Volume 1: Student Life Chapter 136 Raising Problems and Solving Problems
Double stars are also called binary stars, a term coined by Herschel, the first president of the Royal Astronomical Society of Britain.
A binary star refers more to a physically related pair of stars, a star system in which two stars each orbit around a common center of mass.
As Yang Yiyi said, Altair and Vega are not binary stars.
Herschel also discovered Uranus and its two satellites through a large reflecting telescope of his own design, and compiled the first catalog of double stars and clusters.
Therefore, when Chen Zhou and his companions were searching for literature, this person was the first person they thought of.
The three of them searched for the necessary literature according to their respective goals.
[In a binary star system, the gravitational force of one star is provided by the other star, and vice versa. The ratio of their centripetal accelerations is inversely proportional to their masses...]
Chen Zhou took out a piece of draft paper and wrote down this information.
From this, we can directly derive the ratio of the centripetal acceleration of the binary star system in the question.
[When a planet moves in a uniform circular motion around a star, the distance at which gravity acts is exactly the radius of the planet's orbit. However, in a binary star system, the distance at which gravity acts is different from the radius of the binary star's orbit . The angular velocity and period of the two stars in a binary star system when they move in a circular motion must be the same. The ratio of their linear velocities is the same as the ratio of their respective orbital radii...]
Yang Yiyi also recorded the corresponding element information while searching.
9pm.
Chen Zhou, Yang Yiyi and Fang Jieming began to summarize the information they had collected.
Afterwards, Chen Zhou began to assist Yang Yiyi in conducting relevant theoretical analysis.
Fang Jieming walked aside and prepared to rest.
For him, what he needs to do now is to ensure rest, as his working hours have not yet come.
"There is too little information in this question. Even the key factors are incomplete," said Yang Yiyi.
Chen Zhou also frowned, then relaxed his brows and said with a smile: "It doesn't matter, just follow the information we found. This can be considered a test of the competition itself. "
Yang Yiyi nodded, pointed at the recorded information with a pen, and analyzed: "There are a total of five types of orbits of planets around binary stars, namely large outer orbits, small outer orbits, eccentric outer orbits, complex outer orbits, and inner orbits."
"Large outer orbits are the simplest of the binary orbits, because the planet is so far away that the gravitational pull from the binary is similar to that of a star of equal mass. In this case, the planet will orbit both stars in a normal elliptical orbit."
Chen Zhou thought for a while and said, "This situation is indeed the simplest, but such a planet will be very far away from the center of mass of the binary star."
"That's right." Yang Yiyi continued, "Among them, we also need to consider the direct and retrograde motion of the planets..."
At this point, she looked up at Chen Zhou and said, "Adding the analysis of other orbits, the amount of calculation involved is huge. I want to share the burden with you."
Chen Zhou looked at Yang Yiyi, hesitated for a moment, and nodded slowly.
Seeing that Chen Zhou agreed, Yang Yiyi smiled.
The two continued to analyze the problem of the orbits of planets around binary stars.
After careful consideration, the physical principles involved are basically clear.
Now it’s time for theoretical calculations.
Chen Zhou raised his hand and looked at the time. It was already one o'clock in the morning.
The noise in the computer room was not as noisy as it was at the beginning.
Many people lay down on their computer desks and began to sleep.
Chen Zhou turned his head to look at Fang Jieming who was also lying on the computer desk and smiled slightly.
Yang Yiyi also turned her head and glanced at the senior who seemed to be asleep.
Regarding the calculation of the orbit around the binary star, Chen Zhou handed over the large outer orbit and small outer orbit to Yang Yiyi, and reminded her: "Don't force yourself, go to sleep if you feel sleepy. Don't worry, leave the problem to me."
Yang Yiyi nodded slightly.
[A planet orbiting a binary star in a highly eccentric retrograde elliptical orbit has an orbital period of about 12.5 times the binary period, and the farthest distance will reach 10 times the binary separation. The elliptical orbit will drift around the core of the binary star in the same direction as the planet's orbit...]
Chen Zhou started from the eccentric outer orbit and gradually got into the state.
Analyze problems, raise questions, and solve problems.
There is no sense of obstruction in thinking and calculations are very smooth.
After solving the problem of the eccentric outer track, Chen Zhou was not in a hurry to solve the problem of the complex outer track.
Instead, he started thinking about the issue of direct and retrograde motion of planets that Yang Yiyi had mentioned earlier.
He held a pen and tapped the draft paper habitually.
"Stability?" Chen Zhou thought of this word.
The reason why a binary star system is called a system is that the two stars revolve stably around a common mass center in their respective orbits.
Therefore, the key issue is how to maintain this stability after the planet intervenes.
Ultimately, the ultimate goal of this question is the stable coexistence of binary star systems and planets.
Chen Zhou glanced at Yang Yiyi and patted her gently.
Yang Yiyi stopped writing and looked up at Chen Zhou in confusion.
Chen Zhou said: "Yiyi, we need to solve the problem of planetary direct and retrograde motion first, so that we can reduce unnecessary calculations."
Yang Yiyi pondered for a moment, then picked up her draft paper, took a look at it, and handed it to Chen Zhou.
Chen Zhou took it and looked at it for a while. After putting down the draft paper, he said, "Yes, this is it."
Yang Yiyi had completed the relevant calculations for the retrograde motion of the planets on her draft paper, but the calculations for the direct motion could not be carried out .
Originally, Yang Yiyi was going to calculate the direct motion of the planets first, but as she was calculating, she felt there was something wrong.
He stopped temporarily and turned to calculate the retrograde motion of the planets.
Yang Yiyi said: "It should be that the retrograde motion of the planet will affect the stability of the binary star system, and eventually cause the binary star system to become unbalanced."
Chen Zhou was a little surprised. He didn't expect that she had already thought of this.
Chen Zhou thought for a moment and said, "How about we compete to see who can solve this problem first?"
Yang Yiyi looked at Chen Zhou and smiled: "Come on, just like we did in the summer vacation competition."
The two of them started looking for relevant literature on the computer at the same time.
After spending a lot of time, Chen Zhou finally deduced the relevant solution information based on the information he found.
[If this planet is not retrograde but prograde, the entire system will not be stable, and the planet will either be swallowed by the star or fly out. This is because the gravitational field intensity fluctuations experienced by the prograde planet have the same amplitude as the retrograde planet but with a longer period. The longer period will weaken the stabilizing effect and eventually lead to imbalance...]
Chen Zhou took a look at the conclusion written on the draft paper and was about to give it to Yang Yiyi when Yang Yiyi tilted her head to look at him.
