136 - Three Laws

Harof contemplated for a while without any results, then sighed and turned to Theresa, asking, "Where's today's research material?"

"It's right here, Teacher," Theresa respectfully handed over a stack of parchment.

Harof casually took a piece of parchment and began to examine it. Although the various ideas proposed by official wizards were full of flaws, sometimes their wild imaginations sparked a glimmer of inspiration.

After all, that's what he was lacking the most right now.

Harof scanned through the pages one by one and soon became impatient. The quality of the theories in this issue was extremely poor, with many having no factual basis, just baseless speculations.

It felt like a waste of time!

Well, he might as well finish reading them just in case he stumbled upon something insightful.

Harof shook his head in frustration and picked up an exquisitely decorated envelope left on the table.

"Next time, tell them to bring plain parchment; there's no need for all these unnecessary embellishments," Harof grumbled.

"Yes, Teacher, I'll remind them," Theresa nodded in agreement, increasingly disliking the male witch, Lynn, from the Beyond the Wizard Lands, who had delivered this letter.

"Hmm?" Harof opened the envelope, and his whole demeanor froze.

The envelope contained not research papers filled with magical theories but an invitation.

[To the esteemed legendary wizard Mr. Harof,

We have heard that you are researching the laws of celestial movements, dedicating yourself to unravel the secrets of gravity, space, and time. We hereby invite you to join the Society of Mystical Arts to explore the mysteries of the cosmic truth.]

Harof furrowed his brows, realizing that this invitation from an academic research organization was something he rejected numerous times each month. Now it was mixed in with his research materials.

"I'm sorry, Teacher, that was my mistake. I should have reviewed it first," Theresa replied in a fluster, as this was her responsibility. However, she had brought it in without checking, causing the delay.

"The Society of Mystical Arts..." Harof did not immediately discard the letter because he vaguely remembered hearing that name somewhere. "Who brought this letter?"

"It was a wizard named Lynn, the one from the Misty Sea who proposed the theory of planetary motion," Theresa said, her voice filled with resentment. "That arrogant fellow even claimed to have brought three laws and a formula that could solve the problems you're facing."

"What are those laws and the formula?" Harof inquired further.

Since this wizard organization could understand and propose the theory of planets and the law of free fall, it meant they might have something valuable to offer. It wouldn't hurt to take a look.

Theresa hesitated for a moment, unable to find the words.

Fortunately, Harof quickly found the formulas and laws written on the back of the invitation.

[First Law: The orbits of all planets around stars are elliptical, with the star located at one of the foci of the ellipse,] Harof muttered thoughtfully as he read the first line.

Indeed, in his research on celestial motion, he had also observed this phenomenon. However, the problem was why it happened. According to his calculations, the gravitational field should form a perfect circle, with the star at the center.

This had been one of the issues that had been troubling him.

He quickly read the next two laws, which were entirely new and unfamiliar to him.

[Second Law: For any planet, the area swept out by the line connecting it and the star is directly proportional to the time it takes to sweep that area; the planet's speed at closest approach remains constant.]

[Third Law: The ratio of the cube of the semi-major axis of an orbit to the square of the orbital period is the same for all celestial bodies in orbit.]

Harof's expression immediately turned serious. These were two brand new laws and principles that he hadn't discovered yet.

"Quick, bring me paper and a pen; I need to verify this," Harof exclaimed loudly.

Could it be that these so-called laws were really useful for him? Theresa was taken aback and quickly brought paper and a pen.

However, Harof was too impatient to wait and began scribbling in the air with magic, then compared the data with the star maps.

Theresa was in awe and couldn't even breathe as she waited patiently for several hours, unable to leave her spot.

When it was already bright outside, Harof finally stopped and muttered to himself, "It matches perfectly, it really does!"

Harof felt like he was closer to the truth than ever before.

With that in mind, he looked at the end of the invitation, where there was a short formula.

[ F=GMm/r^2 ]

But he had no idea what these mathematical symbols meant. What did "F" represent, and what was "G"?

Harof was clueless about these mathematical notations from another world and could only guess based on his recent study. He had a feeling that what he had been seeking was hidden within this short formula.

"Where is this Lynn now? Where can I find him?" Harof suddenly remembered the person who sent the letter and urgently asked, as Lynn was the one who likely understood the meaning of this formula.

"Te-Teacher, because it was so late yesterday, the wizard named Lynn has already left... As for now, he's probably attending the conference," Theresa replied hesitantly, not daring to mention that she had intentionally kept him out.

"I'll go get him right away!" Theresa hurriedly decided to fetch Lynn.

She had a clear understanding of her own abilities as an ordinary third-tier wizard. Initially, she gained Harof's appreciation by providing him with some inspiration through an academic paper. If the legendary wizard found out about such a significant oversight, her current position might not be secure.

"No need, it's too slow. I'll go myself." Harof's thoughts raced, and he quickly gathered his scattered research notes, summoning them into his hand with magic. Then, he flew out of the wide-open window.

TL/n - 

Johannes Kepler's laws of planetary motion describe how planets orbit the Sun. 

Here they are:

Law of Ellipses: Planets move in elliptical orbits with the Sun at one focus. It's not a perfect circle, but a stretched one, like an oval.

Law of Equal Areas: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means planets move faster when they are closer to the Sun and slower when they are further away.

Law of Harmonies: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Essentially, the farther a planet is from the Sun, the longer it takes to complete one orbit.