to the phone: Yes, but I want to try it, you may have heard my name.

Li Mo? The person on the phone thought for a while, and finally remembered, So it's you, how about it, my office is on the 8th floor of the Astronomical Building, you can come directly, let's meet and chat.

Professor Tian seems to be very interested in the mathematical model of the movement of stars. The learning assistance system once said that fame is also a kind of power, which seems to make sense. Li Mo hung up the phone.

The Astronomical Building is in Area A, and its white exterior glistens in the sunlight. Looking at this majestic building, one can imagine that Huaguo attaches great importance to the emerging discipline of astronomy.

Professor Tian, ​​I'm Li Mo who was on the phone with you just now. Pushing open the door of the office, Li Mo saw a young professor sitting at the desk.

Li Mo, please sit down. Professor Tian let him take a seat, Let me see what the baby in the mathematics department looks like.

As he said that, he took a closer look and looked a little disappointed, It's just like this, with one nose and two mouths, it's no wonder that old man Wu called me just now because of you.

Last year, I asked the Department of Mathematics to make a measurement error standard for our Department of Astronomy, to see how awesome it is. This time, it must have been flat. Professor Tian showed a hearty smile.

Li Mo nodded, Although the measurement error standard is not difficult, the calculation is too heavy, and many students don't like to do it.

Professor Tian, ​​you are so young. The professor in front of him seems to be only in his 20s, with thick eyebrows, big eyes, and delicate skin. Could it be that he is also a young genius?

When Professor Tian heard this, he laughed at Li Mo's straightforwardness: I can't tell, I'm over 40 years old this year, and I'm a natural child.

Okay, let's stop talking about this, tell me what your mathematical model of planetary movement does? Professor Tian said anxiously.

Li Mo looked around, and there were all kinds of planet models around, and even the background of the office computer was also the universe starry sky. He thought for a while and said: I want to make a mathematical model that can describe the orbits of the major planets in the solar system.

Describe the orbit accurately? Professor Tian couldn't believe it. Do you know that although the orbits of the major planets have been accurately recorded, they are not determined by mathematical models.

There are also many mathematicians who have made various mathematical models, but there are large errors from the actual orbits of the planets. He stared at the seemingly bragging student in front of him with bright eyes, The universe There are too many mysteries, and the planets will be disturbed by various factors during their rotation.

Are you sure you can make such a mathematical model?

Li Mo nodded firmly, Mathematics will not deceive people. Although there are many unknown factors in the universe, they can all be avoided in advance through mathematical fuzzy equations.

What I'm missing now is a lot of astronomical observation data.

Looking at the immature student in front of him swearing, Professor Tian thought to himself, is he really old?

Okay, in a project just completed by our astronomy department, there are currently the most complete astronomical observation data in the world. Professor Tian stood up and picked up the phone, This will let my graduate students who have done the project cooperate you.

After making a phone call, Professor Tian and Li Mo exchanged a few words about the current exploration of the universe. He found that the young man in front of him had profound astronomy knowledge, which made him full of confidence in this cross-department cooperation.

The two were talking, and four students, three men and one woman, pushed open the door of the office. Teacher, are you looking for us? The leader stepped forward and greeted.

These four are my best students, and they are also the team members of the last astronomy project. Professor Tian gave a brief introduction to the two parties, This is Fang Shan, Zhou Kangnian, Wang Xin, and Li Tiantian.

This is Li Mo from the Department of Mathematics.

This time we are going to cooperate with the Department of Mathematics to make a mathematical model to describe the exact trajectory of the planets. Professor Tian assigned the task straightforwardly, You have to assist Li Mo to pass the astronomy project last time. data to complete the project.”

Li Mo, this is the prepared location data of massive celestial bodies in the solar system that we collected last time within 5 years.

This is the orbit data of comets in the solar system within 5 years.

This is Jupiter satellite data.

This is Saturn satellite data.

The Department of Astronomy has collected so many detailed celestial body operation data. Li Mo went back to the Xiaoshan Laboratory and checked the USB disk carefully. Facing this mountain of data, he took out energy coffee from his backpack and cheered!

The first step is to use python to write a small program to arrange the data according to the law, and input the data of the unknown planet into the calculation formula.

The second step is to write the mathematical model

V1/r=－P/r (P is a constant related to the system)

Under the influence of , when the orbital motion of an object in it satisfies the following formula, or more precisely, when its orbit is in the vicinity specified by the following formula, the stability of its orbit has a small and sharp peak value:

Tn=n3T0, (n=1, 2, 3...), (2)

Among them, a0 and T0 are constants related to the system, and an and Tn are the semi-major diameter and period of the nth orbit.

When V1/r is the Coulomb field produced by hydrogen-like nuclei, the above formula and Bohr's first and second hypotheses are equivalent, and can be derived from each other, so there is no need to verify them here.

a0 = k1M 1 , ⑶

T0 = ​​k2M 2 , (4)

where M is the mass of the central celestial body, a constant

c2 =0.5650±0.0015, k2 =2.141×10-12.

Finally, according to the limitation of gravity, the specific trajectory of the unknown star is calculated.