Why are planetary orbits elliptical? One might think that knowing the law of universal gravitation alone would solve it... But that's not the case.
That equation describes the 'force' between two objects with mass. However, in this world, there is still no clear definition of force. Therefore, a definition of what force is must first be established.
Pfft.
Are they saying these otherworlders don't even know what force is?! ... Unfortunately, before Newton wrote 'a certain book', people on Earth were the same. And now, in Doloren's hands was 'a certain book' whose readability I had improved in my own way.
In short, the Principia. Mathematical Principles of Natural Philosophy. The greatest of all time in human history.
A work authored by Sir Isaac Newton.
Tremble, tremble.
Doloren's hand was shaking.
"Is this how you've been seeing the world?"
"..."
"..."
I had nothing to say. If I said yes, it would seem like I was acting like a world-class figure, and if I said no, it would be a lie. So I kept my mouth shut.
Originally, I had no intention of revealing the [Principia] so soon. I had planned to end it at deriving Kepler's laws from the observational data so far, and then using calculus to reveal the existence of universal gravitation.
However, the thirst for knowledge of Doloren and Giuseppe did not stop there. -'So... what exactly is this 'force' you're talking about?' -'Is it impetus? No... the theory of impetus was discarded after the law of inertia was discovered.' They were so curious that I just stuffed it into their mouths.
I told them about the Principia, the essence of classical mechanics.
"Of course, I'm not expecting an answer of this level for the freshman selection problem. As long as they get to the inverse-square law, they should pass..."
"You... you give me a paper like this and you're talking about freshmen? Just look at Giuseppe!"
I turned my gaze to Giuseppe.
"..."
"..."
Giuseppe was just staring blankly at the lab ceiling. He had been in that state ever since he read the [Principia] before Doloren. Just as I was wondering if I should cover Giuseppe with a blanket, Doloren's mouth opened.
"Crazy, I've realized something."
"Yes?"
"I think I can just use this as magic."
"..."
"..."
She realized it faster than I thought.
Doloren continued.
"There was no need to bother reciting incantations and magic circles in my head."
Our eyes met.
"F=ma... it can be applied to mana too, right...?!"
"Yes. Probably only by a very small number of mages."
Doloren reached her hand out towards a teacup in the lab. Is she really going to try it now?
"Hup!"
Doloren let out a spirited cry.
"... But nothing happened to the teacup."
"... What. It's not working."
I used a detection spell to see what had just happened.
Hmm.
So that's how it is. Doloren doesn't know how an object moves in the air, which is not a vacuum. Furthermore, she failed to accurately measure the physical quantities, such as the exact weight of the teacup, the direction of the force, the atmospheric pressure, and so on.
Even if I gave Doloren all the information up to this point, she would slip up at the calculation part. While I was figuring out the cause of her failure, Doloren was still envisioning a spell that had no chance of working. ... Is she not afraid of the rebound?
This won't do. I said to Doloren.
"I think my idea was wrong."
"Huh?"
Doloren stopped trying to cast the spell and looked at me.
"It seems impossible, for now, to directly translate this law into magic."
Seeing that even Doloren couldn't do it properly, it seemed that for now, only I could use physics-based magic. Doloren despaired at my declaration of 'magical unusability'.
"... Really?"
"Yes."
"No...! Why! A new world was right before my eyes!"
Shake, shake.
Doloren grabbed my shoulders and shook me. My head kept shaking, making me feel dizzy. Still, I had to say what I had to say.
"There's no reason for not being able to do it. You just can't." "Then what's the use of knowing about things like force and acceleration?!"
"It could be used as a benchmark when increasing the efficiency of magic circles and incantations."
"Graaaah!"
You can't have it all on the first try.
Selfish Doloren.
If we do everything now, what will future generations have to research? Leave something like instant-cast physics magic for the future, after a computer that can connect to the brain is created.
There were many twists and turns, but... The freshman recruitment problem was decided: 'What is the reason for planetary orbits being elliptical?' I wonder if there is a person of Johannes Kepler's or Isaac Newton's caliber in this world...
I'm looking forward to it. After the recruitment problem was decided, Doloren said to me.
"The problem itself is neat and good, but..."
"Right?"
"... Do you think the undergrads can figure out on their own a discovery that astounded me and Giuseppe?"
Don't jinx it already. Could she still be sulking because she can't use physics magic yet? But the train moves on even if the dog barks.
The advancement of knowledge can no longer be stopped.
"Huhu, Head of the school, are you afraid of the advancement of knowledge?"
"What?"
I have faith. In the intellect of the citizens of the Empire. The Empire is a country that has Valerius, who created the Method of Continuity, and Gedrick, who defined one atmosphere of pressure.
Since calculus and elliptical orbits have been given, they should be able to do it. Doloren had an expression of utter confusion. She probably found it hard to understand, that school head.
A junior in the School of Magical Surveying. She looked at me with the kind of eyes one would use to glance at and pass by a crazy master's student.
A few days later, I listened to Laura's work report with an excited heart.
Laura said.
"... As shown in the data below, thanks to the newly established workshop, the production of suspensions has increased by about three times."
It seems the workshop Doloren whipped up is functioning properly. She can be childish at times, but she's certainly helpful when needed. I asked Laura.
"Then you must have cleared a lot of the backlogged reservations. Has it been reduced to about a year?"
Laura shook her head.
"No. It's still three years."
"... What?"
"While the production volume increased, the order volume also increased."
The power hammer might have saved Tobin's shoulder health... But it doesn't seem like it could prevent him from overworking.
"According to rumors, 'carriage tea time' is trending among the young ladies of noble families. The increase in orders is likely due to that."
Haha.
An empty laugh escaped me. I then continued to listen to the report on the 'Upperhills Foundation'. 'This is also progressing well.'
After the work was done, Laura asked me.
"Sir Upperhills, you seem to be in a very good mood today."
"Ah. Do I look like it?"
"Yes. Did something good happen?"
"Well..."
I began to tell her that I would soon be getting a junior colleague.
"I even gave them an interesting problem, so the person who solves it must be an interesting person too, right?"
Laura's expression was not very bright.
"... It, it might not go as you expect, Sir Upperhills."
"Pardon?"
"It's possible that no one can solve that problem."
"Nah. No way."
I really gave them everything they needed to know. And still no second Newton appears? That's impossible. ...
It's really impossible. However, after returning to the lab, I heard the grim news from Giuseppe.
"No way. You're joking, right?"
"..."
"Tell me it's a joke."
"I know you don't want to believe it, but not a single applicant solved your problem, junior."
"..."
"It's more surprising that you expected undergrads to solve that problem. Aren't you overestimating them?"
"..."
I gently closed my eyes. If I kept them open, I felt like I would get dizzy and collapse.
"... Hey. Are you alright?"
Of course not. My amazing plan to snatch a junior colleague collapsed before it even began...
"Um... Senior Giuseppe. I'm sorry, but may I check the answer sheets myself?"
"Sure. See for yourself."
Just how did everyone write their answers that not a single person passed? I flipped through the applicants' answer sheets, one by one. There was no need for a tedious, pedantic evaluation.
It was just a spectacle. I asked Giuseppe again.
"No. Senior. Is this really the undergraduate level?"
"... Junior, that's just how undergrads are."
"That can't be. Even my Anna would do better than this."
"That's because Lady Anna is special..."
"..."
"..."
At the same time. Anna Upperhills was attending a liberal arts lecture on natural studies at the Magic Academy.
"Now, the ways to explain the movement of planets can be broadly divided into two."
The white-haired old professor explained as he drew concentric circles on the blackboard.
"The first is the theological perspective. The claim that someone, usually a god, makes the celestial bodies move eternally in a perfect circle. This is what most theologians believe."
The professor drew a spiral pattern on the other side.
"The second is the magical perspective. The theory is that mana particles, which are more densely gathered in space than on the ground, push against each other, creating a giant vortex, and the planets are swept along by this flow. Most mages accept this as the established theory."
At this point, Anna lost interest in the lecture. According to her brother, both of those theories were wrong. But the class continued.
A student raised his hand and asked a question.
"Then which of the two is correct?"
"You. You're making things difficult for me when you already know."
"Pardon?"
"... Although there is much controversy, I personally support the mages' theory. If there is inertia, the eternity of motion is guaranteed even without a god."
Another student raised his hand.
"Professor. I've heard recently that planetary orbits can actually be seen as elliptical. Is this true?"
Ears perked.
Anna's attention was drawn to the student's question.
'Elliptical?'
This was the first time she had heard this. The professor answered.
"A good question. Based on observation alone, yes. But most scholars insist that the essential orbit of a planet is a circle."
"Why is that?"
"The reasons vary among scholars. But there is a hypothesis that is accepted as the established theory these days."
"It's the claim that because the dense mana filling space distorts light, it only 'appears' elliptical to our eyes."
Anna tilted her head at the professor's words.
Flash.
Anna raised her hand. Then, murmurs could be heard.
"Hey. The top student is asking a question."
"Wonder what she'll say."
A little heat rose to Anna's cheeks. The professor chuckled and asked.
"Yes. Go ahead, Anna Upperhills."
"Yes. Thank you, professor. Um... mana does not interact with other matter, so how can it distort light?"
"That is because the laws of the earth and the heavens are different. All motion on earth is based on straight lines, whereas all motion in the heavens is circular, is it not?"
"..."
"... If you have more questions, it would be good to research them on your own."
With those words, the professor took no more questions. Anna read a troubled emotion on the professor's face. It seemed that he didn't know anything beyond this point.
However, Anna's curiosity was not yet satisfied. Since it had come to this, it didn't seem like a bad idea to research it on her own, just as the professor said. 'I was bored, so this is perfect.'
Scratch, scratch.
Anna's quill pen scraped across the parchment.