Chapter 160: 160 - G & M Value
To ensure the accurate calculation of the gravitational constant, Lynn had the Grand Wizard create a vacuum field once again, and Jenny and the others withdrew from the platform to minimize interference. After several experiments, the final value of the gravitational constant quickly appeared before them.
[ 6.67×10^-11 N·m^2/kg^2 ]
This value was essentially the same as in Lynn's previous world. It seemed that apart from the existence of magic as a unique energy, the fundamental parameters of the two universes were quite similar.
However, the symbol representing gravity, N, needed to be replaced with their own symbol, L. Another crucial piece of data, the gravitational acceleration, had been calculated by Lynn long ago, measuring approximately 10 m/s^2, slightly higher than Earth's value of 9.8.
With these two values, calculating the weight of the planet beneath their feet became straightforward. All they needed was to use the universal law of gravitation to derive the golden substitution formula:
[ GM = gR^2, ]
where G represented the gravitational constant, M represented the mass of the planet, g was the gravitational acceleration, and R stood for the radius.
After Lynn explained the formula's derivation, Harof and the others immediately began calculating. The enormity of the planetary values squared, divided by the minuscule gravitational constant, made their heads spin.
"I can't figure this out. It's too hard." Rol exclaimed, staring at the calculations sprawled across the parchment, his head spinning.
Beside him, Raphael gripped his few strands of hair, sweat beads forming on his forehead, all in an attempt to calculate the final result.
Even with numerous obstacles, few chose to give up. After all, the planet's ultimate mystery lay right before them, and they stood at the doorstep of truth, ready to kick it open. The only issue was that the door was exceptionally tough, easily breaking their bones.
A full hour and a half later, an excited mage stood up, nearly driven to madness. He shouted, "I've got it. It's 670 trillion tons."
However, Lynn simply shook his head, and Harof, who had just calculated the data, was even more direct, saying, "Wrong, and terribly so."
"Wrong? How could it be wrong?" The mage's excitement faded as he examined the calculations on the parchment and discovered that he had made a mistake when writing the radius of the planet, using kilometers instead of meters. In other words, he needed to add several more zeros and recalculate. His entire hour and a half of work had been in vain.
Realizing this, the mage's body trembled, and he spat out a mouthful of blood, fainting on the spot.
Elok looked at him with pity, and he stopped writing. Even full-fledged wizard found the calculations challenging. It was probably better for them as apprentices to simply wait for the answer.
The calculation of such massive values was difficult, but as time passed, more and more people arrived at the result. It was a number that couldn't be accurately described using any existing unit, only an arcane formula could make it visually comprehensible.
[ 7.08×10^24 kg ]
"No wonder, in the Society of Mystical Arts, arcane mathematics is the foundation of everything," Harof finally understood.
Values like gravity and celestial bodies, either immense or minuscule, required arcane mathematics to be calculated clearly.
Thinking of this, Harof announced the result. After Lynn confirmed it, he secretly breathed a sigh of relief. Even with repeated checks, such a massive value could easily lead to errors.
Carol and the others looked at Ogest with peculiar expressions. They remembered that the Magic Star had estimated the planet's weight to be around 30 trillion trillion tons. Wasn't this quite a significant difference?
It seemed the title of Magic Star wasn't all it was cracked up to be. Compared to Lynn's straightforward application of the universal law of gravitation, his method of dividing and calculating soil weight was barely worth mentioning.
Faced with Carol and the others' mocking gazes, Ogest remained unruffled. When he mentioned a 20% deviation, he was referring to the number of zeros.
The discussion about the gravitational constant and the planet's weight continued into the evening. Some enthusiastic divination scholars estimated the masses of other planets in the stellar system based on the universal law of gravitation, attempting to reconstruct a picture of celestial motion.
The witches at the conference were more interested in the round mirrors Lynn used during his experiments. When they learned that these smooth, flawless glass mirrors could be mass-produced and sold for just twenty magic gold coins each, their joy knew no bounds.
It wasn't until the seminar ended that Lynn finally escaped the relentless questions. To help the wizard understand certain terms, he had to think hard, as there was a multitude of concepts to explain. The two worlds had different cultures, vocabularies, scientific knowledge, and even ways of thinking. For instance, explaining that weight was essentially mass multiplied by acceleration and then elaborating on what mass was itself took a considerable amount of time.
Fortunately, this effort yielded results far beyond Lynn's expectations. The Society of Mystical Arts, arcane mathematics, and the Iyeta Academy became well-known among the local wizard. Some independent wizard even started testing the waters, asking if they could join the Iyeta Academy.
"Regarding your nomination for the Sun Crown Medal, it has been approved by the Council. In a couple of days, there will be an award ceremony. You should prepare for it," Harof said with a smile.
"Are there any rules or things I need to be aware of?" Lynn asked. He had thought that receiving the award would be straightforward.
"Not really, but this is the first time we're awarding the highest accolade in magical academia to a formal mage. You should speak a bit more to impress the audience," Harof quipped, then became serious. "I believe there are still some gaps in your theory of universal gravitation."
Lynn's expression turned serious as well, but Harof continued solemnly, "What can affect space-time is not just mass but also magic."
Lynn couldn't help but smile at this. Of course, he knew that matter was energy and energy was matter. However, it wasn't yet time to bring out the mass-energy equivalence equation.
As for the universal law of gravitation, even if it wasn't for Lynn, Harof would eventually deduce it in a few years at most. The only difference was a matter of inspiration.
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