Imperial Master of the Ming Dynasty

"The sun and moon are bright."

Zhu Gaoxu's thinking seemed to be extremely active today, and he immediately asked another strange question.

"Mr. Jiang just said that there is a law of gravitation, which means that the greater the mass of the objects, the greater the gravitation between them; the farther the distance between the objects, the smaller the gravitation between them."

"That's right." Jiang Xinghuo affirmed.

"Then let me ask Mr. Jiang, if universal gravitation is true and the sun is the center, then the sun is so far away from our earth and can emit gravitational force and pull our earth to rotate. How much mass does the sun have to have? In other words, how big is the sun? ?" Zhu Gaoxu asked curiously.

Hearing this question, Old Man Zhuo also looked at Jiang Xinghuo.

Obviously Old Man Zhuo is also very concerned about this issue.

After all, everyone has been looking at the sun hanging there since ancient times, but no one can tell clearly how big the sun is and whether it is larger or smaller than the earth.

And based on the theory of universal gravitation, Old Man Zhuo derived an obvious conclusion.

That is, the sun is the center of the universe, or the center of the earth and celestial bodies such as metal, wood, water, fire, and earth, so the mass, or weight, of the sun must be extremely large.

Otherwise, it is obviously extremely unreliable for a small sun to attract a bunch of large celestial bodies.

But Old Man Zhuo is not very hopeful about this issue.

Old Man Zhuo didn't have any hope that Jiang Xinghuo would answer this question, but he didn't have any hope at all whether there was an answer to this question.

The reason is also very simple. Guo Shoujing used human power to measure the area of ​​the earth. In Zhuo's view, this was the limit that astronomy and geography could achieve.

After all, the area of ​​the earth does indeed exist. It is just difficult to measure. It does not mean that it cannot be measured.

But the question is, how to measure the mass, area, and distance of the sun?

Fly to the sun and use a ruler to measure it?

It's obviously impossible.

Therefore, Old Man Zhuo really didn't expect Jiang Xinghuo, a young man with astonishing talent, to give any answers.

but,

but,

Jiang Xinghuo opened and closed his lips.

"Easy to handle."

——————

"Is this wall broken?"

Zhu Gaochi turned his head in disbelief and asked the two clerks.

The two petty officials, Guo Jing and Chai Che, shook their heads together.

The eavesdropping amplification wall is not broken at present, and the sound is transmitted very clearly. This is an indisputable fact.

"The wall is not broken, but the ears are broken?"

Zhu Gaochi stretched out his fingers and tried to dig out his ears, but his short and thick little finger was obviously unable to do this.

Zhu Gaochi was finally convinced that the wall was not broken and the ears were not broken either.

Jiang Xinghuo actually said that he could measure the mass and size of the sun!

In Zhu Gaochi's opinion, this is just like listening to the myths about Hou Yi shooting the sun and Jingwei filling up the sea.

Zhu Yuanzhang only forbade civilians to study astronomy privately, but there was no prohibition on the study of astronomy in the Qintian Prison, as well as on the princes and grandsons who wanted to study it.

After all, in a sense, astronomy is closely related to imperial power, and there is no problem for the royal family to learn it.

Zhu Gaochi had also learned some astronomical knowledge since he was a child. There were also some astronomy-related books in Prince Yan's Mansion (formerly the Imperial Palace of the Yuan Dynasty). Zhu Gaochi believed that he still had some skills in astronomy.

But even so, the so-called measurement of the sun's movement trajectory only exists in some notes. Traditional Chinese astronomy methods are still unable to draw the sun's movement trajectory.

And even the movement trajectory of the sun cannot be drawn. It can only rely on the vague model of the armillary sphere and traditional Chinese astronomy that uses algebraic calculations on a large amount of data accumulated over thousands of years. Naturally, it has no ability to measure the distance between the earth and the sun. distance, and something more profound like the mass and surface area of ​​the sun.

Of course, this does not mean that Chinese literature is not good, but that no one can predict the times.

How can we observe if we haven’t even figured out the basic technology of an astronomical telescope? How to measure?

Therefore, Zhu Gaochi did not believe it.

Moreover, Zhu Gaochi felt that if we really wanted to calculate the position and size of the sun, we would definitely need some specific opportunities and good timing before we could make a fuzzy calculation.

Now Jiang Xinghuo said that he could measure the position and size of the sun, but Zhu Gaochi didn't believe it at all.

But... Jiang Xinghuo, who came from across the wall, spoke faster than usual, and his mood swings became a little stronger when he spoke, as if he was being stimulated by some kind of stimulus, which made Zhu Gaochi dare not underestimate what Jiang Xinghuo said. possibility, and I dare not interrupt my listening train of thought by speaking casually.

——————

"How to measure the sun?"

Jiang Xinghuo asked and answered: "The first step is, of course, the torsion scale experiment just mentioned. First, we have to measure the constant of universal gravity."

"This experiment is very easy to do. As long as you insist on repeated testing to eliminate interference, anyone with qualified mathematical knowledge can calculate the universal gravitational constant by themselves."

"As for the second step," Jiang Xinghuo paused and continued, "it is to calculate the mass of the earth through the universal gravitational constant through an experiment of throwing a ball from a high tower."

"Little friend, wait a minute."

Old Man Zhuo quickly interrupted Jiang Xinghuo's speech.

Jiang Xinghuo's step from the first step to the second step is as if a person took a piece of iron ore, then "popped" it, turned out a steel knife, and then told you - "Look, just do it like this." And then that was it.”

Jiang Xinghuo stopped speaking as he was told.

"I wonder if the old gentleman has any advice?"

"Guidance is out of the question." There was a bit of confusion in Zhuo Jing's old eyes, "The twisting scale experiment can calculate the universal gravitational constant. I can still understand it, but why can the mass of the earth be calculated by throwing a ball from a tower?"

Jiang Xinghuo silently continued to write on the ground with a small branch.

Mass of the Earth = (gravity * square of the radius of the Earth) / gravitational constant * mass of the object in the high tower iron ball experiment

Jiang Xinghuo wrote another line of small words to note: * means multiplying.

After writing the formula for calculating the earth's mass, Jiang Xinghuo raised his head and asked.

"Do we know the radius of the Earth?"

This question sounds a bit outrageous, but Old Man Zhuo really knows the answer.

"Guo Shoujing measured it, it's 120,000 miles."

Jiang Xinghuo continued to ask: "After doing the torsion scale experiment, do you know the universal gravitational constant?"

"Know."

Old Man Zhuo was still a little confused: "What does that have to do with the mass of the iron ball experimental object in the tower?"

"Of course it does."

Jiang Xinghuo explained: "Gravity is the manifestation of universal gravitation on the earth. Can you understand this?"

The three of them nodded in unison. This is another way of saying that gravity is gravity on the earth. Of course they can understand it.

"Then how do you measure gravity? It doesn't matter if you don't know. I'm telling you, take a look and judge whether what I said makes sense." Jiang Xinghuo said.

Jiang Xinghuo wrote on the ground.

Gravity = experimental object * acceleration of falling object

This time Zhu Gaoxu's claws were numb, but Zheng He and Zhuo Jing, two people who were quite accomplished in this area, understood in an instant.

Zhuo Jing even picked up a small stone, raised his arm and placed it on a high place, then let the stone fall down.

This was repeated four or five times, and even Zhu Gaoxu came to his senses.

The principle is actually clear at a glance.

Zhu Gaoxu suddenly said: "To put it bluntly, this thing has the same principle as the strength of a bow and arrow, and the torque of a trebuchet?"

"Almost." Zheng He stiffly maintained the state of stroking his beard, his arms were numb, for fear that his beard would fall off.

"So, as long as you do the torsion scale experiment and the ball-throwing experiment from a high tower, don't you have the four numbers needed to calculate the mass of the earth: gravity, radius of the earth, universal gravitational constant, and object mass?"

Jiang Xinghuo pointed at the formula on the ground.

"Put it in and calculate it, and the mass of the earth will come out."

"My little friend, this is still not right."

Old Man Zhuo waited patiently for Jiang Xinghuo to finish this time, and asked again: "How do you know this formula and be able to calculate the mass of the earth? In other words, how do you prove that the formula is correct? If the formula is incorrect, then even if Even if you can calculate the numbers, it doesn’t mean it’s correct.”

Jiang Xinghuo chuckled.

Afterwards, Jiang Xinghuo continued to write a formula on the sand with a small branch.

Gravity = Universal gravitational constant * [(Mass of experimental object * Mass of Earth) / Square of Earth’s radius]

"Can you understand this formula?" Jiang Xinghuo asked.

The three of them meditated on the formula for a while, combined with their previous understanding of archery and stone throwing, and after discussing it for a while, they understood it. It seemed that there was no problem.

Next, as if by magic, Jiang Xinghuo drew a few lines between the two formulas, matching all the numbers one by one.

Wait for Jiang Xinghuo to finish drawing the corresponding lines.

Under the tree, several exclamations suddenly sounded!

"Is this so true?"

"I understand! I understand!"

"I knew Mr. Jiang would not be wrong."

Despite his age, Old Man Zhuo's mind was spinning very fast. He first combined Jiang Xinghuo's previous words, and then remembered the answer Jiang Xinghuo gave him to calculate the steps of the sun, and he immediately understood.

"So, the next step should be to measure the distance between the sun and our earth!"

"exactly."

Jiang Xinghuo nodded and said affirmatively: "You only need to measure the distance between the sun and the earth to get the area of ​​the sun, and you only need to get the distance and area of ​​the sun, and then combine it with the rotation period (revolution) of the sun and the earth. You can accomplish something as simple as measuring the sun."

The secret room next door.

The eldest prince Zhu Gaochi and the two minor officials Guo Jing and Chai Che had completely lost their minds.

You told me that measuring the sun is a very simple thing?

If someone had dared to say that a day ago, the result would have been a big mouth.

But now, Zhu Gaochi couldn't help but have an idea.

If you follow the steps Mr. Jiang said.

It seems that measuring the sun is not difficult?